Pearson
Edexcel Level 1/Level 2
GCSE (9 – 1) in
Mathematics (1MA1)
Higher tier diagnostic document
For first teaching from September 2015
2
Pearson Edexcel Level 1/Level 2 GCSE (9 – 1) in Mathematics
Higher tier diagnostic document – Issue 1 April 2016 © Pearson Education Limited 2016
Contents
Introduction
5
Higher course overview
6
Higher units
7
4
Pearson Edexcel Level 1/Level 2 GCSE (9 – 1) in Mathematics
Higher tier diagnostic document – Issue 1 April 2016 © Pearson Education Limited 2016
Introduction
This Higher tier diagnostic document is intended to support students in accessing the Higher tier of the new GCSE
(9–1) Mathematics specification.
This document lists the units in the Higher tier scheme of work, suggests questions to establish whether a student has
the required prior knowledge, and provides a mapping of references to the Foundation scheme of work (and
occasionally the Access to Foundation tier scheme of work) should the student need to refresh their understanding or
develop a particular skill. Teachers can then turn to the relevant unit(s) in the Foundation scheme of work for additional
support, including objectives, possible success criteria, opportunities for reasoning and problem-solving, and common
misconceptions.
For later Higher tier units, prior knowledge has sometimes not been covered in the Foundation scheme of work. In these
instances, a reference to an earlier Higher tier unit is provided, along with diagnostic questions to check that this
knowledge has been acquired.
Our free support for the GCSE Mathematics specification (1MA1) can be found on the Edexcel mathematics website
(http://qualifications.pearson.com/en/home.html) and on the Emporium (www.edexcelmaths.com).
Pearson Edexcel Level 1/Level 2 GCSE (9 – 1) in Mathematics
Higher tier diagnostic document – Issue 1 April 2016 © Pearson Education Limited 2016
5
Unit
1
2
3
4
5
6
7
8
9
Title
a
Calculations, checking and rounding
b
Indices, roots, reciprocals and hierarchy of operations
c
Factors, multiples, primes, standard form and surds
a
Algebra: the basics, setting up, rearranging and solving equations
b
Sequences
a
Averages and range
b
Representing and interpreting data and scatter graphs
a
Fractions and percentages
b
Ratio and proportion
a
Polygons, angles and parallel lines
b
Pythagoras’ Theorem and trigonometry
a
Graphs: the basics and real-life graphs
b
Linear graphs and coordinate geometry
c
Quadratic, cubic and other graphs
a
Perimeter, area and circles
b
3D forms and volume, cylinders, cones and spheres
c
Accuracy and bounds
a
Transformations
b
Constructions, loci and bearings
a
Solving quadratic and simultaneous equations
b
Inequalities
10
Probability
11
Multiplicative reasoning
12
Similarity and congruence in 2D and 3D
13
14
a
Graphs of trigonometric functions
b
Further trigonometry
a
Collecting data
b
Cumulative frequency, box plots and histograms
Quadratics, expanding more than two brackets, sketching graphs,
graphs of circles, cubes and quadratics
15
16
a
Circle theorems
b
Circle geometry
17
Changing the subject of formulae (more complex), algebraic
fractions, solving equations arising from algebraic fractions,
rationalising surds, proof
18
Vectors and geometric proof
19
6
a
Reciprocal and exponential graphs; Gradient and area under graphs
b
Direct and inverse proportion
Pearson Edexcel Level 1/Level 2 GCSE (9 – 1) in Mathematics
Higher tier diagnostic document – Issue 1 April 2016 © Pearson Education Limited 20156
Foundation tier
UNIT 1: Powers, decimals, HCF and LCM, positive and negative, roots,
rounding, reciprocals, standard form, indices and surds
Return to Overview
SUB-UNITS
a
Calculations, checking and rounding
b
Indices, roots, reciprocals and hierarchy of operations
c
Factors, multiples, primes, standard form and surds
PRIOR KNOWLEDGE
Students will be able to:

understand place value,
order integers and
decimals and use the four
operations
Possible diagnostic
questions
Given the digits 2, 5, 7 and
9, make all the possible
three-digit number with one
decimal place and put them
in order.
Students will need to work on the
objectives covered in:
Foundation Unit 1: Number, powers,
decimals, HCF and LCM, roots and
rounding
Addition, subtraction,
multiplication and division
questions with up to three
digits and one decimal place

