Highertierdiagnostic Document

Pearson
Edexcel Level 1/Level 2 GCSE (9 – 1) in Mathematics (1MA1)

Highertierdiagnostic document

For first teaching from September 2015

Contents

Introduction5

Higher course overview6

Higher units7

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 Highertier 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 Highertier 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 withdiagnostic 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 ( and on the Emporium (

Unit / Title
1 / a / Calculations, checking and rounding
b / Indices, roots, reciprocals and hierarchy of operations
c / Factors, multiples, primes, standard form and surds
2 / a / Algebra: the basics, setting up, rearranging and solving equations
b / Sequences
3 / a / Averages and range
b / Representing and interpreting data and scatter graphs
4 / a / Fractions and percentages
b / Ratio and proportion
5 / a / Polygons, angles and parallel lines
b / Pythagoras’ Theorem and trigonometry
6 / a / Graphs: the basics and real-life graphs
b / Linear graphs and coordinate geometry
c / Quadratic, cubic and other graphs
7 / a / Perimeter, area and circles
b / 3D forms and volume, cylinders, cones and spheres
c / Accuracy and bounds
8 / a / Transformations
b / Constructions, loci and bearings
9 / a / Solving quadratic and simultaneous equations
b / Inequalities
10 / Probability
11 / Multiplicative reasoning
12 / Similarity and congruence in 2D and 3D
13 / a / Graphs of trigonometric functions
b / Further trigonometry
14 / a / Collecting data
b / Cumulative frequency, box plots and histograms
15 / Quadratics, expanding more than two brackets, sketching graphs, graphs of circles, cubes and quadratics
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 / a / Reciprocal and exponential graphs; Gradient and area under graphs
b / Direct and inverse proportion

1

Pearson Edexcel Level 1/Level 2 GCSE (9 – 1) in Mathematics
Higher tier diagnostic document – Issue 1 April 2016 © Pearson Education Limited 2016

Foundation tier

UNIT 1: Powers, decimals, HCF and LCM, positive and negative, roots, rounding, reciprocals, standard form, indices and surds

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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: / Possible diagnostic questions / Students will need to work on the objectives covered in:

• understand place value, order integers and decimals and use the four operations

/ Given the digits 2, 5, 7 and 9, make all the possible three-digit number with one decimal place and put them in order.
Addition, subtraction, multiplication and division questions with up to three digits and one decimal place / Foundation Unit 1: Number, powers, decimals, HCF and LCM, roots and rounding

• 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
Divide 72430 by 10, 100, 1000. / Foundation Unit 1a: Integers and place value

• 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
UNIT 2: Expressions, substituting into simple formulae, expanding and factorising, equations, sequences and inequalities, simple proof

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SUB-UNITS

a / Algebra: the basics, setting up, rearranging and solving equations
b / Sequences

PRIOR KNOWLEDGE

Students will be able to: / Possible diagnostic questions / Students will need to work on the objectives covered in:

• use negative numbers with the four operations, recall and use the hierarchy of operations and understand inverse operations

/ 4 – (–6) =
–6 × 3 =
18 ÷ = –3
4 × 7 – 16 ÷ 2 = / Foundation Unit 1a: Integers and place value
Foundation Unit 1c: Indices, powers and roots

• deal with decimals and negatives on a calculator

/ Use a calculator to calculate:
–6.5 × –4.2 = / Foundation Unit 1c: Indices, powers and roots

• use index laws numerically

/ 43 × 45 =
67 ÷ 62 = / Foundation Unit 1c: Indices, powers and roots
UNIT 3:Averages and range, collecting data, representing data

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SUB-UNITS

a / Averages and range
b / Representing and interpreting data and scatter graphs

PRIOR KNOWLEDGE

Students will be able to: / Possible diagnostic questions / Students will need to work on the objectives covered in:

• read scales on graphs, draw circles, measure angles and plot coordinates in the first quadrant

/ 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.
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 3a: Tables, charts and graphs
Foundation Unit 3b: Pie charts
Foundation Unit 6a: Properties of shapes, parallel lines and angle facts
Foundation Unit 15a: Plans and elevations

• use tally charts

/ What number does this represent?
Write 24 in tallies. / Foundation Unit 3: Drawing and interpreting graphs, tables and charts
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
UNIT 4:Fractions, percentages, ratio and proportion

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SUB-UNITS

a / Fractions and percentages
b / Ratio and proportion

PRIOR KNOWLEDGE

Students will be able to: / Possible diagnostic questions / Students will need to work on the objectives covered in:

• use the four operations of number

/ See questions for Unit 1 / Foundation Unit 1a: Integers and place value

• find common factors

/ What factor is common to 8 and 12? To 14 and 35? / Foundation Unit 1d: Factors, multiples and primes

• understand fractions as being ‘parts of a whole’

/ Shade of
Shade of
/ Foundation Unit 4a: Fractions, decimals and percentages
See also Access Unit 11: Fractions, decimals and percentages 2

• understand percentage as ‘number of parts per hundred’ and recognise that percentages are used in everyday life

/ Shannon got the questions in a test correct. What is as a percentage?
In a sale, prices are reduced by 10%. What is 10% as a fraction? / Foundation Unit 4b: Percentages
UNIT 5: Angles, polygons, parallel lines; Right-angled triangles: Pythagoras and trigonometry

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SUB-UNITS

a / Polygons, angles and parallel lines
b / Pythagoras’ Theorem and trigonometry

PRIOR KNOWLEDGE

Students will be able to: / Possible diagnostic questions / Students will need to work on the objectives covered in:

• rearrange simple formulae and equations

/ If t = 6h – 3, write an expression for h / 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.
Find the size of the angles marked x and y.

