Heinemann Maths Zone 10 VELS Edition: Teaching and Assessment Program
This Teaching and Assessment Program (TAP) is presented to assist teachers in planning their school’s courses, and to demonstrate that a
program incorporating the Victorian Essential Learning Standards (VELS) may be constructed using the curriculum package of resources
published by Heinemann. There are three versions (A, B and C) provided for Years 9 and 10, while the Years 7 and 8 format involves core,
background and extension. The TAPs for the other year levels are available on this website. The Heinemann Maths Zone 10 VELS Edition fully
integrates VELS Design Tasks, graphics calculator and computer material.
Summary
The three courses A, B and C are presented – the topics covered in each vary.
Level A
Unit no.
Unit title
1
Consumer maths and mathematical structure
4
2
Measurement
4
3
Linear equations and graphs
4
4
Trigonometry
4
Heinemann Maths Zone 10 VELS Edition
Length in weeks
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Page 2 of 92
5
Statistics
4
6
Geometry
5
7
Probability
3
8
Measurement – volume and capacity
4
1
Consumer maths and mathematical structure
4
2
Surds and exponentials
3
3
Algebra
4
4
Measurement
3
5
Linear relationships
4
6
Trigonometry
4
7
Statistics and probability
4
8
Geometry
3
9
Quadratics, variations, graphs
3
Level B
Heinemann Maths Zone 10 VELS Edition
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Page 3 of 92
Level C
1
Consumer maths and mathematical structure
3
2
Surds and exponentials
4
3
Algebra
4
4
Measurement
4
5
Linear relationships
3
6
Trigonometry
4
7
Statistics and probability
3
8
Geometry
3
9
Equations and relationships
4
Abbreviations
The following abbreviations have been used in the Year 10 TAP grids:
Heinemann Maths Zone 10 VELS Edition
Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd)
Page 4 of 92
VELS refs
The appropriate parts of the standards are included. The VELS correlation grid and the audit appear both on this website and at the front of the
Maths Zone 10 VELS Edition.
Heinemann references
MZ10 refers to the textbook Heinemann Maths Zone 10 VELS Edition. GC Investigation refers to graphics calculator investigations and
C Investigation refers to computer investigation.
Assessment
FT10 refers to questions on the Heinemann Maths Zone 10 VELS Edition FlexiTest. Specific section references are provided.
Heinemann Maths Zone 10 VELS Edition
Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd)
Page 5 of 92
Unit 1: Consumer maths and mathematical structure
Level: A
VELS refs
Course
Dimensions: Structure
Time: 4 weeks
Heinemann references
Assessment
MZ10 p3 (1.1)
MZ10 p8 (VELS
Consumer maths
Students choose, use and develop mathematical models and
Paying the bills
Design Task)
procedures to investigate and solve problems set in a wide range of
FT10 1.1 Short answer
practical, theoretical and historical contexts.
FT10 1.1 Multiple
choice
FT10 1.1 Applications
and analysis
Interest
Students carry out arithmetic computations involving natural
Compound interest
numbers, integers and finite decimals using mental and/or written
algorithms (one- or two-digit divisors in the case of division).
Students choose, use and develop mathematical models and
procedures to investigate and solve problems set in a wide range of
practical, theoretical and historical contexts.
Heinemann Maths Zone 10 VELS Edition
Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd)
MZ10 p11 (1.2)
FT10 1.2 Short answer
FT10 1.2 Multiple
choice
FT10 1.2 Applications
and analysis
Page 6 of 92
VELS refs
Course
Heinemann references
Assessment
Students carry out arithmetic computations involving natural
Inflation
MZ10 p21 (1.3); p26
FT10 1.3 Short answer
numbers, integers and finite decimals using mental and/or written
(Investigation)
algorithms (one- or two-digit divisors in the case of division).
FT10 1.3 Multiple
choice
Students choose, use and develop mathematical models and
FT10 1.3 Applications
procedures to investigate and solve problems set in a wide range of
and analysis
practical, theoretical and historical contexts.
Mathematical notation
Students carry out arithmetic computations involving natural
Scientific notation
numbers, integers and finite decimals using mental and/or written
algorithms (one- or two-digit divisors in the case of division). They
perform computations involving very large or very small numbers in
-3
scientific notation (for example, 0.0045 × 0.000028 = 4.5 × 10 ×
2.8 × 10-5 = 1.26 × 10-7). They carry out computations to a required
accuracy in terms of decimal places and/or significant figures.
Heinemann Maths Zone 10 VELS Edition
Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd)
MZ10 p80 (2.13)
FT10 2.13 Short
answer
FT10 2.13 Multiple
choice
Page 7 of 92
Unit 1: Consumer maths and mathematical structure
Level: B
VELS refs
Course
Dimensions: Structure
Time: 4 weeks
Heinemann references
Assessment
MZ10 p3 (1.1); p9 (Maths in
FT10 1.1 Short answer
Consumer maths
Students choose, use and develop mathematical models and
Paying the bills
Action)
procedures to investigate and solve problems set in a wide range of
FT10 1.1 Multiple
choice
practical, theoretical and historical contexts.
FT10 1.1 Applications
and analysis
Students formulate and test conjectures, generalisations and
Understanding call costs
arguments in natural language and symbolic form.
MZ10 p8 (VELS Design
Task)
Students choose, use and develop mathematical models and
procedures to investigate and solve problems set in a wide range of
practical, theoretical and historical contexts (for example, exact and
approximate measurement formulae for the volumes of various threedimensional objects such as truncated pyramids). They generalise
from one situation to another, and investigate it further by changing
the initial constraints or other boundary conditions.
Students carry out arithmetic computations involving natural
Compound interest
MZ10 p11 (1.2); p19
numbers, integers and finite decimals using mental and/or written
(Graphics calculator
algorithms (one- or two-digit divisors in the case of division).
investigation)
Students choose, use and develop mathematical models and
procedures to investigate and solve problems set in a wide range of
practical, theoretical and historical contexts.
Heinemann Maths Zone 10 VELS Edition
Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd)
FT10 1.2 Short answer
FT10 1.2 Multiple
choice
FT10 1.2 Applications
and analysis
Page 8 of 92
VELS refs
Course
Heinemann references
Assessment
Students carry out arithmetic computations involving natural
Inflation
MZ10 p21 (1.3); p26
FT10 1.3 Short answer
numbers, integers and finite decimals using mental and/or written
(Investigation)
algorithms (one- or two-digit divisors in the case of division).
FT10 1.3 Multiple
choice
Students choose, use and develop mathematical models and
FT10 1.3 Applications
procedures to investigate and solve problems set in a wide range of
and analysis
practical, theoretical and historical contexts.
Mathematical structure
Students classify and describe the properties of the real number
Sets and subsets
MZ10 p27 (1.4)
system and the subsets of rational and irrational numbers. They
FT10 1.4 Short answer
FT10 1.4 Multiple
identify subsets of these as discrete or continuous, finite or infinite
choice
and provide examples of their elements and apply these to functions
and relations and the solution of related equations.
Students classify and describe the properties of the real number
Number theory
system and the subsets of rational and irrational numbers. They
identify subsets of these as discrete or continuous, finite or infinite
and provide examples of their elements and apply these to functions
and relations and the solution of related equations.
Students apply the algebraic properties (closure, associative,
commutative, identity, inverse and distributive) to computation with
number, to rearrange formulae, rearrange and simplify algebraic
expressions involving real variables.
Heinemann Maths Zone 10 VELS Edition
Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd)
MZ10 p30 (1.5)
FT10 1.5 Short answer
FT10 1.5 Multiple
choice
Page 9 of 92
Unit 1: Consumer maths and mathematical structure
Level: C
VELS refs
Course
Dimensions: Algebra
Time: 3 weeks
Heinemann references
Assessment
MZ10 p3 (1.1); p9 (Maths in
FT10 1.1 Short answer
Consumer maths
Students choose, use and develop mathematical models and
Paying the bills
Action)
procedures to investigate and solve problems set in a wide range of
FT10 1.1 Multiple
choice
practical, theoretical and historical contexts
FT10 1.1 Applications
and analysis
Students formulate and test conjectures, generalisations and
Compound interest
MZ10 p11 (1.2)
arguments in natural language and symbolic form.
FT10 1.2 Short answer
FT10 1.2 Multiple
Students choose, use and develop mathematical models and
choice
procedures to investigate and solve problems set in a wide range of
FT10 1.2 Applications
practical, theoretical and historical contexts (for example, exact and
and analysis
approximate measurement formulae for the volumes of various threedimensional objects such as truncated pyramids). They generalise
from one situation to another, and investigate it further by changing
the initial constraints or other boundary conditions.
Students carry out arithmetic computations involving natural
Inflation
numbers, integers and finite decimals using mental and/or written
algorithms (one- or two-digit divisors in the case of division).
Students choose, use and develop mathematical models and
procedures to investigate and solve problems set in a wide range of
practical, theoretical and historical contexts.
Heinemann Maths Zone 10 VELS Edition
Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd)
MZ10 p21 (1.3)
FT10 1.3 Short answer
FT10 1.3 Multiple
choice
FT10 1.3 Applications
and analysis
Page 10 of 92
VELS refs
Course
Heinemann references
Assessment
MZ10 p27 (1.4)
FT10 1.4 Short answer
Mathematical structure
Students classify and describe the properties of the real number
Sets and subsets
system and the subsets of rational and irrational numbers. They
FT10 1.4 Multiple
identify subsets of these as discrete or continuous, finite or infinite
choice
and provide examples of their elements and apply these to functions
FT10 1.4 Applications
and relations and the solution of related equations.
Students classify and describe the properties of the real number
and analysis
Number theory
system and the subsets of rational and irrational numbers. They
identify subsets of these as discrete or continuous, finite or infinite
and provide examples of their elements and apply these to functions
and relations and the solution of related equations.
Students apply the algebraic properties (closure, associative,
commutative, identity, inverse and distributive) to computation with
number, to rearrange formulae, rearrange and simplify algebraic
expressions involving real variables.
Heinemann Maths Zone 10 VELS Edition
Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd)
MZ10 p30 (1.5)
FT10 1.5 Short answer
FT10 1.5 Multiple
choice
FT10 1.5 Applications
and analysis
Page 11 of 92
Unit 2: Measurement
Level: A
Dimensions: Measurement, chance and data Time: 4 weeks
VELS refs
Course
Heinemann references
Assessment
MZ10 p163 (4.1); p168
FT10 4.1 Short answer
Time
Students estimate and measure length, area, surface area, mass,
Timetables, time zones and speed
volume, capacity and angle. They select and use appropriate units,
(Problem solving)
converting between units as required. They calculate constant rates
FT10 4.1 Multiple
choice
such as the density of substances (that is, mass in relation to volume),
FT10 4.1 Applications
concentration of fluids, average speed and pollution levels in the
and analysis
atmosphere.
Areas
Students estimate and measure length, area, surface area, mass,
Area of composite shapes
volume, capacity and angle. They select and use appropriate units,
MZ10 p169 (4.2); p175
(VELS Design Task)
converting between units as required.
FT10 4.2 Short answer
FT10 4.2 Multiple
choice
FT10 4.2 Applications
and analysis
Students form and test mathematical conjectures; for example, ‘What
Area of triangle (Hero’s formula)
relationship holds between the lengths of the three sides of a
triangle?’
Students choose, use and develop mathematical models and
procedures to investigate and solve problems set in a wide range of
practical, theoretical and historical contexts.
Surface area
Heinemann Maths Zone 10 VELS Edition
Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd)
MZ10 p176 (Investigation)
Page 12 of 92
VELS refs
Course
Heinemann references
Assessment
They recognise and describe boundaries, surfaces and interiors of
Total surface area
MZ10 p177 (4.3 Q 1–13)
FT10 4.3 Short answer
common plane and three-dimensional shapes, including cylinders,
FT10 4.3 Multiple
spheres, cones, prisms and polyhedra.
choice
Students estimate and measure length, area, surface area, mass,
volume, capacity and angle. They select and use appropriate units,
converting between units as required.
They recognise and describe boundaries, surfaces and interiors of
Surface area of composite solids
common plane and three-dimensional shapes, including cylinders,
spheres, cones, prisms and polyhedra.
FT10 4.4 Short answer
FT10 4.4 Multiple
choice
Students estimate and measure length, area, surface area, mass,
volume, capacity and angle. They select and use appropriate units,
converting between units as required.
They determine the effect of changing the scale of one characteristic
of two- and three-dimensional shapes (for example, side length, area,
volume and angle measure) on related characteristics.
Heinemann Maths Zone 10 VELS Edition
MZ10 p185 (4.4 Q 1–4)
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Page 13 of 92
Unit 2: Surds and exponentials
Level: B
Dimensions: Number
Time: 3 weeks
VELS refs
Course
Heinemann references
Assessment
Students comprehend the set of real numbers containing natural,
Rational and irrational numbers
MZ10 p41 (2.1)
FT10 2.1 Short answer
integer, rational and irrational numbers. They represent rational
FT10 2.1 Multiple
numbers in both fractional and decimal (terminating and infinite
recurring) forms (for example,
,
choice
). They
comprehend that irrational numbers have an infinite non-terminating
decimal form. They specify decimal rational approximations for
square roots of primes, rational numbers that are not perfect squares,
the golden ratio φ , and simple fractions of π correct to a required
decimal place accuracy.
They carry out exact arithmetic computations involving fractions and
Multiplying and dividing surds
MZ10 p44 (2.2)
FT10 2.2 Short answer
FT10 2.2 Multiple
irrational numbers such as square roots (for example,
,
) and multiples and fractions of π (for example,
). They use appropriate estimates to evaluate the
reasonableness of the results of calculations involving rational and
irrational numbers, and the decimal approximations for them. They
carry out computations to a required accuracy in terms of decimal
places and/or significant figures.
Heinemann Maths Zone 10 VELS Edition
Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd)
choice
Page 14 of 92
VELS refs
Course
Heinemann references
Assessment
They carry out exact arithmetic computations involving fractions and
Simplifying surds
MZ10 p47 (2.3); p63 (CAS
FT10 2.3 Short answer
investigation)
irrational numbers such as square roots (for example,
,
FT10 2.3 Multiple
choice
) and multiples and fractions of π (for example,
). They use appropriate estimates to evaluate the
reasonableness of the results of calculations involving rational and
irrational numbers, and the decimal approximations for them. They
carry out computations to a required accuracy in terms of decimal
places and/or significant figures.