find integer complements
to 10 and to 100
46 +
= 100
Foundation Unit 1a: Integers and
place value
See also Access Unit 5: Addition and
subtraction 2

recall multiplication facts
to 10 × 10
Quick-fire multiplication and
division questions. e.g.
6×7=
8×9=
35 ÷ 5 =
132 ÷ 12 =
Foundation Unit 1a: Integers and
place value

multiply and divide by 10,
100 and 1000
Multiply 24.75 by 10, 100,
1000
Foundation Unit 1a: Integers and
place value
Divide 72430 by 10, 100,
1000.

recall and identify
squares, square roots,
cubes and cube roots
Which of these numbers is a
square number? Which is a
cube? Explain your answers.
2, 5, 8, 12, 16, 20, 28
Foundation Unit 1c: Indices, powers
and roots
Pearson Edexcel Level 1/Level 2 GCSE (9 – 1) in Mathematics
Higher tier diagnostic document – Issue 1 April 2016 © Pearson Education Limited 2016
7
Foundation tier
UNIT 2: Expressions, substituting into simple formulae, expanding and
factorising, equations, sequences and inequalities, simple proof
Return to Overview
SUB-UNITS
a
Algebra: the basics, setting up, rearranging and solving equations
b
Sequences
PRIOR KNOWLEDGE
Students will be able to:



use negative numbers
with the four operations,
recall and use the
hierarchy of operations
and understand inverse
operations
Possible diagnostic
questions
4 – (–6) =
–6 × 3 =
18 ÷
= –3
Foundation Unit 1c: Indices, powers
and roots
4 × 7 – 16 ÷ 2 =
deal with decimals and
negatives on a calculator
Use a calculator to calculate:
use index laws
numerically
43 × 4 5 =
8
Students will need to work on the
objectives covered in:
Foundation Unit 1a: Integers and
place value
–6.5 × –4.2 =
67 ÷ 6 2 =
Foundation Unit 1c: Indices, powers
and roots
Foundation Unit 1c: Indices, powers
and roots
Pearson Edexcel Level 1/Level 2 GCSE (9 – 1) in Mathematics
Higher tier diagnostic document – Issue 1 April 2016 © Pearson Education Limited 20156
Foundation tier
UNIT 3: Averages and range, collecting data, representing data
Return to Overview
SUB-UNITS
a
Averages and range
b
Representing and interpreting data and scatter graphs
PRIOR KNOWLEDGE
Students will be able to:


read scales on graphs,
draw circles, measure
angles and plot
coordinates in the first
quadrant
use tally charts
Possible diagnostic
questions
On cm-squared paper, draw
axes for x and y from 0 to 8.
Plot these points:
(1, 0), (2, 6), (7, 8).
Join to make a triangle.
Measure the angles.
Students will need to work on the
objectives covered in:
Foundation Unit 3a: Tables, charts
and graphs
Foundation Unit 3b: Pie charts
Foundation Unit 6a: Properties of
shapes, parallel lines and angle facts
On the same coordinate grid,
use a pair of compasses to
draw a circle centre (5, 4),
radius 4 cm. What are the
coordinates of the point
where the circle touches the
x-axis?
Foundation Unit 15a: Plans and
elevations
What number does this
represent?
Foundation Unit 3: Drawing and
interpreting graphs, tables and charts
Write 24 in tallies.
See also Access Unit 22: Data
handling 2

use inequality notation
Take a pair of two-digit
numbers and use < and >
correctly.
e.g. 46 and 78 or 62 and 35
Foundation Unit 1a: Integers and
place value

find the midpoint of two
numbers
What number is in the middle
of 3 and 9? 42 and 50?
Foundation Unit 7: Statistics,
sampling and the averages
See also Access Unit 22: Data
handling 2
Pearson Edexcel Level 1/Level 2 GCSE (9 – 1) in Mathematics
Higher tier diagnostic document – Issue 1 April 2016 © Pearson Education Limited 2016
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Foundation tier
UNIT 4: Fractions, percentages, ratio and proportion
Return to Overview
SUB-UNITS
a
Fractions and percentages
b
Ratio and proportion
PRIOR KNOWLEDGE
Students will be able to:

use the four operations of
number

find common factors

understand fractions as
being ‘parts of a whole’
Possible diagnostic
questions
See questions for Unit 1
Students will need to work on the
objectives covered in:
Foundation Unit 1a: Integers and
place value
What factor is common to 8
and 12? To 14 and 35?
Foundation Unit 1d: Factors,
multiples and primes
Shade
5
of
8
Foundation Unit 4a: Fractions,
decimals and percentages
See also Access Unit 11: Fractions,
decimals and percentages 2
Shade

understand percentage as
‘number of parts per
hundred’ and recognise
that percentages are used
in everyday life
2
of
3
1
the questions
2
1
in a test correct. What is
as
2
a percentage?
Shannon got
Foundation Unit 4b: Percentages
In a sale, prices are reduced
by 10%. What is 10% as a
fraction?
10
Pearson Edexcel Level 1/Level 2 GCSE (9 – 1) in Mathematics
Higher tier diagnostic document – Issue 1 April 2016 © Pearson Education Limited 20156
Foundation tier
UNIT 5: Angles, polygons, parallel lines; Right-angled triangles: Pythagoras
and trigonometry
Return to Overview
SUB-UNITS
a
Polygons, angles and parallel lines
b
Pythagoras’ Theorem and trigonometry
PRIOR KNOWLEDGE
Students will be able to:
Possible diagnostic
questions

rearrange simple
formulae and equations
If
Students will need to work on the
objectives covered in:
Foundation Unit 2: Expressions,
substituting into simple formulae,
expanding and factorising

recall basic angle facts
On squared paper, draw a
right-angled triangle with one
acute and one obtuse angle.
Foundation Unit 6a: Properties of
shapes, parallel lines and angle facts
6b - G3, G6
t = 6h – 3, write an
expression for h
Find the size of the angles
marked x and y.
x
30°
y

understand that fractions
are more accurate in
calculations than rounded
percentage or decimal
equivalents
45°
1
≈ 0.3
3
Which of the following give
the most accurate answer?
1
2
× 50 = 16
3
3
Foundation Unit 4a: Fractions,
decimals and percentages
0.3 × 50 = 15
Pearson Edexcel Level 1/Level 2 GCSE (9 – 1) in Mathematics
Higher tier diagnostic document – Issue 1 April 2016 © Pearson Education Limited 2016
11
Foundation tier
UNIT 6: Real-life and algebraic linear graphs, quadratic and cubic graphs, the
equation of a circle, plus rates of change and area under graphs made from
straight lines
Return to Overview
SUB-UNITS
a
Graphs: the basics and real-life graphs
b
Linear graphs and coordinate geometry
c
Quadratic, cubic and other graphs
PRIOR KNOWLEDGE
Students will be able to:
Possible diagnostic
questions

identify coordinates of
given points in the first
quadrant or all four
quadrants
Draw axes for values of
use Pythagoras’ Theorem
Find the length of the
unknown side.

x and
Students will need to work on the
objectives covered in:
Foundation Unit 9a: Real-life graphs
y from –5 to +5.
Plot the points (2, 3), (–3, 2)
and (–2, –3), which form
three corners of a square.
What are the coordinates of
the fourth corner?
5 cm
x cm
Foundation Unit 12: Right-angled
triangles: Pythagoras and
trigonometry
12 cm

calculate the area of
compound shapes
Find the area of this shape.
3 cm
Foundation Unit 8: Perimeter, area
and volume
6 cm
7 cm
12
Pearson Edexcel Level 1/Level 2 GCSE (9 – 1) in Mathematics
Higher tier diagnostic document – Issue 1 April 2016 © Pearson Education Limited 20156
Foundation tier
Students will be able to:

use and draw conversion
graphs for common units
Possible diagnostic
questions
5 miles ≈ 8 kilometres
Draw axes with scales from 0
to 80 km on the horizontal
axis and 0 to 50 miles on the
vertical axis. Plot a line to
show the relationship
between miles and
kilometres.
Students will need to work on the
objectives covered in:
Foundation Unit 9a: Real-life graphs
Estimate 20 km in miles.
Estimate 40 m in kilometres.

