HIGHFIELDS SCHOOL
OVERVIEW - SCHEME OF WORK 2015-2018
SUBJECT: GCSE HIGHER MATHEMATICS
AUTUMN TERM - YEAR 10
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Round numbers to a given number of decimal
places and significant figures
Estimate powers and roots
Find prime factors, lowest common multiples
and highest common factors, include Venn
diagrams
Express numbers using standard form
Use an extended range of calculator functions,
including +, -, x, ÷, memory, xv, x1/v and brackets
Use index laws for multiplication and division of
integer, fractional and negative powers
Multiply and divide fractions
Use fractions in ratio problems
Find a fraction or percentage of a quantity
Increase and decrease by a percentage (also
using a multiplier)
Solve problems involving repeated percentage
change
Use compo
Und interest
Find the upper and lower bounds of
calculations involving measurements e.g area,
volume or substituting in formulae
Problem solving with algebra
ASSESSMENT AUTUMN 1: Past GCSE exam questions
based on the above topics
EXAMINATION BOARD: EDEXCEL
SPRING TERM - YEAR 10
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Calculate and simplify with surds
Rationalise the denominator
Understand and use Pythagoras’ theorem in 2D, then in 3-D problems
Understand the language of planes and
recognise the diagonals of a cuboid
Use the basic congruence criteria for triangles
(SSS, SAS, ASA, RHS)
Identify, describe and construct congruent and
similar shapes
Use the trigonometric ratios to solve 2-D and 3-D
problems
Calculating the missing angle sing trigonometry
Solving problems using trigonometry
Know the exact values for sinx and cosx for x =
0o, 30o, 45o, 60o, and 90o
know the exact values of tanx for x = 0o, 30o, 45o,
60o
use the sine and cosine rules to solve 2-D and 3D problems
SUMMER TERM - YEAR 10
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ASSESSMENT SPRING 1: Past GCSE exam questions
based on the above topics
Manipulate and simplify algebraic expressions,
by multiplying terms together, expanding
brackets and collecting like terms
Factorise a linear expression
Expand a factorise quadratic expressions
including both forms x2 + ax + b and ax2 + bx +
c
Expand products of two or more binomials
Simplify algebraic fractions using factorising
Solve a quadratic equation by factorisation,
quadratic formula or completing the square
Draw and read values from a quadratic graph
Recognise and calculate the significant points of
a quadratic graph
Record, describe and analyse the frequency of
outcomes of probability experiments using
tables and frequency trees
List all outcomes for single events and give
probabilities as fractions (or
Draw sample space diagrams and use them to
work out probabilities
Use laws of probability
Use a tree diagram to calculate probabilities
ASSESSMENT SUMMER 1: Past GCSE exam questions
based on the above topics
HIGHFIELDS SCHOOL
OVERVIEW - SCHEME OF WORK 2015-2018
SUBJECT: GCSE HIGHER MATHEMATICS
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Give reasons for angle calculations
Understand and use the angle properties of parallel
lines
Find interior and exterior angles in polygons
Construct triangles
Use Loci
Apply and prove the standard circle theorems
concerning angles, radii, tangents and chords, and
use them to prove related results.
Understand and use standard mathematical
formulae and rearrange formula to change the
subject
Produce, interpret and draw conclusions for a wide
range of graphs, charts and diagrams
These include, composite bar charts, comparative
and dual bar charts, pie charts, stem and leaf
diagrams, scatter graphs, line graphs, frequency
polygons, box plots, cumulative frequency diagrams
and histograms
Explain and isolated point on a scatter graph
Draw and use a line of best fit, predict values of one
variable given values of the other variable
Understand that correlation does not imply causality
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ASSESSMENT AUTUMN 2: Past GCSE exam questions
based on the above topics
www.hswv.co.uk
EXAMINATION BOARD: EDEXCEL
Finding an expression for the nth term of linear
and quadratic sequences
Find the coordinates of the midpoint of a line
segment
Plot and draw graphs of straight lines with
equations of the form y=mx+c
Recognise that equations of the form y=mx+c
correspond to straight line graphs
Find the gradient of a straight line from a graph
and also from a given equation
Find the intersection point of two straight line
graphs
Draw quadratic graphs
Recognise and calculate the significant points
of a quadratic graph
Draw simple cubic functions
Draw the reciprocal graph of y = 1/k
Exponential functions y = kx
Find the exact solutions of two simultaneous
equations in two unknowns
Use substitution method to solve simultaneous
equations where one is linear and the other is
quadratic in one unknown or in the form x2 + y2
= r2
Describe and transform 2-D shapes using single
or combined rotations, reflections and
translations and enlargement (including
negative or fractional scale factor)
ASSESSMENT SPRING 2 (SCHOOL EXAM): GCSE past
paper
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Area and circumference of circles
Volume and surface area of prisms and cylinders
Divide a quantity in a given ratio
Solve a ratio problem in a context
Fractions in ratio problems
Recognise and solve problems using direct
proportion
Calculate an unknown quantity from quantities
that vary in direct and inverse proportion.