They carry out exact arithmetic computations involving fractions and
Adding and subtracting surds
MZ10 p50 (2.4)
FT10 2.4 Short answer
FT10 2.4 Multiple
irrational numbers such as square roots (for example,
,
choice
) and multiples and fractions of π (for example,
). They use appropriate estimates to evaluate the
reasonableness of the results of calculations involving rational and
irrational numbers, and the decimal approximations for them. They
carry out computations to a required accuracy in terms of decimal
places and/or significant figures.
Indices
Heinemann Maths Zone 10 VELS Edition
Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd)
Page 15 of 92
VELS refs
Course
Heinemann references
Assessment
Students apply the algebraic properties (closure, associative,
Raising to a power
MZ10 p59 (2.7)
FT10 2.7 Short answer
commutative, identity, inverse and distributive) to computation with
FT10 2.7 Multiple
number, to rearrange formulae, rearrange and simplify algebraic
choice
expressions involving real variables. They verify the equivalence or
FT10 2.7 Applications
otherwise of algebraic expressions (linear, square, cube, exponent,
and reciprocal, (for example, 4x − 8 = 2(2x − 4) = 4(x − 2); (2a − 3)
= 4a2 − 12a + 9; (3w)3 = 27w3;
;
and analysis
2
).
Students apply the algebraic properties (closure, associative,
Simplifying index expressions
commutative, identity, inverse and distributive) to computation with
choice
expressions involving real variables. They verify the equivalence or
FT10 2.8 Applications
otherwise of algebraic expressions (linear, square, cube, exponent,
= 4a2 − 12a + 9; (3w)3 = 27w3;
Heinemann Maths Zone 10 VELS Edition
;
FT10 2.8 Short answer
FT10 2.8 Multiple
number, to rearrange formulae, rearrange and simplify algebraic
and reciprocal, (for example, 4x − 8 = 2(2x − 4) = 4(x − 2); (2a − 3)
MZ10 p64 (2.8)
and analysis
2
).
Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd)
Page 16 of 92
VELS refs
Course
Heinemann references
Assessment
Students apply the algebraic properties (closure, associative,
Negative powers
MZ10 p66 (2.9)
FT10 2.9 Short answer
commutative, identity, inverse and distributive) to computation with
FT10 2.9 Multiple
number, to rearrange formulae, rearrange and simplify algebraic
choice
expressions involving real variables. They verify the equivalence or
FT10 2.9 Applications
otherwise of algebraic expressions (linear, square, cube, exponent,
and reciprocal, (for example, 4x − 8 = 2(2x − 4) = 4(x − 2); (2a − 3)
= 4a2 − 12a + 9; (3w)3 = 27w3;
;
and analysis
2
).
Students apply the algebraic properties (closure, associative,
Fractional powers
MZ10 p70 (2.10)
commutative, identity, inverse and distributive) to computation with
FT10 2.10 Short
answer
number, to rearrange formulae, rearrange and simplify algebraic
FT10 2.10 Multiple
expressions involving real variables. They verify the equivalence or
choice
otherwise of algebraic expressions (linear, square, cube, exponent,
and reciprocal, (for example, 4x − 8 = 2(2x − 4) = 4(x − 2); (2a − 3)2
= 4a2 − 12a + 9; (3w)3 = 27w3;
;
).
They select and use technology in various combinations to assist in
Using a calculator
mathematical inquiry, to manipulate and represent data, to analyse
functions and carry out symbolic manipulation.
MZ10 p72 (2.11)
FT10 2.11 Short
answer
FT10 2.11 Multiple
choice
FT10 2.11 Applications
and analysis
Heinemann Maths Zone 10 VELS Edition
Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd)
Page 17 of 92
VELS refs
Course
Heinemann references
Assessment
Students apply the algebraic properties (closure, associative,
Summary of index laws
MZ10 p75 (2.12)
FT10 2.12 Short
commutative, identity, inverse and distributive) to computation with
answer
number, to rearrange formulae, rearrange and simplify algebraic
FT10 2.12 Multiple
expressions involving real variables. They verify the equivalence or
choice
otherwise of algebraic expressions (linear, square, cube, exponent,
and reciprocal, (for example, 4x − 8 = 2(2x − 4) = 4(x − 2); (2a − 3)2
= 4a2 − 12a + 9; (3w)3 = 27w3;
;
).
Scientific notation
Students carry out arithmetic computations involving natural
Scientific notation and standard form
numbers, integers and finite decimals using mental and/or written
algorithms (one- or two-digit divisors in the case of division). They
perform computations involving very large or very small numbers in
-3
scientific notation (for example, 0.0045 × 0.000028 = 4.5 × 10 ×
2.8 × 10-5 = 1.26 × 10-7). They carry out computations to a required
accuracy in terms of decimal places and/or significant figures.
Heinemann Maths Zone 10 VELS Edition
Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd)
MZ10 p80 (2.13)
FT10 2.13 Short
answer
FT10 2.13 Multiple
choice
FT10 2.13 Applications
and analysis
Page 18 of 92
Unit 2: Surds and exponentials
Level: C
Dimensions: Number
Time: 4 weeks
VELS refs
Course
Heinemann references
Assessment
Students comprehend the set of real numbers containing natural,
Rational and irrational numbers
MZ10 p41 (2.1)
FT10 2.1 Short answer
integer, rational and irrational numbers. They represent rational
FT10 2.1 Multiple
numbers in both fractional and decimal (terminating and infinite
choice
FT10 2.1 Applications
recurring) forms (for example,
,
). They
and analysis
comprehend that irrational numbers have an infinite non-terminating
decimal form. They specify decimal rational approximations for
square roots of primes, rational numbers that are not perfect squares,
the golden ratio φ , and simple fractions of π correct to a required
decimal place accuracy.
They carry out exact arithmetic computations involving fractions and
Multiplying and dividing surds
MZ10 p44 (2.2)
FT10 2.2 Short answer
FT10 2.2 Multiple
irrational numbers such as square roots (for example,
,
) and multiples and fractions of π (for example,
choice
FT10 2.2 Applications
and analysis
). They use appropriate estimates to evaluate the
reasonableness of the results of calculations involving rational and
irrational numbers, and the decimal approximations for them. They
carry out computations to a required accuracy in terms of decimal
places and/or significant figures.
Heinemann Maths Zone 10 VELS Edition
Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd)
Page 19 of 92
VELS refs
Course
Heinemann references
Assessment
They carry out exact arithmetic computations involving fractions and
Simplifying surds
MZ10 p47 (2.3); p63 (CAS
FT10 2.3 Short answer
investigation)
irrational numbers such as square roots (for example,
,
FT10 2.3 Multiple
choice
FT10 2.3 Applications
) and multiples and fractions of π (for example,
and analysis
). They use appropriate estimates to evaluate the
reasonableness of the results of calculations involving rational and
irrational numbers, and the decimal approximations for them. They
carry out computations to a required accuracy in terms of decimal
places and/or significant figures.
They carry out exact arithmetic computations involving fractions and
Adding and subtracting surds
MZ10 p50 (2.4)
FT10 2.4 Short answer
FT10 2.4 Multiple
irrational numbers such as square roots (for example,
,
) and multiples and fractions of π (for example,
choice
FT10 2.4 Applications
and analysis
). They use appropriate estimates to evaluate the
reasonableness of the results of calculations involving rational and
irrational numbers, and the decimal approximations for them. They
carry out computations to a required accuracy in terms of decimal
places and/or significant figures.
Heinemann Maths Zone 10 VELS Edition
Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd)
Page 20 of 92
VELS refs
Course
Heinemann references
Assessment
Students apply the algebraic properties (closure, associative,
Surds and the Distributive law
MZ10 p52 (2.5)
FT10 2.5 Short answer
commutative, identity, inverse and distributive) to computation with
FT10 2.5 Multiple
number, to rearrange formulae, rearrange and simplify algebraic
choice
expressions involving real variables. They verify the equivalence or
FT10 2.5 Applications
otherwise of algebraic expressions (linear, square, cube, exponent,
and reciprocal, (for example, 4x − 8 = 2(2x − 4) = 4(x − 2); (2a − 3)
= 4a2 − 12a + 9; (3w)3 = 27w3;
;
and analysis
2
).
They carry out exact arithmetic computations involving fractions and
Rationalising the denominator
MZ10 p56 (2.6)
FT10 2.6 Short answer
FT10 2.6 Multiple
irrational numbers such as square roots (for example,
,
choice
) and multiples and fractions of π (for example,
FT10 2.6 Applications
and analysis
). They use appropriate estimates to evaluate the
reasonableness of the results of calculations involving rational and
irrational numbers, and the decimal approximations for them. They
carry out computations to a required accuracy in terms of decimal
places and/or significant figures.
Indices
Heinemann Maths Zone 10 VELS Edition
Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd)
Page 21 of 92
VELS refs
Course
Heinemann references
Assessment
Students apply the algebraic properties (closure, associative,
Raising to a power
MZ10 p59 (2.7)
FT10 2.7 Short answer
commutative, identity, inverse and distributive) to computation with
FT10 2.7 Multiple
number, to rearrange formulae, rearrange and simplify algebraic
choice
expressions involving real variables. They verify the equivalence or
FT10 2.7 Applications
otherwise of algebraic expressions (linear, square, cube, exponent,
and reciprocal, (for example, 4x − 8 = 2(2x − 4) = 4(x − 2); (2a − 3)
= 4a2 − 12a + 9; (3w)3 = 27w3;
;
and analysis
2
).
Students apply the algebraic properties (closure, associative,
Simplifying index expressions
commutative, identity, inverse and distributive) to computation with
choice
expressions involving real variables. They verify the equivalence or
FT10 2.8 Applications
otherwise of algebraic expressions (linear, square, cube, exponent,
= 4a2 − 12a + 9; (3w)3 = 27w3;
Heinemann Maths Zone 10 VELS Edition
;
FT10 2.8 Short answer
FT10 2.8 Multiple
number, to rearrange formulae, rearrange and simplify algebraic
and reciprocal, (for example, 4x − 8 = 2(2x − 4) = 4(x − 2); (2a − 3)
MZ10 p64 (2.8)
and analysis
2
).
Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd)
Page 22 of 92
VELS refs
Course
Heinemann references
Assessment
Students apply the algebraic properties (closure, associative,
Negative powers
MZ10 p66 (2.9)
FT10 2.9 Short answer
commutative, identity, inverse and distributive) to computation with
FT10 2.9 Multiple
number, to rearrange formulae, rearrange and simplify algebraic
choice
expressions involving real variables. They verify the equivalence or
FT10 2.9 Applications
otherwise of algebraic expressions (linear, square, cube, exponent,
and reciprocal, (for example, 4x − 8 = 2(2x − 4) = 4(x − 2); (2a − 3)
= 4a2 − 12a + 9; (3w)3 = 27w3;
;
and analysis
2
).
Students apply the algebraic properties (closure, associative,
Fractional powers
MZ10 p70 (2.10)
commutative, identity, inverse and distributive) to computation with
answer
number, to rearrange formulae, rearrange and simplify algebraic
FT10 2.10 Multiple
expressions involving real variables. They verify the equivalence or
choice
otherwise of algebraic expressions (linear, square, cube, exponent,
and reciprocal, (for example, 4x − 8 = 2(2x − 4) = 4(x − 2); (2a − 3)
= 4a2 − 12a + 9; (3w)3 = 27w3;
;
FT10 2.10 Short
FT10 2.10 Applications
2
and analysis
).
They select and use technology in various combinations to assist in
Using a calculator
mathematical inquiry, to manipulate and represent data, to analyse
functions and carry out symbolic manipulation.
MZ10 p72 (2.11)
FT10 2.11 Short
answer
FT10 2.11 Multiple
choice
FT10 2.11 Applications
and analysis
Heinemann Maths Zone 10 VELS Edition
Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd)
Page 23 of 92
VELS refs
Course
Heinemann references
Assessment
Students carry out arithmetic computations involving natural
Summary of index laws
MZ10 p75 (2.12); p69
FT10 2.12 Short
numbers, integers and finite decimals using mental and/or written
(Investigation); p74
algorithms (one- or two-digit divisors in the case of division). They
(Problem solving); p79
perform computations involving very large or very small numbers in
(VELS Design Task) p87;
scientific notation (for example, 0.0045 × 0.000028 = 4.5 × 10 -3 ×
(Graphics calculator
-5
-7
2.8 × 10 = 1.26 × 10 ). They carry out computations to a required
investigation)
answer
FT10 2.12 Multiple
choice
FT10 2.12 Applications
and analysis
accuracy in terms of decimal places and/or significant figures.
Scientific notation
Students carry out arithmetic computations involving natural
Scientific notation and standard form
numbers, integers and finite decimals using mental and/or written
in Action)
algorithms (one- or two-digit divisors in the case of division). They
FT10 2.13 Short
answer
FT10 2.13 Multiple
perform computations involving very large or very small numbers in
choice
scientific notation (for example, 0.0045 × 0.000028 = 4.5 × 10-3 ×
FT10 2.13 Applications
2.8 × 10-5 = 1.26 × 10-7). They carry out computations to a required
and analysis
accuracy in terms of decimal places and/or significant figures.
Exponentials
Heinemann Maths Zone 10 VELS Edition
MZ10 p80 (2.13); p89 (Maths
Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd)
Page 24 of 92
VELS refs
Course
Heinemann references
Assessment
Students identify and represent linear, quadratic and exponential
Exponential relationships
MZ10 p91 (2.14)
FT10 2.14 Short
functions by table, rule and graph (all four quadrants of the Cartesian
coordinate system) with consideration of independent and dependent
variables, domain and range.
FT10 2.14 Multiple
choice
They verify the equivalence or otherwise of algebraic expressions
(linear, square, cube, exponent, and reciprocal (for example, 4x − 8 =
2(2x − 4) = 4(x − 2); (2a − 3)2 = 4a2 − 12a + 9; (3w)3 = 27w3;
;
answer
).
Heinemann Maths Zone 10 VELS Edition
Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd)
FT10 2.14 Applications
and analysis
Page 25 of 92
Unit 3: Linear equations and graphs
Level: A
VELS refs
Dimensions: Structure
Time: 4 weeks
Course
Heinemann references
Assessment
MZ10 p219 (5.1 Q1–3)
FT10 5.1 Short answer
Linear relationships
They recognise and explain the roles of the relevant constants in the
Solving linear equations
relationships f(x) = ax + c, with reference to gradient and y-axis
2
FT10 5.1 Multiple
x
intercept, f(x) = a(x + b) + c and f(x) = ca .
choice
They solve equations of the form f(x) = k, where k is a real constant
(for example, x(x + 5) = 100).