use function machines
and inverse operations
Find
y when x = 3.
x → ×2 → +5 = y
Foundation Unit 1a: Integers and
place value
Find
Foundation Unit 5a: Equations and
inequalities
x when y = 11.
x → ×3 → –4 = y
Pearson Edexcel Level 1/Level 2 GCSE (9 – 1) in Mathematics
Higher tier diagnostic document – Issue 1 April 2016 © Pearson Education Limited 2016
13
Foundation tier
UNIT 7: Perimeter, area and volume, plane shapes and prisms, circles,
cylinders, spheres, cones; Accuracy and bounds
Return to Overview
SUB-UNITS
a
Perimeter, area and circles
b
3D forms and volume, cylinders, cones and spheres
Accuracy and bounds
c
PRIOR KNOWLEDGE
Students will be able to:

name and identify the
properties of 3D forms
Possible diagnostic
questions
Sketch a cuboid, a cylinder
and a square-based pyramid.
Students will need to work on the
objectives covered in:
Foundation Unit 15a: Plans and
elevations
How many faces does each
shape have? How many
vertices? How many edges?

find perimeter and area
by measuring lengths of
sides
Measure the sides of this
rectangle. Find its perimeter
and area.

substitute numbers into
an equation and give
answers to an appropriate
degree of accuracy
Use the formula
A = πr2 to
find the area of this circle.
Give your answer to an
appropriate degree of
accuracy.
Foundation Unit 8: Perimeter, area
and volume
Foundation Unit 5a: Equations and
inequalities
Foundation Unit 1b: Decimals
1.7 cm
14
Pearson Edexcel Level 1/Level 2 GCSE (9 – 1) in Mathematics
Higher tier diagnostic document – Issue 1 April 2016 © Pearson Education Limited 20156
Foundation tier
Students will be able to:

understand the various
metric units
Possible diagnostic
questions
Match each item to the most
appropriate unit you could
use to measure it.
mm
capacity of an egg cup
cm
capacity of a bath
m
length of a pencil
km
diameter of a coin
g
mass of a horse
kg
journey from London
to Edinburgh
ml
mass of a mouse
l
length of a room
Students will need to work on the
objectives covered in:
Foundation Unit 8: Perimeter, area
and volume
Pearson Edexcel Level 1/Level 2 GCSE (9 – 1) in Mathematics
Higher tier diagnostic document – Issue 1 April 2016 © Pearson Education Limited 2016
15
Foundation tier
UNIT 8: Transformations; Constructions: triangles, nets, plan and elevation,
loci, scale drawings and bearings
Return to Overview
SUB-UNITS
a
Transformations
b
Constructions, loci and bearings
PRIOR KNOWLEDGE
Students will be able to:
Possible diagnostic
questions
Make different shapes using
two congruent right-angled
triangles by matching equal
sides, and name the shapes
produced. (There are six:
rectangle, kite, two
parallelograms, two isosceles
triangles.)
Students will need to work on the
objectives covered in:
Foundation Unit 6: Angles, polygons
and parallel lines

recognise 2D shapes

plot coordinates in four
quadrants
See questions for Unit 6.
Foundation Unit 9a: Real-life graphs

plot linear equations
parallel to the coordinate
axes
On cm-squared paper, draw
axes for x and y from 0 to 8.
Foundation Unit 9b: Straight-line
graphs
Plot the lines
x = 4 and
y = –2.
16
Pearson Edexcel Level 1/Level 2 GCSE (9 – 1) in Mathematics
Higher tier diagnostic document – Issue 1 April 2016 © Pearson Education Limited 20156
Foundation tier
UNIT 9: Algebra: Solving quadratic equations and inequalities, solving
simultaneous equations algebraically
Return to Overview
SUB-UNITS
a
Solving quadratic and simultaneous equations
b
Inequalities
PRIOR KNOWLEDGE
Students will be able to:

understand the ≥ and ≤
symbols
Possible diagnostic
questions
List the positive integers that
satisfy the inequality
10 >
Students will need to work on the
objectives covered in:
Foundation Unit 1a: Integers and
place value
x ≥ 6.
List the integers that satisfy
the inequality 10 <

y ≤ 14.
substitute into, solve and
rearrange linear
equations
What is the value of