Solve linear inequalities
Apply
to
the
graph
of 𝑦𝑦 = 𝑓𝑓(𝑥𝑥) the
transformations
𝑦𝑦 = 𝑓𝑓(𝑥𝑥) + 𝑎𝑎, 𝑦𝑦 = 𝑓𝑓(𝑎𝑎𝑎𝑎), 𝑦𝑦 =
𝑓𝑓(𝑥𝑥 + 𝑎𝑎), 𝑦𝑦 = 𝑎𝑎𝑎𝑎(𝑥𝑥) for linear, quadratic, sine and
cosine functions𝑓𝑓(𝑥𝑥).
Recognise, sketch and interpret graphs of the
trigonometric functions (with arguments in
degrees) y = sinx, y = cosx and y = tanx
Sketch translations and reflections of these
functions
Know the exact values for sinx and cosx for x =
0°, 30°, 45°, 60° and 90°
Know the exact values of tanx for x = 0°, 30°, 45°,
60°
ASSESSMENT SUMMER 1: Past GCSE exam questions
based on the above topics
HIGHFIELDS SCHOOL
OVERVIEW - SCHEME OF WORK 2015-2018
SUBJECT: GCSE HIGHER MATHEMATICS
AUTUMN TERM - YEAR 11
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Use elimination or substitution to solve simultaneous
equations
Use substitution method to solve simultaneous
equations where one is linear and the other is
quadratic
Change the subject of a formula when the new
subject occurs twice in the formula.
Apply to the graph of 𝑦𝑦 = 𝑓𝑓(𝑥𝑥)the transformations
𝑦𝑦 = 𝑓𝑓(𝑥𝑥) + 𝑎𝑎, 𝑦𝑦 = 𝑓𝑓(𝑎𝑎𝑎𝑎), 𝑦𝑦 = 𝑓𝑓(𝑥𝑥 + 𝑎𝑎), 𝑦𝑦 = 𝑎𝑎𝑎𝑎(𝑥𝑥) for
linear, quadratic, sine and cosine functions𝑓𝑓(𝑥𝑥).
Find missing lengths and angles using the Sine Rule
and Cosine Rule
ASSESSMENT AUTUMN 1: EDEXCEL GCSE past paper
Use systematic trial and improvement to solve
quadratic and cubic equations
• Write large & small numbers in standard form and
convert between ordinary and standard form
• Interpret a calculator display
• Calculate with standard form either with or without
a calculator
• Fractions, Percentages, Decimals
• Express recurring decimals as fractions.
• Find missing angles on diagrams
• Circle theorems
• Understand and use vector notation
• Use laws of probability (Probabilities add to 1
/Addition and multiplication rules)
• Draw tree diagrams based on given information
• Use a tree diagram to calculate probabilities
YEAR 11 SCHOOL EXAMS: GCSE PAST PAPER
www.hswv.co.uk
EXAMINATION BOARD: EDEXCEL
SPRING TERM - YEAR 11
Find the upper and lower bounds of calculations
Algebraic proof
Convert between units of measure and know
rough metric equivalents of pounds, feet, miles,
pints and gallons.
• Understand and use compound measures,
including speed and density
• Understand and use bearings
• Volume and surface area of pyramids, cones,
spheres and frustums.
• Solve complex problems involving compound 3D shapes
• Calculate an unknown quantity from quantities
that vary in direct and inverse proportion.
ASSESSMENT SPRING 1: EDEXCEL GCSE past paper
SUMMER TERM - YEAR 11
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REVISION
REVISION AND FINAL EXAMINATIONS