They recognise and explain the roles of the relevant constants in the
Understanding gradient
MZ10 p226 (5.2 Q1–3)
relationships f(x) = ax + c, with reference to gradient and y-axis
FT10 5.2 Multiple
intercept, f(x) = a(x + b)2 + c and f(x) = cax.
Students identify and represent linear, quadratic and exponential
choice
Sketching linear graphs
functions by table, rule and graph (all four quadrants of the Cartesian
coordinate system) with consideration of independent and dependent
variables, domain and range.
MZ10 p 233 (5.3 Q1–9)
FT10 5.3 Short answer
FT10 5.3 Multiple
choice
FT10 5.3 Applications
They recognise and explain the roles of the relevant constants in the
relationships f(x) = ax + c, with reference to gradient and y-axis
intercept, f(x) = a(x + b)2 + c and f(x) = cax.
Heinemann Maths Zone 10 VELS Edition
FT10 5.2 Short answer
Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd)
and analysis
Page 26 of 92
Unit 3: Algebra
Level: B
Dimensions: Structure
VELS refs
Time: 4 weeks
Course
Heinemann references
Assessment
MZ10 p107 (3.1 Q1–10)
FT10 3.1 Short answer
Quadratic expressions
Students apply the algebraic properties (closure, associative,
Expansion
commutative, identity, inverse and distributive) to computation with
FT10 3.1 Multiple
number, to rearrange formulae, rearrange and simplify algebraic
choice
expressions involving real variables. They verify the equivalence or
otherwise of algebraic expressions (linear, square, cube, exponent,
and reciprocal, (for example, 4x − 8 = 2(2x − 4) = 4(x − 2); (2a − 3)2
= 4a2 − 12a + 9; (3w)3 = 27w3;
;
).
Students apply the algebraic properties (closure, associative,
Perfect squares
commutative, identity, inverse and distributive) to computation with
number, to rearrange formulae, rearrange and simplify algebraic
expressions involving real variables. They verify the equivalence or
otherwise of algebraic expressions (linear, square, cube, exponent,
and reciprocal, (for example, 4x − 8 = 2(2x − 4) = 4(x − 2); (2a − 3)2
= 4a2 − 12a + 9; (3w)3 = 27w3;
Heinemann Maths Zone 10 VELS Edition
;
).
Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd)
MZ10 p111 (3.2 Q3, 4)
FT10 3.2 Short answer
FT10 3.2 Multiple
choice
Page 27 of 92
VELS refs
Course
Heinemann references
Assessment
Students apply the algebraic properties (closure, associative,
Difference of two squares
MZ10 p111 (3.2 Q 1, 2, 5–7)
FT10 3.2 Short answer
commutative, identity, inverse and distributive) to computation with
FT10 3.2 Multiple
number, to rearrange formulae, rearrange and simplify algebraic
choice
expressions involving real variables. They verify the equivalence or
otherwise of algebraic expressions (linear, square, cube, exponent,
and reciprocal, (for example, 4x − 8 = 2(2x − 4) = 4(x − 2); (2a − 3)2
= 4a2 − 12a + 9; (3w)3 = 27w3;
;
).
Factorising
Students carry out arithmetic computations involving natural
Common factors
MZ10 p120 (3.4 Q1–10)
numbers, integers and finite decimals using mental and/or written
FT10 3.4 Short answer
FT10 3.4 Multiple
algorithms (one- or two-digit divisors in the case of division).
choice
Students choose, use and develop mathematical models and
procedures to investigate and solve problems set in a wide range of
practical, theoretical and historical contexts.
Students choose, use and develop mathematical models and
Difference of two squares
MZ10 p123 (3.5 Q1–10)
procedures to investigate and solve problems set in a wide range of
FT10 3.5 Multiple
practical, theoretical and historical contexts.
Students choose, use and develop mathematical models and
choice
Perfect squares, grouping
procedures to investigate and solve problems set in a wide range of
practical, theoretical and historical contexts.
Heinemann Maths Zone 10 VELS Edition
FT10 3.5 Short answer
Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd)
MZ10 p129 (3.6 Q1–10)
FT10 3.6 Short answer
FT10 3.6 Multiple
choice
Page 28 of 92
VELS refs
Course
Heinemann references
Assessment
Students choose, use and develop mathematical models and
Trinomials where coefficient of x2 is 1
MZ10 p134 (3.7 Q1)
FT10 3.7 (Q1–3) Short
procedures to investigate and solve problems set in a wide range of
practical, theoretical and historical contexts.
answer
FT10 3.7 (Q1–3)
Multiple choice
selected
Heinemann Maths Zone 10 VELS Edition
Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd)
Page 29 of 92
Unit 3: Algebra
Level: C
Dimensions: Structure
VELS refs
Time: 4 weeks
Course
Heinemann references
Assessment
MZ10 p107 (3.1)
FT10 3.1 Short answer
Quadratic expressions
Students apply the algebraic properties (closure, associative,
Expansion
commutative, identity, inverse and distributive) to computation with
FT10 3.1 Multiple
number, to rearrange formulae, rearrange and simplify algebraic
choice
expressions involving real variables. They verify the equivalence or
FT10 3.1 Applications
otherwise of algebraic expressions (linear, square, cube, exponent,
and analysis
and reciprocal, (for example, 4x − 8 = 2(2x − 4) = 4(x − 2); (2a − 3)2
= 4a2 − 12a + 9; (3w)3 = 27w3;
;
).
Students apply the algebraic properties (closure, associative,
Perfect squares
commutative, identity, inverse and distributive) to computation with
choice
expressions involving real variables. They verify the equivalence or
FT10 3.2 Applications
otherwise of algebraic expressions (linear, square, cube, exponent,
= 4a2 − 12a + 9; (3w)3 = 27w3;
Heinemann Maths Zone 10 VELS Edition
;
FT10 3.2 Short answer
FT10 3.2 Multiple
number, to rearrange formulae, rearrange and simplify algebraic
and reciprocal, (for example, 4x − 8 = 2(2x − 4) = 4(x − 2); (2a − 3)
MZ10 p111 (3.2)
and analysis
2
).
Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd)
Page 30 of 92
VELS refs
Course
Heinemann references
Assessment
Students apply the algebraic properties (closure, associative,
Difference of two squares
MZ10 p111 (3.2)
MZ10 p115 (VELS
commutative, identity, inverse and distributive) to computation with
Design task)
number, to rearrange formulae, rearrange and simplify algebraic
FT10 3.2 Short answer
expressions involving real variables. They verify the equivalence or
FT10 3.2 Multiple
otherwise of algebraic expressions (linear, square, cube, exponent,
and reciprocal, (for example, 4x − 8 = 2(2x − 4) = 4(x − 2); (2a − 3)
choice
2
FT10 3.2 Applications
and analysis
= 4a2 − 12a + 9; (3w)3 = 27w3;
;
).
Students apply the algebraic properties (closure, associative,
Expanding three factors
MZ10 p116 (3.3); p119
commutative, identity, inverse and distributive) to computation with
(Graphics calculator
number, to rearrange formulae, rearrange and simplify algebraic
investigation); p142 (Maths
expressions involving real variables. They verify the equivalence or
in Action)
otherwise of algebraic expressions (linear, square, cube, exponent,
and reciprocal, (for example, 4x − 8 = 2(2x − 4) = 4(x − 2); (2a − 3)
= 4a2 − 12a + 9; (3w)3 = 27w3;
;
FT10 3.3 Multiple
choice
FT10 3.3 Applications
and analysis
2
).
Factorising
Heinemann Maths Zone 10 VELS Edition
FT10 3.3 Short answer
Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd)
Page 31 of 92
VELS refs
Course
Heinemann references
Assessment
Students carry out arithmetic computations involving natural
Common factors
MZ10 p120 (3.4) Limited
FT10 3.4 Short answer
numbers, integers and finite decimals using mental and/or written
number of questions as this
algorithms (one- or two-digit divisors in the case of division).
should be revision.
Students choose, use and develop mathematical models and
FT10 3.4 Multiple
choice
FT10 3.4 Applications
procedures to investigate and solve problems set in a wide range of
and analysis
practical, theoretical and historical contexts.
Students choose, use and develop mathematical models and
Difference of two squares
MZ10 p123 (3.5)
procedures to investigate and solve problems set in a wide range of
FT10 3.5 Short answer
FT10 3.5 Multiple
practical, theoretical and historical contexts.
choice
FT10 3.5 Applications
and analysis
Students choose, use and develop mathematical models and
Perfect squares, grouping
MZ10 p129 (3.6)
procedures to investigate and solve problems set in a wide range of
FT10 3.6 Short answer
FT10 3.6 Multiple
practical, theoretical and historical contexts.
choice
FT10 3.6 Applications
and analysis
Students choose, use and develop mathematical models and
Factorising quadratic trinomials
procedures to investigate and solve problems set in a wide range of
practical, theoretical and historical contexts.
MZ10 p134 (3.7); p144
(Computer investigation)
FT10 3.7 Short answer
FT10 3.7 Multiple
choice
FT10 3.7 Applications
and analysis
Heinemann Maths Zone 10 VELS Edition
Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd)
Page 32 of 92
VELS refs
Course
Heinemann references
Assessment
Students choose, use and develop mathematical models and
Factorising by completing the square
MZ10 p137 (3.8)
FT10 3.8 Short answer
procedures to investigate and solve problems set in a wide range of
FT10 3.8 Multiple
practical, theoretical and historical contexts.
choice
FT10 3.8 Applications
and analysis
Algebraic manipulations
Students apply the algebraic properties (closure, associative,
Algebraic fractions
commutative, identity, inverse and distributive) to computation with
number, to rearrange formulae, rearrange and simplify algebraic
expressions involving real variables. They verify the equivalence or
otherwise of algebraic expressions (linear, square, cube, exponent,
and reciprocal, (for example, 4x − 8 = 2(2x − 4) = 4(x − 2); (2a − 3)2
= 4a2 − 12a + 9; (3w)3 = 27w3;
Heinemann Maths Zone 10 VELS Edition
;
).
Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd)
MZ10 p145 (3.9)
FT10 3.9 Short answer
FT10 3.9 Multiple
choice
FT10 3.9 Applications
and analysis
Page 33 of 92
Unit 4: Trigonometry
Level: A
Dimensions: Space
VELS refs
Time: 4 weeks
Course
Heinemann references
Assessment
MZ10 p283 (6.1 Q1)
FT10 6.1 Short answer
Trigonometric ratios
Students use Pythagoras’ theorem and trigonometric ratios (sine,
Identifying sides of a right-angled triangle
cosine and tangent) to obtain lengths of sides, angles and the area of
FT10 6.1 Multiple
right-angled triangles.
choice
FT10 6.1 Applications
and analysis
Students use Pythagoras’ theorem and trigonometric ratios (sine,
Using trigonometric ratios
MZ10 p283 (6.1 Q2–5)
cosine and tangent) to obtain lengths of sides, angles and the area of
FT10 6.1 Short answer
FT10 6.1 Multiple
right-angled triangles.
choice
FT10 6.1 Applications
and analysis
Finding values
Students use Pythagoras’ theorem and trigonometric ratios (sine,
cosine and tangent) to obtain lengths of sides, angles and the area of
Making use of the calculator to find trigonometric
values
right-angled triangles.
FT10 6.2 Short answer
FT10 6.2 Multiple
choice
They select and use technology in various combinations to assist in
mathematical inquiry, to manipulate and represent data, to analyse
functions and carry out symbolic manipulation.
Heinemann Maths Zone 10 VELS Edition
MZ10 p288 (6.2)
Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd)
FT10 6.2 Applications
and analysis
Page 34 of 92
VELS refs
Course
Heinemann references
Assessment
Students use Pythagoras’ theorem and trigonometric ratios (sine,
Finding side lengths using trigonometry
MZ10 p291 (6.3)
FT10 6.3 Short answer
cosine and tangent) to obtain lengths of sides, angles and the area of
FT10 6.3 Multiple
right-angled triangles.
choice
Students choose, use and develop mathematical models and
procedures to investigate and solve problems set in a wide range of
practical, theoretical and historical contexts.
Students use Pythagoras’ theorem and trigonometric ratios (sine,
Finding more difficult lengths
MZ10 p298 (6.5 Q1–3)
cosine and tangent) to obtain lengths of sides, angles and the area of
FT10 6.5 Short answer
FT10 6.5 Multiple
right-angled triangles.
choice
Students choose, use and develop mathematical models and
procedures to investigate and solve problems set in a wide range of
practical, theoretical and historical contexts.
Students use Pythagoras’ theorem and trigonometric ratios (sine,
Finding angles
MZ10 p301 (6.6 Q 1–4)
cosine and tangent) to obtain lengths of sides, angles and the area of
FT10 6.6 Short answer
FT10 6.6 Multiple
right-angled triangles.
choice
Students choose, use and develop mathematical models and
procedures to investigate and solve problems set in a wide range of
practical, theoretical and historical contexts.
Students use Pythagoras’ theorem and trigonometric ratios (sine,
Solving triangles and finding angles
cosine and tangent) to obtain lengths of sides, angles and the area of
right-angled triangles.
FT10 6.7 Short answer
FT10 6.7 Multiple
choice
Students choose, use and develop mathematical models and
procedures to investigate and solve problems set in a wide range of
practical, theoretical and historical contexts.
Heinemann Maths Zone 10 VELS Edition
MZ10 p303 (6.7 Q 1–5)
Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd)
Page 35 of 92
VELS refs
Course
Heinemann references
Assessment
MZ10 p314 (6.9 Q1–6)
FT10 6.9 Short answer
Bearings
Students choose, use and develop mathematical models and
Bearings
procedures to investigate and solve problems set in a wide range of
practical, theoretical and historical contexts.
Students use Pythagoras’ theorem and trigonometric ratios (sine,
cosine and tangent) to obtain lengths of sides, angles and the area of
right-angled triangles.
Heinemann Maths Zone 10 VELS Edition
Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd)
FT10 6.9 Multiple
choice
Page 36 of 92
Unit 4: Measurement
Level: B
Dimensions: Measurement, chance and data
VELS refs
Course
Time: 3 weeks
Heinemann references
Assessment
MZ10 p 163 (4.1)
FT10 4.1 Short answer
Time
Students estimate and measure length, area, surface area, mass,
Timetables, time zones and speed
volume, capacity and angle. They select and use appropriate units,
FT10 4.1 Multiple
converting between units as required. They calculate constant rates
choice
such as the density of substances (that is, mass in relation to volume),
FT10 4.1 Applications
concentration of fluids, average speed and pollution levels in the
and analysis
atmosphere.