factorise simple quadratic
expressions
Factorise

recognise the equation of
a circle
Which of these equations is
the equation of a circle?
y = x2 + 16
formula, if
h in this
C = 10?
Foundation Unit 2b: Expressions and
substitution into formulae
C = 5h + 20
x2 – x – 6,
Foundation Unit 16a: Quadratic
equations: expanding and factorising
Higher Unit 6c: Quadratic, cubic and
other graphs
x2 + y2 = 52
x + y = 25
Pearson Edexcel Level 1/Level 2 GCSE (9 – 1) in Mathematics
Higher tier diagnostic document – Issue 1 April 2016 © Pearson Education Limited 2016
17
Foundation tier
UNIT 10: Probability
Return to Overview
PRIOR KNOWLEDGE
Students will be able to:

distinguish between
events which are
impossible, unlikely, even
chance, likely, and certain
to occur
Possible diagnostic
questions
Match to events to how likely
they are to occur.
Students will need to work on the
objectives covered in:
Foundation Unit 13: Probability
1 Christmas will fall on 25
December this year.
2 The sun will rise at
midnight tonight.
3 You will score an even
number if you roll an
ordinary, fair dice.
4 The next person you meet
likes chocolate.
5 If you buy a lottery ticket,
you will win the jackpot.
A Impossible
B Unlikely
C Even chance D Likely
E Certain

understand that a
probability is a number
between 0 and 1 and
mark events and/or
probabilities on a
probability scale of 0 to 1
A bag contains 20 marbles.
Tessa picks a marble at
random.
Foundation Unit 13: Probability
Mark these probabilities on
the number line.
P(blue) =
1
2
P(red) =
1
4
1
3
P(pink) =
5
10
P(black) = 0 P(marble) = 1
P(green) =
0


add and multiply fractions
and decimals
express one number as a
fraction of another
number
18
1
4
3
+
=
5
4
2
1
×
=
5
3
0.35 + 1.7 =
0.2 × 0.6 =
What is 15 as a fraction of
25?
Foundation Unit 4a: Fractions,
decimals and percentages
Foundation Unit 4a: Fractions,
decimals and percentages
Pearson Edexcel Level 1/Level 2 GCSE (9 – 1) in Mathematics
Higher tier diagnostic document – Issue 1 April 2016 © Pearson Education Limited 20156
Foundation tier
UNIT 11: Multiplicative reasoning: direct and inverse proportion, relating to
graph form for direct, compound measures, repeated proportional change
Return to Overview
PRIOR KNOWLEDGE
Students will be able to:


find a percentage of an
amount and relate
percentages to decimals
rearrange equations and
use these to solve
problems
Possible diagnostic
questions
What is 45% of 300?
Students will need to work on the
objectives covered in:
Foundation Unit 4b: Fractions and
percentages
What is the decimal
equivalent of 6%?
A square has sides of
d + 3.
A rectangle has sides of
3d + 1 and d – 3. They have
Foundation Unit 5a: Equations and
inequalities
the same length perimeter.
Find d.

understand
speed = distance/time,
density = mass/volume
A car travels 70 miles in 2
hours. What is its average
speed?
Foundation Unit 14: Multiplicative
reasoning
Cobalt has a density of
8.9 gm/cm3. What is the
mass of a cm cube of cobalt?
Pearson Edexcel Level 1/Level 2 GCSE (9 – 1) in Mathematics
Higher tier diagnostic document – Issue 1 April 2016 © Pearson Education Limited 2016
19
Foundation tier
UNIT 12: Similarity and congruence in 2D and 3D
Return to Overview
PRIOR KNOWLEDGE
Students will be able to:

recognise and enlarge
shapes and calculate
scale factors
Possible diagnostic
questions
Enlarge this triangle by a
scale factor of 2.
Students will need to work on the
objectives covered in:
Foundation Unit 10: Transformations
Shape B is an enlargement of
shape A. What is the scale
factor?
B
A

calculate area and
volume in various metric
measures
What is the area of a
rectangle that measures 4.5
m by 6 m?
Foundation Unit 8: Perimeter, area
and volume
What is the volume of a
cuboid that measures 2 mm
by 5 mm by 7 mm?