Area
Students estimate and measure length, area, surface area, mass,
Areas of composite shapes
MZ10 p169 (4.2)
volume, capacity and angle. They select and use appropriate units,
MZ10 p175 (VELS
Design Task)
converting between units as required.
FT10 4.2 Short answer
FT10 4.2 Multiple
choice
FT10 4.2 Applications
and analysis
Students form and test mathematical conjectures; for example, ‘What
Hero’s formula
relationship holds between the lengths of the three sides of a
triangle?’
Students choose, use and develop mathematical models and
procedures to investigate and solve problems set in a wide range of
practical, theoretical and historical contexts.
Heinemann Maths Zone 10 VELS Edition
Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd)
MZ10 p176 (Investigation)
Page 37 of 92
VELS refs
Course
Heinemann references
Assessment
They recognise and describe boundaries, surfaces and interiors of
Total surface area
MZ10 p 177 (4.3)
FT10 4.3 Short answer
common plane and three-dimensional shapes, including cylinders,
FT10 4.3 Multiple
spheres, cones, prisms and polyhedra.
choice
Students estimate and measure length, area, surface area, mass,
volume, capacity and angle. They select and use appropriate units,
converting between units as required.
They recognise and describe boundaries, surfaces and interiors of
Total surface area of composite solids
common plane and three-dimensional shapes, including cylinders,
FT10 4.4 Short answer
FT10 4.4 Multiple
spheres, cones, prisms and polyhedra.
choice
Students estimate and measure length, area, surface area, mass,
volume, capacity and angle. They select and use appropriate units,
converting between units as required.
They determine the effect of changing the scale of one characteristic
of two- and three-dimensional shapes (for example, side length, area,
volume and angle measure) on related characteristics.
Volume
Heinemann Maths Zone 10 VELS Edition
MZ10 p185 (4.4)
Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd)
Page 38 of 92
VELS refs
Course
Heinemann references
Assessment
Students estimate and measure length, area, surface area, mass,
Volumes of prisms and regular solids
MZ10 p188 (4.5)
FT10 4.5 Short answer
volume, capacity and angle. They select and use appropriate units,
FT10 4.5 Multiple
converting between units as required. They calculate constant rates
choice
such as the density of substances (that is, mass in relation to volume),
concentration of fluids, average speed and pollution levels in the
atmosphere. Students decide on acceptable or tolerable levels of error
in a given situation. They interpret and use mensuration formulae for
calculating the perimeter, surface area and volume of familiar twoand three-dimensional shapes and simple composites of these shapes.
Students choose, use and develop mathematical models and
Volumes of tapered solids
MZ10 p192 (Investigation)
Volumes of other solids
MZ10 p195 (4.6); p203
procedures to investigate and solve problems set in a wide range of
practical, theoretical and historical contexts (for example, exact and
approximate measurement formulae for the volumes of various threedimensional objects such as truncated pyramids).
Students estimate and measure length, area, surface area, mass,
volume, capacity and angle. They select and use appropriate units,
(Graphics calculator
converting between units as required. They calculate constant rates
investigation)
such as the density of substances (that is, mass in relation to volume),
FT10 4.6 Multiple
choice
FT10 4.6 Applications
concentration of fluids, average speed and pollution levels in the
and analysis
atmosphere. Students decide on acceptable or tolerable levels of error
in a given situation. They interpret and use mensuration formulae for
calculating the perimeter, surface area and volume of familiar twoand three-dimensional shapes and simple composites of these shapes.
Capacity, Density and Concentration
Heinemann Maths Zone 10 VELS Edition
FT10 4.6 Short answer
Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd)
Page 39 of 92
VELS refs
Course
Heinemann references
Assessment
Students estimate and measure length, area, surface area, mass,
Capacity
MZ10 p199 (4.7)
FT10 4.7 Short answer
volume, capacity and angle. They select and use appropriate units,
FT10 4.7 Multiple
converting between units as required. They calculate constant rates
choice
such as the density of substances (that is, mass in relation to volume),
concentration of fluids, average speed and pollution levels in the
atmosphere. Students decide on acceptable or tolerable levels of error
in a given situation. They interpret and use mensuration formulae for
calculating the perimeter, surface area and volume of familiar twoand three-dimensional shapes and simple composites of these shapes.
Students estimate and measure length, area, surface area, mass,
Density
volume, capacity and angle. They select and use appropriate units,
converting between units as required. They calculate constant rates
such as the density of substances (that is, mass in relation to volume),
concentration of fluids, average speed and pollution levels in the
atmosphere. Students decide on acceptable or tolerable levels of error
in a given situation. They interpret and use mensuration formulae for
calculating the perimeter, surface area and volume of familiar twoand three-dimensional shapes and simple composites of these shapes.
Heinemann Maths Zone 10 VELS Edition
Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd)
MZ10 p206 (4.8)
FT10 4.8 Short answer
FT10 4.8 Multiple
choice
Page 40 of 92
VELS refs
Course
Heinemann references
Assessment
Students estimate and measure length, area, surface area, mass,
Concentration
MZ10 p208 (4.9)
FT10 4.9 Short answer
volume, capacity and angle. They select and use appropriate units,
converting between units as required. They calculate constant rates
such as the density of substances (that is, mass in relation to volume),
concentration of fluids, average speed and pollution levels in the
atmosphere. Students decide on acceptable or tolerable levels of error
in a given situation. They interpret and use mensuration formulae for
calculating the perimeter, surface area and volume of familiar twoand three-dimensional shapes and simple composites of these shapes.
Heinemann Maths Zone 10 VELS Edition
Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd)
FT10 4.9 Multiple
choice
Page 41 of 92
Unit 4: Measurement
Level: C
Dimensions: Measurement, chance and data
VELS refs
Course
Time: 4 weeks
Heinemann references
Assessment
MZ10 p169 (4.2)
MZ10 p175 (VELS
Area
Students estimate and measure length, area, surface area, mass,
Areas of composite shapes
volume, capacity and angle. They select and use appropriate units,
Design Task)
converting between units as required. They calculate constant rates
FT10 4.2 Short answer
such as the density of substances (that is, mass in relation to volume),
FT10 4.2 Multiple
concentration of fluids, average speed and pollution levels in the
choice
atmosphere.
FT10 4.2 Applications
and analysis
They recognise and describe boundaries, surfaces and interiors of
Total surface area
common plane and three-dimensional shapes, including cylinders,
spheres, cones, prisms and polyhedra.
FT10 4.3 Short answer
FT10 4.3 Multiple
choice
Students estimate and measure length, area, surface area, mass,
volume, capacity and angle. They select and use appropriate units,
converting between units as required.
Heinemann Maths Zone 10 VELS Edition
MZ10 p 177 (4.3)
Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd)
FT10 4.3 Applications
and analysis
Page 42 of 92
VELS refs
Course
Heinemann references
Assessment
They recognise and describe boundaries, surfaces and interiors of
Total surface area of composite solids
MZ10 p185 (4.4)
FT10 4.4 Short answer
common plane and three-dimensional shapes, including cylinders,
FT10 4.4 Multiple
spheres, cones, prisms and polyhedra.
choice
Students estimate and measure length, area, surface area, mass,
FT10 4.4 Applications
volume, capacity and angle. They select and use appropriate units,
and analysis
converting between units as required.
They determine the effect of changing the scale of one characteristic
of two- and three-dimensional shapes (for example, side length, area,
volume and angle measure) on related characteristics.
Volume
They recognise and describe boundaries, surfaces and interiors of
Volumes of prisms and regular solids
common plane and three-dimensional shapes, including cylinders,
spheres, cones, prisms and polyhedra.
FT10 4.5 Short answer
FT10 4.5 Multiple
choice
Students estimate and measure length, area, surface area, mass,
volume, capacity and angle. They select and use appropriate units,
converting between units as required.
Heinemann Maths Zone 10 VELS Edition
MZ10 p188 (4.5)
Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd)
FT10 4.5 Applications
and analysis
Page 43 of 92
VELS refs
Course
Heinemann references
Assessment
They recognise and describe boundaries, surfaces and interiors of
Volumes of other solids
MZ10 p195 (4.6)
FT10 4.6 Short answer
common plane and three-dimensional shapes, including cylinders,
FT10 4.6 Multiple
spheres, cones, prisms and polyhedra.
choice
Students estimate and measure length, area, surface area, mass,
FT10 4.6 Applications
volume, capacity and angle. They select and use appropriate units,
and analysis
converting between units as required.
They determine the effect of changing the scale of one characteristic
of two- and three-dimensional shapes (for example, side length, area,
volume and angle measure) on related characteristics.
Capacity, Density and Concentration
Students estimate and measure length, area, surface area, mass,
Capacity
MZ10 p199 (4.7)
volume, capacity and angle. They select and use appropriate units,
FT10 4.7 Short answer
FT10 4.7 Multiple
converting between units as required. They calculate constant rates
choice
such as the density of substances (that is, mass in relation to volume),
FT10 4.7 Applications
concentration of fluids, average speed and pollution levels in the
and analysis
atmosphere. Students decide on acceptable or tolerable levels of error
in a given situation. They interpret and use mensuration formulae for
calculating the perimeter, surface area and volume of familiar twoand three-dimensional shapes and simple composites of these shapes.
Students choose, use and develop mathematical models and
Density
procedures to investigate and solve problems set in a wide range of
practical, theoretical and historical contexts (for example, exact and
approximate measurement formulae for the volumes of various threedimensional objects such as truncated pyramids).
Heinemann Maths Zone 10 VELS Edition
Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd)
MZ10 p206 (4.8)
FT10 4.8 Short answer
FT10 4.8 Multiple
choice
FT10 4.8 Applications
and analysis
Page 44 of 92
VELS refs
Course
Heinemann references
Assessment
Students estimate and measure length, area, surface area, mass,
Concentration
MZ10 p208 (4.9)
FT10 4.9 Short answer
volume, capacity and angle. They select and use appropriate units,
converting between units as required. They calculate constant rates
such as the density of substances (that is, mass in relation to volume),
concentration of fluids, average speed and pollution levels in the
atmosphere. Students decide on acceptable or tolerable levels of error
in a given situation. They interpret and use mensuration formulae for
calculating the perimeter, surface area and volume of familiar twoand three-dimensional shapes and simple composites of these shapes.
Heinemann Maths Zone 10 VELS Edition
Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd)
FT10 4.9 Multiple
choice
FT10 4.9 Applications
and analysis
Page 45 of 92
Unit 5: Statistics
Level: A
Dimensions: Chance and data
VELS refs
Time: 4 weeks
Course
Heinemann references
Assessment
MZ10 p337 (7.1 Q1–9)
FT10 7.1 Short answer
Surveys
Students comprehend the difference between a population and a
Designing questions, sampling and population
sample. They generate data using surveys, experiments and sampling
FT10 7.1 Multiple
procedures.
choice
Summarising data
They calculate summary statistics for centrality (mode, median and
Mean and mode of grouped data
mean), spread (boxplot, interquartile range, outliers) and association
MZ10 p345 (7.2 Q1–5); p351
(Investigation)
(by-eye estimation of the line of best fit from a scatter plot).
They calculate summary statistics for centrality (mode, median and
FT10 7.2 Multiple
choice
Median of grouped data
mean), spread (boxplot, interquartile range, outliers) and association
(by-eye estimation of the line of best fit from a scatter plot).
Heinemann Maths Zone 10 VELS Edition
FT10 7.2 Short answer
Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd)
MZ10 p352 (7.3 Q1–5)
FT10 7.3 Short answer
FT10 7.3 Multiple
choice
Page 46 of 92
VELS refs
Course
Heinemann references
Assessment
MZ10 p358 (7.4 Q1–7)
FT10 7.4 Short answer
Graphing data
They calculate summary statistics for centrality (mode, median and
Cumulative frequency graphs
mean), spread (boxplot, interquartile range, outliers) and association
FT10 7.4 Multiple
(by-eye estimation of the line of best fit from a scatter plot). They
choice
distinguish informally between association and causal relationships in
bivariate data, and make predictions based on an estimated line of
best fit for scatter-plot data with strong association between two
variables.
Examining data
They calculate summary statistics for centrality (mode, median and
Outliers
mean), spread (boxplot, interquartile range, outliers) and association
(by-eye estimation of the line of best fit from a scatter plot).
Heinemann Maths Zone 10 VELS Edition
Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd)
MZ10 p365 (7.5 Q1–4)
FT10 7.5 Short answer
FT10 7.5 Multiple
choice
Page 47 of 92
VELS refs
Course
Heinemann references
Assessment
Students form and test mathematical conjectures; for example, ‘What
Statistics in the media
MZ10 p369 (7.6)
FT10 7.6 Short answer
relationship holds between the lengths of the three sides of a
FT10 7.6 Multiple
triangle?’
choice
Students choose, use and develop mathematical models and
procedures to investigate and solve problems set in a wide range of
practical, theoretical and historical contexts (for example, exact and
approximate measurement formulae for the volumes of various threedimensional objects such as truncated pyramids). They generalise
from one situation to another, and investigate it further by changing
the initial constraints or other boundary conditions. They judge the
reasonableness of their results based on the context under
consideration.
They calculate summary statistics for centrality (mode, median and
Investigating data with box-and-whisker plots
mean), spread (boxplot, interquartile range, outliers) and association
(by-eye estimation of the line of best fit from a scatter plot).
They select and use technology in various combinations to assist in
mathematical inquiry, to manipulate and represent data, to analyse
functions and carry out symbolic manipulation.
Information and communications technology/ICT for visualising
thinking Students use a range of ICT tools and data types to visualise
their thinking strategies when solving problems.
Heinemann Maths Zone 10 VELS Edition
Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd)
MZ10 p374 (Investigation)
Page 48 of 92
Unit 5: Linear relationships
Level: B
Dimensions: Structure
Time: 4 weeks
VELS refs
Course
Heinemann references
Assessment
They recognise and explain the roles of the relevant constants in the
Linear equations
MZ10 p219 (5.1)
FT10 5.1 Short answer
relationships f(x) = ax + c, with reference to gradient and y-axis
2
FT10 5.1 Multiple
x
intercept, f(x) = a(x + b) + c and f(x) = ca .
choice
They solve equations of the form f(x) = k, where k is a real constant
FT10 5.1 Applications
(for example, x(x + 5) = 100).
and analysis
They recognise and explain the roles of the relevant constants in the
Gradient
MZ10 p226 (5.2)
relationships f(x) = ax + c, with reference to gradient and y-axis
FT10 5.2 Short answer
FT10 5.2 Multiple
intercept, f(x) = a(x + b)2 + c and f(x) = cax.
choice
FT10 5.2 Applications
and analysis
Students identify and represent linear, quadratic and exponential
Sketching linear graphs
MZ10 p233 (5.3); p241
functions by table, rule and graph (all four quadrants of the Cartesian
(Graphics calculator
coordinate system) with consideration of independent and dependent
investigation)
variables, domain and range.
They recognise and explain the roles of the relevant constants in the
relationships f(x) = ax + c, with reference to gradient and y-axis
intercept, f(x) = a(x + b)2 + c and f(x) = cax.
Heinemann Maths Zone 10 VELS Edition
Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd)
FT10 5.3 Short answer
FT10 5.3 Multiple
choice
Page 49 of 92
VELS refs
Course
Heinemann references
Assessment
They calculate summary statistics for centrality (mode, median and
Lines of best fit
MZ10 p244 (5.4)
FT10 5.4 Short answer
mean), spread (boxplot, interquartile range, outliers) and association
FT10 5.4 Multiple
(by-eye estimation of the line of best fit from a scatter plot).
choice
Students choose, use and develop mathematical models and
FT10 5.4 Applications
procedures to investigate and solve problems set in a wide range of
and analysis
practical, theoretical and historical contexts.
They select and use technology in various combinations to assist in
mathematical inquiry, to manipulate and represent data, to analyse
functions and carry out symbolic manipulation.
They solve equations of the form f(x) = k, where k is a real constant
Solving simultaneous equations
MZ10 p250 (5.5)
(for example, x(x + 5) = 100) and simultaneous linear equations in
FT10 5.5 Short answer
FT10 5.5 Multiple
two variables (for example {2x − 3y = −4 and 5x + 6y = 27}) using
choice
algebraic, numerical (systematic guess, check and refine or bisection)
and graphical methods.
Linear inequations
Students choose, use and develop mathematical models and
Solving linear inequations
procedures to investigate and solve problems set in a wide range of
practical, theoretical and historical contexts.
Level 5 They solve simple inequalities such as y ≤ 2x + 4 and decide
whether inequalities such as x2 > 2y are satisfied or not for specific
values of x and y.
Heinemann Maths Zone 10 VELS Edition
Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd)
MZ10 p261 (5.6)
FT10 5.6 Short answer
FT10 5.6 Multiple
choice
Page 50 of 92
VELS refs
Course
Heinemann references
Assessment
Students identify and represent linear, quadratic and exponential
Graphing linear inequations
MZ10 p266 (5.7)
FT10 5.7 Short answer
functions by table, rule and graph (all four quadrants of the Cartesian
coordinate system) with consideration of independent and dependent
variables, domain and range.
Heinemann Maths Zone 10 VELS Edition
Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd)
FT10 5.7 Multiple
choice
Page 51 of 92
Unit 5: Linear relationships
Level: C
Dimensions: Space
Time: 3 weeks
VELS refs
Course
Heinemann references
Assessment
They recognise and explain the roles of the relevant constants in the
Revision of linear functions
MZ10 p219 (5.1); p226 (5.2);
FT10 5.1 Short answer
relationships f(x) = ax + c, with reference to gradient and y-axis
2
p233 (5.3); p232 (Problem
x
intercept, f(x) = a(x + b) + c and f(x) = ca .
solving); p242 (Maths in
They solve equations of the form f(x) = k, where k is a real constant
action)
(for example, x(x + 5) = 100).
Limited questions from each
FT10 5.1 Multiple
choice
FT10 5.1 Applications
and analysis
exercise as this should be
FT10 5.2 Short answer
revision for these students.
FT10 5.2 Multiple
choice
FT10 5.2 Applications
and analysis
FT10 5.3 Short answer
FT10 5.3 Multiple
choice
FT10 5.3 Applications
and analysis
They recognise and explain the roles of the relevant constants in the
Equation of the tangent
relationships f(x) = ax + c, with reference to gradient and y-axis
2
x
intercept, f(x) = a(x + b) + c and f(x) = ca .
Students choose, use and develop mathematical models and
procedures to investigate and solve problems set in a wide range of
practical, theoretical and historical contexts.
Heinemann Maths Zone 10 VELS Edition
Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd)
MZ10 p231 (Investigation);
p240 (CAS Investigation)
Page 52 of 92
VELS refs
Course
Heinemann references
Assessment
They calculate summary statistics for centrality (mode, median and
Lines of best fit
MZ10 p244 (5.4)
FT10 5.4 Short answer
mean), spread (boxplot, interquartile range, outliers) and association
FT10 5.4 Multiple
(by-eye estimation of the line of best fit from a scatter plot).
choice
Students choose, use and develop mathematical models and
FT10 5.4 Applications
procedures to investigate and solve problems set in a wide range of
and analysis
practical, theoretical and historical contexts.
They select and use technology in various combinations to assist in
mathematical inquiry, to manipulate and represent data, to analyse
functions and carry out symbolic manipulation.
They solve equations of the form f(x) = k, where k is a real constant
Solving simultaneous equations
MZ10 p250 (5.5)
(for example, x(x + 5) = 100) and simultaneous linear equations in
FT10 5.5 Short answer
FT10 5.5 Multiple
two variables (for example {2x − 3y = −4 and 5x + 6y = 27}) using
choice
algebraic, numerical (systematic guess, check and refine or bisection)
FT10 5.5 Applications
and graphical methods.
and analysis
Linear inequations
Students choose, use and develop mathematical models and
Solving linear inequations
procedures to investigate and solve problems set in a wide range of
practical, theoretical and historical contexts.
Level 5 They solve simple inequalities such as y ≤ 2x + 4 and decide
2
whether inequalities such as x > 2y are satisfied or not for specific
values of x and y.
Heinemann Maths Zone 10 VELS Edition
Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd)
MZ10 p261 (5.6)
FT10 5.6 Short answer
FT10 5.6 Multiple
choice
FT10 5.6 Applications
and analysis
Page 53 of 92
VELS refs
Course
Heinemann references
Assessment
Students identify and represent linear, quadratic and exponential
Graphing linear inequations
MZ10 p266 (5.7)
FT10 5.7 Short answer
functions by table, rule and graph (all four quadrants of the Cartesian
coordinate system) with consideration of independent and dependent
variables, domain and range.
FT10 5.7 Multiple
choice
FT10 5.7 Applications
and analysis
Heinemann Maths Zone 10 VELS Edition
Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd)
Page 54 of 92
Unit 6: Geometry
Level: A
Dimensions: Space
VELS refs
Time: 5 weeks
Course
Heinemann references
Assessment
MZ10 p393 (8.1 Q 1–6)
FT10 8.1 Short answer
Circle facts
They recognise the features of circles (centre, radius, diameter,
Parts of circles
chord, arc, semicircle, circumference, segment, sector and tangent)
FT10 8.1 Multiple
and use associated angle properties.
choice
FT10 8.1 Applications
and analysis
They recognise the features of circles (centre, radius, diameter,
Arc length
MZ10 p405 (8.3 Q1–7)
chord, arc, semicircle, circumference, segment, sector and tangent)
FT10 8.3 Short answer
FT10 8.3 Multiple
and use associated angle properties.
choice
They use degrees and radians as units of measurement for angles and
convert between units of measurement as appropriate.
They use latitude and longitude to locate places on the Earth’s
Latitude and longitude
MZ10 p434 (Investigation)
surface and measure distances between places using great circles.
Three dimensions
Students represent two- and three-dimensional shapes using lines,
Isometric drawings, elevations and plans
curves, polygons and circles. They make representations using
perspective, isometric drawings, nets and computer-generated
images.
MZ10 p410 (8.4)
FT10 8.4 Short answer
FT10 8.4 Multiple
choice
FT10 8.4 Applications
and analysis
Heinemann Maths Zone 10 VELS Edition
Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd)
Page 55 of 92
VELS refs
Course
Heinemann references
Assessment
They recognise and describe boundaries, surfaces and interiors of
Polyhedra and Euler’s rule
MZ10 p415 (8.5 Q 1–6)
FT10 8.5 Short answer
common plane and three-dimensional shapes, including cylinders,
FT10 8.5 Multiple
spheres, cones, prisms and polyhedra.
choice
Constructions
They recognise and describe boundaries, surfaces and interiors of
Constructions by drawing
MZ10 p419 (8.6 Q1–5)
common plane and three-dimensional shapes, including cylinders,
FT10 8.6 Short answer
FT10 8.6 Multiple
spheres, cones, prisms and polyhedra.
choice
Students form and test mathematical conjectures; for example, ‘What
Paper constructions
MZ10 p426 (Problem solving)
relationship holds between the lengths of the three sides of a
triangle?’
Transformations
Students use the conditions for shapes to be congruent or similar.
They apply isometric and similarity transformations of geometric
Transformations including reflection, rotation and
translation
shapes in the plane. They identify points that are invariant under a
given transformation (for example, the point (2, 0) is invariant under
reflection in the x-axis, so the x-axis intercept of the graph of y = 2x −
4 is also invariant under this transformation). They determine the
effect of changing the scale of one characteristic of two- and threedimensional shapes (for example, side length, area, volume and angle
measure) on related characteristics.
Heinemann Maths Zone 10 VELS Edition
Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd)
MZ10 p427 (8.7)
FT10 8.7 Short answer
FT10 8.7 Multiple
choice
FT10 8.7 Applications
and analysis
Page 56 of 92
VELS refs
Course
Heinemann references
Students use the conditions for shapes to be congruent or similar.
Using transformations
MZ10 p435 (Maths in Action)
They apply isometric and similarity transformations of geometric
shapes in the plane. They identify points that are invariant under a
given transformation (for example, the point (2, 0) is invariant under
reflection in the x-axis, so the x-axis intercept of the graph of y = 2x −
4 is also invariant under this transformation). They determine the
effect of changing the scale of one characteristic of two- and threedimensional shapes (for example, side length, area, volume and angle
measure) on related characteristics.
Heinemann Maths Zone 10 VELS Edition
Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd)
Assessment
Page 57 of 92
Unit 6: Trigonometry
Level: B
Dimensions: Measurement, chance and data
VELS refs
Course
Time: 4 weeks
Heinemann references
Assessment
MZ10 p283 (6.1); p288 (6.2);
FT10 6.1 Short answer
Trigonometry
Students use Pythagoras’ theorem and trigonometric ratios (sine,
Revision of trigonometry
cosine and tangent) to obtain lengths of sides, angles and the area of
p291 (6.3) Choose a limited
right-angled triangles.
number of questions from
each exercise.
FT10 6.1 Multiple
choice
FT10 6.1 Applications
and analysis
FT10 6.2 Short answer
FT10 6.2 Multiple
choice
FT10 6.2 Applications
and analysis
FT10 6.3 Short answer
FT10 6.3 Multiple
choice
FT10 6.3 Applications
and analysis
Heinemann Maths Zone 10 VELS Edition
Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd)
Page 58 of 92
VELS refs
Course
Heinemann references
Assessment
They use degrees and radians as units of measurement for angles and
Understanding the unit circle
MZ10 p295 (6.4)
FT10 6.4 Short answer
convert between units of measurement as appropriate.
FT10 6.4 Multiple
Students use Pythagoras’ theorem and trigonometric ratios (sine,
choice
cosine and tangent) to obtain lengths of sides, angles and the area of
FT10 6.4 Applications
right-angled triangles.
and analysis
Students use Pythagoras’ theorem and trigonometric ratios (sine,
Finding lengths using trigonometry
cosine and tangent) to obtain lengths of sides, angles and the area of
MZ10 p298 (6.5); p310
(Investigation)
right-angled triangles.
FT10 6.5 Short answer
FT10 6.5 Multiple
choice
They select and use technology in various combinations to assist in
FT10 6.5 Applications
mathematical inquiry, to manipulate and represent data, to analyse
and analysis
functions and carry out symbolic manipulation.
Students use Pythagoras’ theorem and trigonometric ratios (sine,
Finding angles using trigonometry
MZ10 p301 (6.6); p303 (6.7)
cosine and tangent) to obtain lengths of sides, angles and the area of
FT10 6.6 Short answer
FT10 6.6 Multiple
right-angled triangles.
choice
Students choose, use and develop mathematical models and
FT10 6.7 Short answer
procedures to investigate and solve problems set in a wide range of
FT10 6.7 Multiple
practical, theoretical and historical contexts.
Students use Pythagoras’ theorem and trigonometric ratios (sine,
choice
Angles of elevation and depression
cosine and tangent) to obtain lengths of sides, angles and the area of
right-angled triangles.
FT10 6.8 Short answer
FT10 6.8 Multiple
choice
Students choose, use and develop mathematical models and
procedures to investigate and solve problems set in a wide range of
practical, theoretical and historical contexts.
Heinemann Maths Zone 10 VELS Edition
MZ10 p306 (6.8)
Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd)
Page 59 of 92
VELS refs
Course
Heinemann references
Assessment
Students use Pythagoras’ theorem and trigonometric ratios (sine,
Bearings
MZ10 p314 (6.9)
FT10 6.9 Short answer
cosine and tangent) to obtain lengths of sides, angles and the area of
FT10 6.9 Multiple
right-angled triangles.
choice
Students choose, use and develop mathematical models and
FT10 6.9 Applications
procedures to investigate and solve problems set in a wide range of
and analysis
practical, theoretical and historical contexts.
Students use Pythagoras’ theorem and trigonometric ratios (sine,
Two-dimensional problems
MZ10 p319 (6.10)
cosine and tangent) to obtain lengths of sides, angles and the area of
answer
right-angled triangles.
FT10 6.10 Multiple
Students choose, use and develop mathematical models and
choice
procedures to investigate and solve problems set in a wide range of
FT10 6.10 Applications
practical, theoretical and historical contexts.
Students choose, use and develop mathematical models and
and analysis
Three-dimensional problems
procedures to investigate and solve problems set in a wide range of
practical, theoretical and historical contexts.
Students use Pythagoras’ theorem and trigonometric ratios (sine,
cosine and tangent) to obtain lengths of sides, angles and the area of
right-angled triangles.
Heinemann Maths Zone 10 VELS Edition
FT10 6.10 Short
Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd)
MZ10 p325 (6.11 Q1–8)
FT10 6.11 Short
answer
FT10 6.11 Multiple
choice
Page 60 of 92
Unit 6: Trigonometry
Level: C
Dimensions: Space
VELS refs
Time: 4 weeks
Course
Heinemann references
Assessment
MZ10 p283 (6.1); p288 (6.2);
FT10 6.1 Short answer
Trigonometry
Students use Pythagoras’ theorem and trigonometric ratios (sine,
Revision of trigonometry
cosine and tangent) to obtain lengths of sides, angles and the area of
p291 (6.3) Choose a limited
right-angled triangles.
number of questions from
each exercise as this should
be revision.