measure lines and angles
and use compasses, ruler
and protractor to
construct standard
constructions
Use compasses and a ruler to
construct this triangle
accurately.
x
a
40°
y
35°
6 cm
Foundation Unit 3b: Pie charts
Foundation Unit 6a: Properties of
shapes, parallel lines and angle facts
Foundation Unit 8: Perimeter, area
and volume
Foundation Unit 15b: Constructions,
loci and bearings
Measure the length of sides
x
and y and the size of angle a.
20
Pearson Edexcel Level 1/Level 2 GCSE (9 – 1) in Mathematics
Higher tier diagnostic document – Issue 1 April 2016 © Pearson Education Limited 20156
Foundation tier
UNIT 13: Sine and cosine rules,
1
2
ab sin C, trigonometry and Pythagoras’
Theorem in 3D, trigonometric graphs, and accuracy and bounds
Return to Overview
SUB-UNITS
a
Graphs of trigonometric functions
b
Further trigonometry
PRIOR KNOWLEDGE
Students will be able to:

use axes and coordinates
to specify points in all
four quadrants

recall and apply
Pythagoras’ Theorem and
trigonometric ratios
Possible diagnostic
questions
See questions for Unit 6.
Students will need to work on the
objectives covered in:
Foundation Unit 9a: Real-life graphs
See questions for Unit 6.
Foundation Unit 12: Right-angled
triangles: Pythagoras and
trigonometry
Use the cosine rule to find
the value of a.
11 cm
32°
a cm

substitute into formulae
See questions for Unit 9.
Foundation Unit 5a: Equations and
inequalities
Pearson Edexcel Level 1/Level 2 GCSE (9 – 1) in Mathematics
Higher tier diagnostic document – Issue 1 April 2016 © Pearson Education Limited 2016
21
Foundation tier
UNIT 14: Statistics and sampling, cumulative frequency and histograms
Return to Overview
SUB-UNITS
a
Collecting data
b
Cumulative frequency, box plots and histograms
PRIOR KNOWLEDGE
Students will be able to:

understand the different
types of data:
discrete/continuous
Possible diagnostic
questions
Sort the following data into
two groups: discrete and
continuous.
Students will need to work on the
objectives covered in:
Foundation Unit 3a: Tables, charts
and graphs
A Heights of 10 students
B Number of pets owned by
30 students
C Favourite colours of 15
students
D Mass of 20 apples

use inequality notation
See questions for Unit 3.
Foundation Unit 1a: Integers and
place value

multiply a fraction by a
number
What is
2
of 48?
3
Foundation Unit 4a: Fractions,
decimals and percentages

understand the data
handling cycle
Put these four steps in the
correct order.
Foundation Unit 7: Statistics,
sampling and the averages
A Analyse the data.
B Draw conclusions.
C Collect data.
D Specify the problem and
plan an investigation.
22
Pearson Edexcel Level 1/Level 2 GCSE (9 – 1) in Mathematics
Higher tier diagnostic document – Issue 1 April 2016 © Pearson Education Limited 20156
Foundation tier
UNIT 15: Quadratics, expanding more than two brackets, sketching graphs,
graphs of circles, cubes and quadratics
Return to Overview
PRIOR KNOWLEDGE
Students will be able to:

solve quadratics and
linear equations
Possible diagnostic
questions
Solve these equations.
3(x – 6) = 6
x2 – 3x – 28 = 0

solve simultaneous
equations algebraically
Solve these simultaneous
equations:
3x – y = 23
2x +
y=7
Students will need to work on the
objectives covered in:
Foundation Unit 5a: Equations and
inequalities
Foundation Unit 16: Algebra:
quadratic equations and graphs
Foundation Unit 20: Rearranging
equations, graphs of cubic and
reciprocal functions and simultaneous
equations
Pearson Edexcel Level 1/Level 2 GCSE (9 – 1) in Mathematics
Higher tier diagnostic document – Issue 1 April 2016 © Pearson Education Limited 2016
23
Foundation tier
UNIT 16: Circle theorems and circle geometry
Return to Overview
SUB-UNITS
a
Circle theorems
b
Circle geometry
PRIOR KNOWLEDGE
Students will be able to:

draw circles with
compasses

recall the words, centre,
radius, diameter and
circumference
Possible diagnostic
questions
See questions for Unit 3.
Students will need to work on the
objectives covered in:
Foundation Unit 15a: Plans and
elevations
Use the following words to fill
in the gaps.
Foundation Unit 17: Circles,
cylinders, cones and spheres
centre circumference
diameter radius
The ___ of a circle is a
straight line from the ___ to
the ___. It is half the length
of the ___.