FT10 6.1 Multiple
choice
FT10 6.1 Applications
and analysis
FT10 6.2 Short answer
FT10 6.2 Multiple
choice
FT10 6.2 Applications
and analysis
FT10 6.3 Short answer
FT10 6.3 Multiple
choice
FT10 6.3 Applications
and analysis
They use degrees and radians as units of measurement for angles and
Understanding the unit circle
convert between units of measurement as appropriate.
Students use Pythagoras’ theorem and trigonometric ratios (sine,
cosine and tangent) to obtain lengths of sides, angles and the area of
right-angled triangles.
Heinemann Maths Zone 10 VELS Edition
MZ10 p295 (6.4)
FT10 6.4 Short answer
FT10 6.4 Multiple
choice
FT10 6.4 Applications
and analysis
Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd)
Page 61 of 92
VELS refs
Course
Heinemann references
Assessment
Students use Pythagoras’ theorem and trigonometric ratios (sine,
Finding lengths using trigonometry
MZ10 p298 (6.5); p310
FT10 6.5 Short answer
cosine and tangent) to obtain lengths of sides, angles and the area of
(Investigation); p312 (Maths
right-angled triangles.
in Action); p318 (Problem
They select and use technology in various combinations to assist in
solving)
mathematical inquiry, to manipulate and represent data, to analyse
FT10 6.5 Multiple
choice
FT10 6.5 Applications
and analysis
functions and carry out symbolic manipulation.
Students use Pythagoras’ theorem and trigonometric ratios (sine,
Finding angles using trigonometry
MZ10 p301 (6.6); p303 (6.7)
cosine and tangent) to obtain lengths of sides, angles and the area of
MZ10 p305 (VELS
Design Task)
right-angled triangles.
FT10 6.6 Short answer
Students choose, use and develop mathematical models and
FT10 6.6 Multiple
procedures to investigate and solve problems set in a wide range of
choice
practical, theoretical and historical contexts.
FT10 6.7 Short answer
FT10 6.7 Multiple
choice
Students use Pythagoras’ theorem and trigonometric ratios (sine,
cosine and tangent) to obtain lengths of sides, angles and the area of
Alternative formula for the area of a triangle using
trigonometry
right-angled triangles.
Students choose, use and develop mathematical models and
procedures to investigate and solve problems set in a wide range of
practical, theoretical and historical contexts.
Heinemann Maths Zone 10 VELS Edition
Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd)
MZ10 p324 (Investigation)
Page 62 of 92
VELS refs
Course
Heinemann references
Assessment
Students use Pythagoras’ theorem and trigonometric ratios (sine,
Angles of elevation and depression
MZ10 p306 (6.8)
FT10 6.8 Short answer
cosine and tangent) to obtain lengths of sides, angles and the area of
FT10 6.8 Multiple
right-angled triangles.
choice
Students choose, use and develop mathematical models and
FT10 6.8 Applications
procedures to investigate and solve problems set in a wide range of
and analysis
practical, theoretical and historical contexts.
Students use Pythagoras’ theorem and trigonometric ratios (sine,
Bearings
MZ10 p314 (6.9)
cosine and tangent) to obtain lengths of sides, angles and the area of
FT10 6.9 Short answer
FT10 6.9 Multiple
right-angled triangles.
choice
Students choose, use and develop mathematical models and
FT10 6.9 Applications
procedures to investigate and solve problems set in a wide range of
and analysis
practical, theoretical and historical contexts.
Students choose, use and develop mathematical models and
Two-dimensional problems
MZ10 p319 (6.10)
procedures to investigate and solve problems set in a wide range of
answer
practical, theoretical and historical contexts.
FT10 6.10 Multiple
Students use Pythagoras’ theorem and trigonometric ratios (sine,
choice
cosine and tangent) to obtain lengths of sides, angles and the area of
FT10 6.10 Applications
right-angled triangles.
and analysis
Students choose, use and develop mathematical models and
Three-dimensional problems
procedures to investigate and solve problems set in a wide range of
practical, theoretical and historical contexts.
Students use Pythagoras’ theorem and trigonometric ratios (sine,
cosine and tangent) to obtain lengths of sides, angles and the area of
right-angled triangles.
Heinemann Maths Zone 10 VELS Edition
FT10 6.10 Short
MZ10 p325 (6.11)
FT10 6.11 Short
answer
FT10 6.11 Multiple
choice
FT10 6.11 Applications
and analysis
Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd)
Page 63 of 92
Unit 7: Probability Level: A
Dimensions: Measurement, chance and data
Time: 3 weeks
VELS refs
Course
Heinemann references
Assessment
Students estimate probabilities based on data (experiments, surveys,
Understanding probability
MZ10 p517 (10.1 Q1–10)
FT10 10.1 Short
samples, simulations) and assign and justify subjective probabilities
in familiar situations. They list event spaces (for combinations of up
to three events) by lists, grids, tree diagrams, Venn diagrams and
Karnaugh maps (two-way tables). They calculate probabilities for
complementary, mutually exclusive, and compound events (defined
using and, or and not). They classify events as dependent or
independent.
Student express relations between sets using membership, ,
complement, ′ , intersection, ∩, union,  , and subset,  , for up to
three sets. They represent a universal set as the disjoint union of
intersections of up to three sets and their complements, and illustrate
this using a tree diagram, Venn diagram or Karnaugh map.
Heinemann Maths Zone 10 VELS Edition
Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd)
answer
FT10 10.1 Multiple
choice
Page 64 of 92
VELS refs
Course
Heinemann references
Assessment
They list event spaces (for combinations of up to three events) by
Multiple events
MZ10 p522 (10.2 Q1–8);
FT10 10.2 Short
lists, grids, tree diagrams, Venn diagrams and Karnaugh maps (two-
p527 (Graphics calculator
way tables). They calculate probabilities for complementary,
investigation)
mutually exclusive, and compound events (defined using and, or and
answer
FT10 10.2 Multiple
choice
not). They classify events as dependent or independent.
Student express relations between sets using membership, ,
complement, ′ , intersection, ∩, union,  , and subset,  , for up to
three sets. They represent a universal set as the disjoint union of
intersections of up to three sets and their complements, and illustrate
this using a tree diagram, Venn diagram or Karnaugh map.
They list event spaces (for combinations of up to three events) by
Venn diagrams and Karnaugh maps
lists, grids, tree diagrams, Venn diagrams and Karnaugh maps (twoway tables). They calculate probabilities for complementary,
mutually exclusive, and compound events (defined using and, or and
not). They classify events as dependent or independent.
Student express relations between sets using membership, ,
complement, ′ , intersection, ∩, union,  , and subset,  , for up to
three sets. They represent a universal set as the disjoint union of
intersections of up to three sets and their complements, and illustrate
this using a tree diagram, Venn diagram or Karnaugh map.
Heinemann Maths Zone 10 VELS Edition
Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd)
MZ10 p529 (10.3 Q1–4)
FT10 10.3 Short
answer
FT10 10.3 Multiple
choice
Page 65 of 92
VELS refs
Course
Heinemann references
Assessment
They list event spaces (for combinations of up to three events) by
Mutually exclusive events
MZ10 p534 (10.4 Q1–4)
FT10 10.4 Short
lists, grids, tree diagrams, Venn diagrams and Karnaugh maps (two-
answer
way tables). They calculate probabilities for complementary,
FT10 10.4 Multiple
mutually exclusive, and compound events (defined using and, or and
choice
not). They classify events as dependent or independent.
They list event spaces (for combinations of up to three events) by
Independent events
MZ10 p538 (10.5 Q1–4)
lists, grids, tree diagrams, Venn diagrams and Karnaugh maps (two-
FT10 10.5 Short
answer
way tables). They calculate probabilities for complementary,
FT10 10.5 Multiple
mutually exclusive, and compound events (defined using and, or and
choice
not). They classify events as dependent or independent.
Students estimate probabilities based on data (experiments, surveys,
Investigating probabilities
MZ10 p542 (Problem solving;
samples, simulations) and assign and justify subjective probabilities
may need some
in familiar situations.
adjustments); p543
Students formulate and test conjectures, generalisations and
arguments in natural language and symbolic form (for example, ‘if m
(Investigation); p550 (VELS
2
Design Task)
is even then m is even, and if m2 is odd then m is odd’).
They list event spaces (for combinations of up to three events) by
Probability tree diagrams
lists, grids, tree diagrams, Venn diagrams and Karnaugh maps (twoway tables). They calculate probabilities for complementary,
mutually exclusive, and compound events (defined using and, or and
not). They classify events as dependent or independent.
Heinemann Maths Zone 10 VELS Edition
Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd)
MZ10 p544 (10.6 Q1–5)
FT10 10.6 Short
answer
FT10 10.6 Multiple
choice
Page 66 of 92
VELS refs
Course
Heinemann references
Assessment
Students estimate probabilities based on data (experiments, surveys,
Odds and payouts
MZ10 p552 (10.7 Q1–8);
FT10 10.7 Short
samples, simulations) and assign and justify subjective probabilities
in familiar situations.
answer
FT10 10.7 Multiple
Students choose, use and develop mathematical models and
procedures to investigate and solve problems set in a wide range of
practical, theoretical and historical contexts.
Heinemann Maths Zone 10 VELS Edition
p556 (Maths@Work)
Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd)
choice
Page 67 of 92
Unit 7: Statistics and probability
Level: B
Dimensions: Measurement, chance and data
VELS refs
Course
Time: 4 weeks
Heinemann references
Assessment
MZ10 p337 (7.1)
FT10 7.1 Short answer
Statistics
Students comprehend the difference between a population and a
Collecting data
sample. They generate data using surveys, experiments and sampling
FT10 7.1 Multiple
procedures.
choice
FT10 7.1 Applications
and analysis
They calculate summary statistics for centrality (mode, median and
Mean and mode of grouped data
mean), spread (boxplot, interquartile range, outliers) and association
MZ10 p345 (7.2); p351
(Investigation)
(by-eye estimation of the line of best fit from a scatter plot).
FT10 7.2 Short answer
FT10 7.2 Multiple
choice
FT10 7.2 Applications
and analysis
They calculate summary statistics for centrality (mode, median and
Median of grouped data
mean), spread (boxplot, interquartile range, outliers) and association
(by-eye estimation of the line of best fit from a scatter plot).
MZ10 p352 (7.3)
FT10 7.3 Short answer
FT10 7.3 Multiple
choice
FT10 7.3 Applications
and analysis
Heinemann Maths Zone 10 VELS Edition
Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd)
Page 68 of 92
VELS refs
Course
Heinemann references
Assessment
They calculate summary statistics for centrality (mode, median and
Using cumulative frequency graphs
MZ10 p358 (7.4)
FT10 7.4 Short answer
mean), spread (boxplot, interquartile range, outliers) and association
FT10 7.4 Multiple
(by-eye estimation of the line of best fit from a scatter plot). They
choice
distinguish informally between association and causal relationship in
FT10 7.4 Applications
bivariate data, and make predictions based on an estimated line of
and analysis
best fit for scatter-plot data with strong association between two
variables.
They calculate summary statistics for centrality (mode, median and
Use of box-and-whisker plots
mean), spread (boxplot, interquartile range, outliers) and association
MZ10 p374 (Graphics
calculator investigation)
(by-eye estimation of the line of best fit from a scatter plot).
They calculate summary statistics for centrality (mode, median and
Outliers
mean), spread (boxplot, interquartile range, outliers) and association
(by-eye estimation of the line of best fit from a scatter plot).
MZ10 p365 (7.5)
FT10 7.5 Short answer
FT10 7.5 Multiple
choice
FT10 7.5 Applications
and analysis
Heinemann Maths Zone 10 VELS Edition
Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd)
Page 69 of 92
VELS refs
Course
Heinemann references
Assessment
Students form and test mathematical conjectures; for example, ‘What
Statistics in the media
MZ10 p369 (7.6)
FT10 7.6 Short answer
relationship holds between the lengths of the three sides of a
FT10 7.6 Multiple
triangle?’
choice
Students choose, use and develop mathematical models and
FT10 7.6 Applications
procedures to investigate and solve problems set in a wide range of
and analysis
practical, theoretical and historical contexts (for example, exact and
approximate measurement formulae for the volumes of various threedimensional objects such as truncated pyramids). They generalise
from one situation to another, and investigate it further by changing
the initial constraints or other boundary conditions. They judge the
reasonableness of their results based on the context under
consideration.
They calculate summary statistics for centrality (mode, median and
Displaying data
MZ10 p376 (Maths in
mean), spread (boxplot, interquartile range, outliers) and association
Action); p379 (VELS
(by-eye estimation of the line of best fit from a scatter plot).
Design Task)
They select and use technology in various combinations to assist in
mathematical inquiry, to manipulate and represent data, to analyse
functions and carry out symbolic manipulation.
Information and communications technology/ICT for visualising
thinking Students use a range of ICT tools and data types to visualise
their thinking strategies when solving problems.
Probability
Heinemann Maths Zone 10 VELS Edition
Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd)
Page 70 of 92
VELS refs
Course
Heinemann references
Assessment
Students estimate probabilities based on data (experiments, surveys,
Basics of probability
MZ10 p517 (10.1 Q1–10)
FT10 10.1 Short
samples, simulations) and assign and justify subjective probabilities
answer
in familiar situations. They list event spaces (for combinations of up
FT10 10.1 Multiple
to three events) by lists, grids, tree diagrams, Venn diagrams and
choice
Karnaugh maps (two-way tables). They calculate probabilities for
FT10 10.1 Applications
complementary, mutually exclusive, and compound events (defined
and analysis
using and, or and not). They classify events as dependent or
independent.
Student express relations between sets using membership, ,
complement, ′ , intersection, ∩, union,  , and subset,  , for up to
three sets. They represent a universal set as the disjoint union of
intersections of up to three sets and their complements, and illustrate
this using a tree diagram, Venn diagram or Karnaugh map.
They list event spaces (for combinations of up to three events) by
Multiple events
lists, grids, tree diagrams, Venn diagrams and Karnaugh maps (twoway tables). They calculate probabilities for complementary,
mutually exclusive, and compound events (defined using and, or and
not). They classify events as dependent or independent.
Student express relations between sets using membership, ,
complement, ′ , intersection, ∩, union,  , and subset,  , for up to
three sets. They represent a universal set as the disjoint union of
intersections of up to three sets and their complements, and illustrate
this using a tree diagram, Venn diagram or Karnaugh map.
Heinemann Maths Zone 10 VELS Edition
Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd)
MZ10 p522 (10.2 Q 1–4)
FT10 10.2 Short
answer
FT10 10.2 Multiple
choice
Page 71 of 92
VELS refs
Course
Heinemann references
Assessment
They list event spaces (for combinations of up to three events) by
Venn diagrams and Karnaugh maps
MZ10 p529 (10.3 Q1–4)
FT10 10.3 Short
lists, grids, tree diagrams, Venn diagrams and Karnaugh maps (two-
answer
way tables). They calculate probabilities for complementary,
FT10 10.3 Multiple
mutually exclusive, and compound events (defined using and, or and
choice
not). They classify events as dependent or independent.
Student express relations between sets using membership, ,
complement, ′ , intersection, ∩, union,  , and subset,  , for up to
three sets. They represent a universal set as the disjoint union of
intersections of up to three sets and their complements, and illustrate
this using a tree diagram, Venn diagram or Karnaugh map.
They list event spaces (for combinations of up to three events) by
Mutually exclusive events
MZ10 p534 (10.4 Q1–4)
lists, grids, tree diagrams, Venn diagrams and Karnaugh maps (two-
FT10 10.4 Short
answer
way tables). They calculate probabilities for complementary,
FT10 10.4 Multiple
mutually exclusive, and compound events (defined using and, or and
choice
not). They classify events as dependent or independent.
They list event spaces (for combinations of up to three events) by
Independent events
lists, grids, tree diagrams, Venn diagrams and Karnaugh maps (twoway tables). They calculate probabilities for complementary,
mutually exclusive, and compound events (defined using and, or and
not). They classify events as dependent or independent.
Heinemann Maths Zone 10 VELS Edition
Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd)
MZ10 p538 (10.5 Q 1– 4)
FT10 10.5 Short
answer
FT10 10.5 Multiple
choice
Page 72 of 92
VELS refs
Course
Heinemann references
Assessment
They list event spaces (for combinations of up to three events) by
Probability tree diagrams
MZ10 p544 (10.6 Q 1–10)
FT10 10.6 Short
lists, grids, tree diagrams, Venn diagrams and Karnaugh maps (twoway tables). They calculate probabilities for complementary,
mutually exclusive, and compound events (defined using and, or and
not). They classify events as dependent or independent.
Heinemann Maths Zone 10 VELS Edition
Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd)
answer
FT10 10.6 Multiple
choice
Page 73 of 92
Unit 7: Statistics and probability
Level: C
Dimensions: Measurement, chance and data
VELS refs
Course
Time: 3 weeks
Heinemann references
Assessment
MZ10 p345 (7.2); p351
FT10 7.2 Short answer
Statistics
They calculate summary statistics for centrality (mode, median and
Mean and mode of grouped data
mean), spread (boxplot, interquartile range, outliers) and association
(Investigation)
(by-eye estimation of the line of best fit from a scatter plot).
FT10 7.2 Multiple
choice
FT10 7.2 Applications
and analysis
They calculate summary statistics for centrality (mode, median and
Median of grouped data
MZ10 p352 (7.3)
mean), spread (boxplot, interquartile range, outliers) and association
FT10 7.3 Short answer
FT10 7.3 Multiple
(by-eye estimation of the line of best fit from a scatter plot).
choice
FT10 7.3 Applications
and analysis
They calculate summary statistics for centrality (mode, median and
Using cumulative frequency graphs
mean), spread (boxplot, interquartile range, outliers) and association
(by-eye estimation of the line of best fit from a scatter plot). They
distinguish informally between association and causal relationship in
bivariate data, and make predictions based on an estimated line of
best fit for scatter-plot data with strong association between two
variables.
Heinemann Maths Zone 10 VELS Edition
Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd)
MZ10 p358 (7.4)
FT10 7.4 Short answer
FT10 7.4 Multiple
choice
FT10 7.4 Applications
and analysis
Page 74 of 92
VELS refs
Course
Heinemann references
They calculate summary statistics for centrality (mode, median and
Use of box-and-whisker plots
MZ10 p374 (Graphics
mean), spread (boxplot, interquartile range, outliers) and association
Assessment
calculator investigation)
(by-eye estimation of the line of best fit from a scatter plot).
They calculate summary statistics for centrality (mode, median and
Outliers
MZ10 p365 (7.5)
mean), spread (boxplot, interquartile range, outliers) and association
FT10 7.5 Short answer
FT10 7.5 Multiple
(by-eye estimation of the line of best fit from a scatter plot).
choice
FT10 7.5 Applications
and analysis
Students form and test mathematical conjectures; for example, ‘What
Statistics in the media
relationship holds between the lengths of the three sides of a
FT10 7.6 Applications
and analysis
triangle?’
Students choose, use and develop mathematical models and
procedures to investigate and solve problems set in a wide range of
practical, theoretical and historical contexts (for example, exact and
approximate measurement formulae for the volumes of various threedimensional objects such as truncated pyramids). They generalise
from one situation to another, and investigate it further by changing
the initial constraints or other boundary conditions. They judge the
reasonableness of their results based on the context under
consideration.
Probability
Heinemann Maths Zone 10 VELS Edition
MZ10 p369 (7.6)
Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd)
Page 75 of 92
VELS refs
Course
Heinemann references
Assessment
Students estimate probabilities based on data (experiments, surveys,
Basics of probability
MZ10 p517 (10.1)
FT10 10.1 Short
samples, simulations) and assign and justify subjective probabilities
answer
in familiar situations. They list event spaces (for combinations of up
FT10 10.1 Multiple
to three events) by lists, grids, tree diagrams, Venn diagrams and
choice
Karnaugh maps (two-way tables). They calculate probabilities for
FT10 10.1 Applications
complementary, mutually exclusive, and compound events (defined
and analysis
using and, or and not). They classify events as dependent or
independent.
Student express relations between sets using membership, ,
complement, ′ , intersection, ∩, union,  , and subset,  , for up to
three sets. They represent a universal set as the disjoint union of
intersections of up to three sets and their complements, and illustrate
this using a tree diagram, Venn diagram or Karnaugh map.
They list event spaces (for combinations of up to three events) by
Multiple events
lists, grids, tree diagrams, Venn diagrams and Karnaugh maps (twoway tables). They calculate probabilities for complementary,
mutually exclusive, and compound events (defined using and, or and
not). They classify events as dependent or independent.
Student express relations between sets using membership, ,
complement, ′ , intersection, ∩, union,  , and subset,  , for up to
three sets. They represent a universal set as the disjoint union of
intersections of up to three sets and their complements, and illustrate
this using a tree diagram, Venn diagram or Karnaugh map.
Heinemann Maths Zone 10 VELS Edition
Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd)
MZ10 p522 (10.2)
FT10 10.2 Short
answer
FT10 10.2 Multiple
choice
FT10 10.2 Applications
and analysis
Page 76 of 92
VELS refs
Course
Heinemann references
Assessment
They list event spaces (for combinations of up to three events) by
Venn diagrams and Karnaugh maps
MZ10 p529 (10.3)
FT10 10.3 Short
lists, grids, tree diagrams, Venn diagrams and Karnaugh maps (two-
answer
way tables). They calculate probabilities for complementary,
FT10 10.3 Multiple
mutually exclusive, and compound events (defined using and, or and
choice
not). They classify events as dependent or independent.
FT10 10.3 Applications
Student express relations between sets using membership, ,
and analysis
complement, ′ , intersection, ∩, union,  , and subset,  , for up to
three sets. They represent a universal set as the disjoint union of
intersections of up to three sets and their complements, and illustrate
this using a tree diagram, Venn diagram or Karnaugh map.
They list event spaces (for combinations of up to three events) by
Mutually exclusive events
MZ10 p534 (10.4)
lists, grids, tree diagrams, Venn diagrams and Karnaugh maps (two-
FT10 10.4 Short
answer
way tables). They calculate probabilities for complementary,
FT10 10.4 Multiple
mutually exclusive, and compound events (defined using and, or and
choice
not). They classify events as dependent or independent.
FT10 10.4 Applications
and analysis
They list event spaces (for combinations of up to three events) by
Independent events
lists, grids, tree diagrams, Venn diagrams and Karnaugh maps (twoway tables). They calculate probabilities for complementary,
mutually exclusive, and compound events (defined using and, or and
not). They classify events as dependent or independent.
MZ10 p538 (10.5)
FT10 10.5 Short
answer
FT10 10.5 Multiple
choice
FT10 10.5 Applications
and analysis
Heinemann Maths Zone 10 VELS Edition
Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd)
Page 77 of 92
VELS refs
Course
Heinemann references
Assessment
They list event spaces (for combinations of up to three events) by
Probability tree diagrams
MZ10 p544 (10.6)
FT10 10.6 Short
lists, grids, tree diagrams, Venn diagrams and Karnaugh maps (twoway tables). They calculate probabilities for complementary,
mutually exclusive, and compound events (defined using and, or and
not). They classify events as dependent or independent.
answer
FT10 10.6 Multiple
choice
FT10 10.6 Applications
and analysis
Heinemann Maths Zone 10 VELS Edition
Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd)
Page 78 of 92
Unit 8: Measurement – volume and capacity
Level: A
VELS refs
Dimensions: Space
Time: 4 weeks
Course
Heinemann references
Assessment
MZ10 p188 (4.5 Q 1–3)
FT10 4.5 Short answer
Volume
Students estimate and measure length, area, surface area, mass,
Volumes of prisms and regular solids
volume, capacity and angle. They select and use appropriate units,
FT10 4.5 Multiple
converting between units as required. They calculate constant rates
choice
such as the density of substances (that is, mass in relation to volume),
concentration of fluids, average speed and pollution levels in the
atmosphere. Students decide on acceptable or tolerable levels of error
in a given situation. They interpret and use mensuration formulae for
calculating the perimeter, surface area and volume of familiar twoand three-dimensional shapes and simple composites of these shapes.
Students choose, use and develop mathematical models and
Volumes of tapered solids
procedures to investigate and solve problems set in a wide range of
practical, theoretical and historical contexts (for example, exact and
approximate measurement formulae for the volumes of various threedimensional objects such as truncated pyramids).
Heinemann Maths Zone 10 VELS Edition
Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd)
MZ10 p192 (Investigation)
Page 79 of 92
VELS refs
Course
Heinemann references
Assessment
Students estimate and measure length, area, surface area, mass,
Volumes of other solids
MZ10 p195 (4.6 Q 1–4)
FT10 4.6 Short answer
volume, capacity and angle. They select and use appropriate units,
FT10 4.6 Multiple
converting between units as required. They calculate constant rates
choice
such as the density of substances (that is, mass in relation to volume),
concentration of fluids, average speed and pollution levels in the
atmosphere. Students decide on acceptable or tolerable levels of error
in a given situation. They interpret and use mensuration formulae for
calculating the perimeter, surface area and volume of familiar twoand three-dimensional shapes and simple composites of these shapes.
Capacity
Students estimate and measure length, area, surface area, mass,
Capacity
volume, capacity and angle. They select and use appropriate units,
converting between units as required. They calculate constant rates
such as the density of substances (that is, mass in relation to volume),
concentration of fluids, average speed and pollution levels in the
atmosphere. Students decide on acceptable or tolerable levels of error
in a given situation. They interpret and use mensuration formulae for
calculating the perimeter, surface area and volume of familiar twoand three-dimensional shapes and simple composites of these shapes.
Heinemann Maths Zone 10 VELS Edition
Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd)
MZ10 p199 (4.7 Q1–3)
FT10 4.7 Short answer
FT10 4.7 Multiple
choice
Page 80 of 92
Unit 8: Geometry
Level: B
Dimensions: Space
VELS refs
Time: 3 weeks
Course
Heinemann references
Assessment
MZ10 p 393 (8.1)
FT10 8.1 Short answer
Circles
They recognise the features of circles (centre, radius, diameter,
Parts of circles
chord, arc, semi-circle, circumference, segment, sector and tangent)
FT10 8.1 Multiple
and use associated angle properties.
choice
FT10 8.1 Applications
and analysis
They recognise the features of circles (centre, radius, diameter,
Arc length
MZ10 p 405 (8.3)
chord, arc, semi-circle, circumference, segment, sector and tangent)
FT10 8.3 Short answer
FT10 8.3 Multiple
and use associated angle properties.
choice
They use degrees and radians as units of measurement for angles and
convert between units of measurement as appropriate.
They use latitude and longitude to locate places on the Earth’s
Lines of latitude and longitude
MZ10 p434 (Investigation)
surface and measure distances between places using great circles.
Drawings
Students represent two- and three-dimensional shapes using lines,
Isometric drawing, elevations and plans
curves, polygons and circles. They make representations using
perspective, isometric drawings, nets and computer-generated
images.
MZ10 p410 (8.4)
FT10 8.4 Short answer
FT10 8.4 Multiple
choice
FT10 8.4 Applications
and analysis
Heinemann Maths Zone 10 VELS Edition
Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd)
Page 81 of 92
VELS refs
Course
Heinemann references
Assessment
They recognise and describe boundaries, surfaces and interiors of
Constructions
MZ10 p419 (8.6)
FT10 8.6 Short answer
common plane and three-dimensional shapes, including cylinders,
FT10 8.6 Multiple
spheres, cones, prisms and polyhedra.
choice
FT10 8.6 Applications
and analysis
Polyhedra
They recognise and describe boundaries, surfaces and interiors of
Polyhedra and Euler’s rule
MZ10 p415 (8.5)
common plane and three-dimensional shapes, including cylinders,
FT10 8.5 Short answer
FT10 8.5 Multiple
spheres, cones, prisms and polyhedra.
choice
Transformations
Students use the conditions for shapes to be congruent or similar.
Translation, reflection and rotation
They apply isometric and similarity transformations of geometric
shapes in the plane. They identify points that are invariant under a
given transformation (for example, the point (2, 0) is invariant under
reflection in the x-axis, so the x-axis intercept of the graph of y = 2x −
4 is also invariant under this transformation). They determine the
effect of changing the scale of one characteristic of two- and threedimensional shapes (for example, side length, area, volume and angle
measure) on related characteristics.
Heinemann Maths Zone 10 VELS Edition
Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd)
MZ10 p427 (8.7); p435
(Maths in Action)
FT10 8.7 Short answer
FT10 8.7 Multiple
choice
Page 82 of 92
Unit 8: Geometry
Level: C
Dimensions: Space
VELS refs
Time: 3 weeks
Course
Heinemann references
Assessment
MZ10 p 393 (8.1)
FT10 8.1 Short answer
Circles
They recognise the features of circles (centre, radius, diameter,
Parts of circles
chord, arc, semi-circle, circumference, segment, sector and tangent)
FT10 8.1 Multiple
and use associated angle properties.
choice
FT10 8.1 Applications
and analysis
They recognise the features of circles (centre, radius, diameter,
Circle theorems
chord, arc, semi-circle, circumference, segment, sector and tangent)
MZ10 p398 (8.2); p399
(Investigation)
and use associated angle properties.