recall the relationship of
the gradient between two
perpendicular lines
Line A has gradient 2.
Line B is perpendicular to
Line A.
Write down the gradient of
Line B.
Higher Unit 6b: Linear graphs and
coordinate geometry

find the equation of the
straight line, given a
gradient and a coordinate
Find the equation of the line
with gradient 3 that passes
through the point (2, 4).
Foundation Unit 20: Rearranging
equations, graphs of cubic and
reciprocal functions and simultaneous
equations
24
Pearson Edexcel Level 1/Level 2 GCSE (9 – 1) in Mathematics
Higher tier diagnostic document – Issue 1 April 2016 © Pearson Education Limited 20156
Foundation tier
UNIT 17: Changing the subject of formulae (more complex), algebraic
fractions, solving equations arising from algebraic fractions, rationalising
surds, proof
Return to Overview
PRIOR KNOWLEDGE
Students will be able to:
Possible diagnostic
questions
Students will need to work on the
objectives covered in:
Higher Unit 1c: Factors, multiples,
primes, standard form and surds

simplify surds
Simplify

use negative numbers
with all four operations
See questions for Unit 2.
Foundation Unit 1a: Integers and
place value

recall and use the
hierarchy of operations
See questions for Unit 2.
Foundation Unit 1a: Integers and
place value
12 .
Foundation Unit 1c: Indices, powers
and roots
Pearson Edexcel Level 1/Level 2 GCSE (9 – 1) in Mathematics
Higher tier diagnostic document – Issue 1 April 2016 © Pearson Education Limited 2016
25
Foundation tier
UNIT 18: Vectors and geometric proof
Return to Overview
PRIOR KNOWLEDGE
Students will be able to:
Possible diagnostic
questions
Write as a column vector the
transformation that maps
shape A onto shape B.
Students will need to work on the
objectives covered in:
Foundation Unit 10: Transformations

use vectors to describe
translations

use Pythagoras’ Theorem
See questions for Unit 6.
Foundation Unit 12: Right-angled
triangles: Pythagoras and
trigonometry

identify properties of
triangles and
quadrilaterals
See questions for Unit 8.
Foundation Unit 6a: Properties of
shapes, parallel lines and angle facts
26
Pearson Edexcel Level 1/Level 2 GCSE (9 – 1) in Mathematics
Higher tier diagnostic document – Issue 1 April 2016 © Pearson Education Limited 20156
Foundation tier
UNIT 19: Direct and indirect proportion: using statements of proportionality,
reciprocal and exponential graphs, rates of change in graphs, functions,
transformations of graphs
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SUB-UNITS
a
Reciprocal and exponential graphs; Gradient and area under graphs
b
Direct and inverse proportion
PRIOR KNOWLEDGE
Students will be able to:

draw linear and quadratic
graphs
Possible diagnostic
questions
Sketch the following graphs.
y = 2x – 3
y = x2
Students will need to work on the
objectives covered in:
Foundation Unit 9: Real-life and
algebraic linear graphs
Foundation Unit 16b: Quadratic
equations: graphs

calculate the gradient of a
linear function between
two points
A line passes through the
points (1, 2) and (7, 5).
Find the gradient of the line.

recall transformations of
trigonometric functions
Sketch the graph of
write statements of direct
proportion and form an
equation to find values
a is directly proportional to b. Foundation Unit 11b: Proportion
a = 18 when b = 1.5.
Form an equation involving a
and b and solve it to find the
value of a when b = 7.

Foundation Unit 9a: Real-life graphs
y = sin x. Higher Unit 13a: Graphs of
On the same axes, sketch
the graph of y = 2 sin x.
trigonometric functions
Pearson Edexcel Level 1/Level 2 GCSE (9 – 1) in Mathematics
Higher tier diagnostic document – Issue 1 April 2016 © Pearson Education Limited 2016
27
Issue 1 – April 2016
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Pearson Edexcel Level 1/Level 2 GCSE (9 – 1) in Mathematics
Higher tier diagnostic document – Issue 1 April 2016 © Pearson Education Limited 20156