FT10 8.2 Short answer
FT10 8.2 Multiple
choice
FT10 8.2 Applications
and analysis
They recognise the features of circles (centre, radius, diameter,
Arc length
chord, arc, semi-circle, circumference, segment, sector and tangent)
and use associated angle properties.
MZ10 p 405 (8.3)
FT10 8.3 Short answer
FT10 8.3 Multiple
choice
FT10 8.3 Applications
and analysis
Heinemann Maths Zone 10 VELS Edition
Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd)
Page 83 of 92
VELS refs
Course
Heinemann references
They use degrees and radians as units of measurement for angles and
Investigating 
MZ10 p424 (Graphics
convert between units of measurement as appropriate.
Assessment
calculator investigation)
They select and use technology in various combinations to assist in
mathematical inquiry, to manipulate and represent data, to analyse
functions and carry out symbolic manipulation. They use geometry
software or graphics calculators to create geometric objects and
transform them, taking into account invariance under transformation.
They use latitude and longitude to locate places on the Earth’s
Lines of latitude and longitude
MZ10 p434 (Investigation)
surface and measure distances between places using great circles.
Polyhedra
They recognise and describe boundaries, surfaces and interiors of
Polyhedra and Euler’s rule
common plane and three-dimensional shapes, including cylinders,
MZ10 p415 (8.5)
FT10 8.5 Short answer
FT10 8.5 Multiple
spheres, cones, prisms and polyhedra.
choice
FT10 8.5 Applications
and analysis
Transformations
Heinemann Maths Zone 10 VELS Edition
Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd)
Page 84 of 92
VELS refs
Course
Heinemann references
Assessment
Students use the conditions for shapes to be congruent or similar.
Translation, reflection and rotation
MZ10 p427 (8.7); p435
FT10 8.7 Short answer
They apply isometric and similarity transformations of geometric
shapes in the plane. They identify points that are invariant under a
given transformation (for example, the point (2, 0) is invariant under
reflection in the x-axis, so the x-axis intercept of the graph of y = 2x −
4 is also invariant under this transformation). They determine the
effect of changing the scale of one characteristic of two- and threedimensional shapes (for example, side length, area, volume and angle
measure) on related characteristics.
Heinemann Maths Zone 10 VELS Edition
Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd)
(Maths in Action)
FT10 8.7 Multiple
choice
FT10 8.7 Applications
and analysis
Page 85 of 92
Unit 9: Quadratics, variations, graphs
Level: B
VELS refs
Dimensions: Structure
Time: 3 weeks
Course
Heinemann references
Assessment
MZ10 p447 (9.1)
FT10 9.1 Short answer
Quadratics
They solve equations of the form f(x) = k, where k is a real constant
Solving quadratic equations
(for example, x(x + 5) = 100) and simultaneous linear equations in
FT10 9.1 Multiple
two variables (for example {2x − 3y = −4 and 5x + 6y = 27}) using
choice
algebraic, numerical (systematic guess, check and refine or bisection)
and graphical methods.
They solve equations of the form f(x) = k, where k is a real constant
Using the quadratic formula
MZ10 p452 (9.2)
(for example, x(x + 5) = 100) and simultaneous linear equations in
FT10 9.2 Short answer
FT10 9.2 Multiple
two variables (for example {2x − 3y = −4 and 5x + 6y = 27}) using
choice
algebraic, numerical (systematic guess, check and refine or bisection)
and graphical methods.
Sketching quadratic graphs
They recognise and explain the roles of the relevant constants in the
Sketching parabolas in turning point form
relationships f(x) = ax + c, with reference to gradient and y-axis
2
x
intercept, f(x) = a(x + b) + c and f(x) = ca .
Students identify and represent linear, quadratic and exponential
functions by table, rule and graph (all four quadrants of the Cartesian
coordinate system) with consideration of independent and dependent
variables, domain and range.
Heinemann Maths Zone 10 VELS Edition
Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd)
MZ10 p458 (9.3)
FT10 9.3 Short answer
FT10 9.3 Multiple
choice
FT10 9.3 Applications
and analysis
Page 86 of 92
VELS refs
Course
Heinemann references
Assessment
They recognise and explain the roles of the relevant constants in the
Sketching parabolas showing x- and y-intercepts
MZ10 p465 (9.4 Q 1–6)
FT10 9.4 Short answer
relationships f(x) = ax + c, with reference to gradient and y-axis
FT10 9.4 Multiple
intercept, f(x) = a(x + b)2 + c and f(x) = cax.
choice
Students identify and represent linear, quadratic and exponential
functions by table, rule and graph (all four quadrants of the Cartesian
coordinate system) with consideration of independent and dependent
variables, domain and range.
Variation
Students apply the algebraic properties (closure, associative,
Direct variation
commutative, identity, inverse and distributive) to computation with
number, to rearrange formulae, rearrange and simplify algebraic
expressions involving real variables. They verify the equivalence or
otherwise of algebraic expressions (linear, square, cube, exponent,
and reciprocal, (for example, 4x − 8 = 2(2x − 4) = 4(x − 2); (2a − 3)2
= 4a2 − 12a + 9; (3w)3 = 27w3;
;
).
They use and interpret the functions in modelling a range of contexts.
Heinemann Maths Zone 10 VELS Edition
Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd)
MZ10 p479 (9.6 Q 1– 10)
FT10 9.6 Short answer
FT10 9.6 Multiple
choice
Page 87 of 92
VELS refs
Course
Heinemann references
Assessment
Students apply the algebraic properties (closure, associative,
Partial variation
MZ10 p490 (9.7 Q1–6)
FT10 9.7 Short answer
commutative, identity, inverse and distributive) to computation with
FT10 9.7 Multiple
number, to rearrange formulae, rearrange and simplify algebraic
choice
expressions involving real variables. They verify the equivalence or
otherwise of algebraic expressions (linear, square, cube, exponent,
and reciprocal, (for example, 4x − 8 = 2(2x − 4) = 4(x − 2); (2a − 3)2
= 4a2 − 12a + 9; (3w)3 = 27w3;
;
).
They use and interpret the functions in modelling a range of contexts.
Students apply the algebraic properties (closure, associative,
Inverse variation
commutative, identity, inverse and distributive) to computation with
choice
expressions involving real variables. They verify the equivalence or
otherwise of algebraic expressions (linear, square, cube, exponent,
and reciprocal, (for example, 4x − 8 = 2(2x − 4) = 4(x − 2); (2a − 3)2
;
).
They use and interpret the functions in modelling a range of contexts.
Relationships
Heinemann Maths Zone 10 VELS Edition
FT10 9.8 Short answer
FT10 9.8 Multiple
number, to rearrange formulae, rearrange and simplify algebraic
= 4a2 − 12a + 9; (3w)3 = 27w3;
MZ10 p494 (9.8 Q1–5)
Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd)
Page 88 of 92
VELS refs
Course
Heinemann references
Assessment
Students identify and represent linear, quadratic and exponential
Identifying relationships between variables using
MZ10 p501 (9.9 Q1–6)
FT10 9.9 Short answer
functions by table, rule and graph (all four quadrants of the Cartesian
finite difference tables
coordinate system) with consideration of independent and dependent
variables, domain and range. They distinguish between these types of
functions by testing for constant first difference, constant second
difference or constant ratio between consecutive terms (for example,
to distinguish between the functions described by the sets of ordered
pairs {(1, 2), (2, 4), (3, 6), (4, 8) …}; {(1, 2), (2, 4), (3, 8), (4, 14)
…}; and {(1, 2), (2, 4), (3, 8), (4, 16) …}). They use and interpret
the functions in modelling a range of contexts.
Heinemann Maths Zone 10 VELS Edition
Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd)
FT10 9.9 Multiple
choice
Page 89 of 92
Unit 9: Equations and relationships
Level: C
VELS refs
Dimensions: Algebra
Time: 4 weeks
Course
Heinemann references
Assessment
MZ10 p447 (9.1)
FT10 9.1 Short answer
Quadratics
They solve equations of the form f(x) = k, where k is a real constant
Solving quadratic equations
(for example, x(x + 5) = 100) and simultaneous linear equations in
FT10 9.1 Multiple
two variables (for example, {2x − 3y = −4 and 5x + 6y = 27}) using
choice
algebraic, numerical (systematic guess, check and refine or bisection)
FT10 9.1 Applications
and graphical methods.
and analysis
They solve equations of the form f(x) = k, where k is a real constant
Using the quadratic formula
MZ10 p452 (9.2)
(for example, x(x + 5) = 100) and simultaneous linear equations in
FT10 9.2 Short answer
FT10 9.2 Multiple
two variables (for example, {2x − 3y = −4 and 5x + 6y = 27}) using
choice
algebraic, numerical (systematic guess, check and refine or bisection)
FT10 9.2 Applications
and graphical methods.
and analysis
Sketching quadratic graphs
They recognise and explain the roles of the relevant constants in the
Sketching parabolas in turning point form
relationships f(x) = ax + c, with reference to gradient and y-axis
2
x
intercept, f(x) = a(x + b) + c and f(x) = ca .
Students identify and represent linear, quadratic and exponential
functions by table, rule and graph (all four quadrants of the Cartesian
coordinate system) with consideration of independent and dependent
variables, domain and range.
Heinemann Maths Zone 10 VELS Edition
Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd)
MZ10 p458 (9.3)
FT10 9.3 Short answer
FT10 9.3 Multiple
choice
FT10 9.3 Applications
and analysis
Page 90 of 92
VELS refs
Course
Heinemann references
Assessment
They recognise and explain the roles of the relevant constants in the
Sketching parabolas showing x- and y-intercepts
MZ10 p465 (9.4); p463
FT10 9.4 Short answer
relationships f(x) = ax + c, with reference to gradient and y-axis
(Graphics calculator
intercept, f(x) = a(x + b)2 + c and f(x) = cax.
investigation)
Students identify and represent linear, quadratic and exponential
FT10 9.4 Multiple
choice
FT10 9.4 Applications
functions by table, rule and graph (all four quadrants of the Cartesian
and analysis
coordinate system) with consideration of independent and dependent
variables, domain and range.
Students identify and represent linear, quadratic and exponential
Solving quadratic inequations using graphs
functions by table, rule and graph (all four quadrants of the Cartesian
(Problem solving)
coordinate system) with consideration of independent and dependent
FT10 9.5 Multiple
FT10 9.5 Applications
Students apply the algebraic properties (closure, associative,
and analysis
commutative, identity, inverse and distributive) to computation with
number, to rearrange formulae, rearrange and simplify algebraic
expressions involving real variables. They verify the equivalence or
otherwise of algebraic expressions (linear, square, cube, exponent,
and reciprocal, (for example, 4x − 8 = 2(2x − 4) = 4(x − 2); (2a − 3)2
;
).
Variation
Heinemann Maths Zone 10 VELS Edition
FT10 9.5 Short answer
choice
variables, domain and range.
= 4a2 − 12a + 9; (3w)3 = 27w3;
MZ10 p474 (9.5); p479
Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd)
Page 91 of 92
VELS refs
Course
Heinemann references
Assessment
Students apply the algebraic properties (closure, associative,
Direct variation
MZ10 p479 (9.6); p487
FT10 9.6 Short answer
commutative, identity, inverse and distributive) to computation with
(Investigation); p488 (Maths
number, to rearrange formulae, rearrange and simplify algebraic
in Action)
expressions involving real variables. They verify the equivalence or
= 4a2 − 12a + 9; (3w)3 = 27w3;
;
choice
FT10 9.6 Applications
otherwise of algebraic expressions (linear, square, cube, exponent,
and reciprocal, (for example, 4x − 8 = 2(2x − 4) = 4(x − 2); (2a − 3)
FT10 9.6 Multiple
and analysis
2
).
They use and interpret the functions in modelling a range of contexts.
Students apply the algebraic properties (closure, associative,
Partial variation
commutative, identity, inverse and distributive) to computation with
number, to rearrange formulae, rearrange and simplify algebraic
expressions involving real variables. They verify the equivalence or
otherwise of algebraic expressions (linear, square, cube, exponent,
and reciprocal, (for example, 4x − 8 = 2(2x − 4) = 4(x − 2); (2a − 3)2
= 4a2 − 12a + 9; (3w)3 = 27w3;
;
).
They use and interpret the functions in modelling a range of contexts
Heinemann Maths Zone 10 VELS Edition
Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd)
MZ10 p490 (9.7)
FT10 9.7 Short answer
FT10 9.7 Multiple
choice
FT10 9.7 Applications
and analysis
Page 92 of 92
VELS refs
Course
Heinemann references
Assessment
Students apply the algebraic properties (closure, associative,
Inverse variation
MZ10 p494 (9.8)
MZ10 p 499 (VELS
commutative, identity, inverse and distributive) to computation with
Design task)
number, to rearrange formulae, rearrange and simplify algebraic
FT10 9.8 Short answer
expressions involving real variables. They verify the equivalence or
FT10 9.8 Multiple
otherwise of algebraic expressions (linear, square, cube, exponent,
choice
and reciprocal, (for example, 4x − 8 = 2(2x − 4) = 4(x − 2); (2a − 3)2
FT10 9.8 Applications
and analysis
= 4a2 − 12a + 9; (3w)3 = 27w3;
;
).
They use and interpret the functions in modelling a range of contexts.
Relationships
Students identify and represent linear, quadratic and exponential
Identifying relationships between variables using
functions by table, rule and graph (all four quadrants of the Cartesian
finite difference tables
coordinate system) with consideration of independent and dependent
variables, domain and range. They distinguish between these types of
functions by testing for constant first difference, constant second
difference or constant ratio between consecutive terms (for example,
to distinguish between the functions described by the sets of ordered
pairs {(1, 2), (2, 4), (3, 6), (4, 8) …}; {(1, 2), (2, 4), (3, 8), (4, 14)
…}; and {(1, 2), (2, 4), (3, 8), (4, 16) …}). They use and interpret
the functions in modelling a range of contexts.
Heinemann Maths Zone 10 VELS Edition
Copyright © Pearson Australia (a division of Pearson Australia Group Pty Ltd)
MZ10 p501 (9.9)
FT10 9.9 Short answer
FT10 9.9 Multiple
choice
FT10 9.9 Applications
and analysis