/ Foundation Unit 6a: Properties of shapes, parallel lines and angle facts 6b - G3, G6

• understand that fractions are more accurate in calculations than rounded percentage or decimal equivalents

/ ≈ 0.3
Which of the following give the most accurate answer?
× 50 = 16
0.3 × 50 = 15 / Foundation Unit 4a: Fractions, decimals and percentages
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

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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 / Students will need to work on the objectives covered in:

• identify coordinates of given points in the first quadrant or all four quadrants

/ Draw axes for values of x and 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? / Foundation Unit 9a: Real-life graphs

• use Pythagoras’ Theorem

/ Find the length of the unknown side.
/ Foundation Unit 12: Right-angled triangles: Pythagoras and trigonometry

• calculate the area of compound shapes

/ Find the area of this shape.
/ Foundation Unit 8: Perimeter, area and volume

• use and draw conversion graphs for common units

/ 5 miles ≈ 8 kilometres
Draw axes with scales from 0 to 80km on the horizontal axis and 0 to 50 miles on the vertical axis. Plot a line to show the relationship between miles and kilometres.
Estimate 20km in miles.
Estimate 40m in kilometres. / Foundation Unit 9a: Real-life graphs

• use function machines and inverse operations

/ Find y when x = 3.
x→ → = y
Find x when y = 11.
x→ → = y / Foundation Unit 1a: Integers and place value
Foundation Unit 5a: Equations and inequalities
UNIT 7: Perimeter, area and volume, plane shapes and prisms, circles, cylinders, spheres, cones; Accuracy and bounds

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SUB-UNITS

a / Perimeter, area and circles
b / 3D forms and volume, cylinders, cones and spheres
c / Accuracy and bounds

PRIOR KNOWLEDGE

Students will be able to: / Possible diagnostic questions / Students will need to work on the objectives covered in:

• name and identify the properties of 3D forms

/ Sketch a cuboid, a cylinder and a square-based pyramid.
How many faces does each shape have? How many vertices? How many edges? / Foundation Unit 15a: Plans and elevations

• find perimeter and area by measuring lengths of sides

/ Measure the sides of this rectangle. Find its perimeter and area.
/ Foundation Unit 8: Perimeter, area and volume

• 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 5a: Equations and inequalities
Foundation Unit 1b: Decimals

• understand the various metric units

/ Match each item to the most appropriate unit you could use to measure it.
mmcapacity of an egg cup
cmcapacity of a bath
mlength of a pencil
kmdiameter of a coin
gmass of a horse
kgjourney from London to Edinburgh
mlmass of a mouse
llength of a room / Foundation Unit 8: Perimeter, area and volume
UNIT 8: Transformations; Constructions: triangles, nets, plan and elevation, loci, scale drawings and bearings

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SUB-UNITS

a / Transformations
b / Constructions, loci and bearings

PRIOR KNOWLEDGE

Students will be able to: / Possible diagnostic questions / Students will need to work on the objectives covered in:

• recognise 2D shapes

/ 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.) / Foundation Unit 6: Angles, polygons and parallel lines

• 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. Plot the lines x = 4 and
y=–2. / Foundation Unit 9b: Straight-line graphs
UNIT 9:Algebra: Solving quadratic equations and inequalities, solving simultaneous equations algebraically

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SUB-UNITS

a / Solving quadratic and simultaneous equations
b / Inequalities

PRIOR KNOWLEDGE

Students will be able to: / Possible diagnostic questions / Students will need to work on the objectives covered in:

• understand the ≥ and ≤ symbols

/ List the positive integers that satisfy the inequality 10x≥6.
List the integers that satisfy the inequality 10 < y≤ 14. / Foundation Unit 1a: Integers and place value

• substitute into, solve and rearrange linear equations

/ What is the value of h in this formula, if C = 10?
C = 5h + 20 / Foundation Unit 2b: Expressions and substitution into formulae

• factorise simple quadratic expressions

/ Factorise x2 – x – 6, / Foundation Unit 16a: Quadratic equations: expanding and factorising

• recognise the equation of a circle

/ Which of these equations is the equation of a circle?
y = x2 + 16
x2 + y2 = 52
x + y = 25 / Higher Unit 6c: Quadratic, cubic and other graphs
UNIT 10: Probability

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PRIOR KNOWLEDGE

Students will be able to: / Possible diagnostic questions / Students will need to work on the objectives covered in:

• distinguish between events which are impossible, unlikely, even chance, likely, and certain to occur

/ Match to events to how likely they are to occur.
1Christmas will fall on 25 December this year.
2The sun will rise at midnight tonight.
3You will score an even number if you roll an ordinary, fair dice.
4The next person you meet likes chocolate.
5If you buy a lottery ticket, you will win the jackpot.
A ImpossibleB Unlikely
C Even chanceD Likely
E Certain / Foundation Unit 13: Probability

• 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.
Mark these probabilities on the number line.
P(blue) = P(red) =
P(green) = P(pink) =
P(black) = 0P(marble) = 1
0 / 1
/ Foundation Unit 13: Probability

• add and multiply fractions and decimals

/ + = × =
0.35 + 1.7 =0.2 × 0.6 = / Foundation Unit 4a: Fractions, decimals and percentages

• express one number as a fraction of another number

/ What is 15 as a fraction of 25? / Foundation Unit 4a: Fractions, decimals and percentages
UNIT 11: Multiplicative reasoning: direct and inverse proportion, relating to graph form for direct, compound measures, repeated proportional change

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PRIOR KNOWLEDGE

Students will be able to: / Possible diagnostic questions / Students will need to work on the objectives covered in:

• find a percentage of an amount and relate percentages to decimals

/ What is 45% of 300?
What is the decimal equivalent of 6%? / Foundation Unit 4b: Fractions and percentages

• rearrange equations and use these to solve problems

/ A square has sides of d+ 3. A rectangle has sides of
3d+ 1 and d– 3. They have the same length perimeter. Find d. / Foundation Unit 5a: Equations and inequalities

• understand
  speed = distance/time, density = mass/volume

/ A car travels 70 miles in 2 hours. What is its average speed?
Cobalt has a density of
8.9 gm/cm3. What is the mass of a cm cube of cobalt? / Foundation Unit 14: Multiplicative reasoning
UNIT 12: Similarity and congruence in 2D and 3D

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PRIOR KNOWLEDGE

Students will be able to: / Possible diagnostic questions / Students will need to work on the objectives covered in:

• recognise and enlarge shapes and calculate scale factors

/ Enlarge this triangle by a scale factor of 2.
Shape B is an enlargement of shape A. What is the scale factor?
B
A
/ Foundation Unit 10: Transformations

• calculate area and volume in various metric measures

/ What is the area of a rectangle that measures 4.5m by 6m?
What is the volume of a cuboid that measures 2mm by 5mm by 7mm? / Foundation Unit 8: Perimeter, area and volume

• measure lines and angles and use compasses, ruler and protractor to construct standard constructions

/ Use compasses and a ruler to construct this triangle accurately.

Measure the length of sides x and y and the size of angle a. / 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
UNIT 13: Sine and cosine rules, ab sin C, trigonometry and Pythagoras’ Theorem in 3D, trigonometric graphs, and accuracy and bounds

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SUB-UNITS

a / Graphs of trigonometric functions
b / Further trigonometry

PRIOR KNOWLEDGE

Students will be able to: / Possible diagnostic questions / Students will need to work on the objectives covered in:

• use axes and coordinates to specify points in all four quadrants

/ See questions for Unit 6. / Foundation Unit 9a: Real-life graphs

• recall and apply Pythagoras’ Theorem and trigonometric ratios

/ See questions for Unit 6.
Use the cosine rule to find the value of a.
/ Foundation Unit 12: Right-angled triangles: Pythagoras and trigonometry

• substitute into formulae

/ See questions for Unit 9. / Foundation Unit 5a: Equations and inequalities
UNIT 14: Statistics and sampling, cumulative frequency and histograms

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SUB-UNITS

a / Collecting data
b / Cumulative frequency, box plots and histograms

PRIOR KNOWLEDGE

Students will be able to: / Possible diagnostic questions / Students will need to work on the objectives covered in:

• understand the different types of data: discrete/continuous

/ Sort the following data into two groups: discrete and continuous.
AHeights of 10 students
BNumber of pets owned by 30 students
CFavourite colours of 15 students
DMass of 20 apples / Foundation Unit 3a: Tables, charts and graphs

• use inequality notation

/ See questions for Unit 3. / Foundation Unit 1a: Integers and place value

• multiply a fraction by a number

/ What is of 48? / Foundation Unit 4a: Fractions, decimals and percentages

• understand the data handling cycle

/ Put these four steps in the correct order.
AAnalyse the data.
BDraw conclusions.
CCollect data.
DSpecify the problem and plan an investigation. / Foundation Unit 7: Statistics, sampling and the averages
UNIT 15: Quadratics, expanding more than two brackets, sketching graphs, graphs of circles, cubes and quadratics

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PRIOR KNOWLEDGE

Students will be able to: / Possible diagnostic questions / Students will need to work on the objectives covered in:

• solve quadratics and linear equations

/ Solve these equations.
3(x – 6) = 6
x2 – 3x – 28 = 0 / Foundation Unit 5a: Equations and inequalities
Foundation Unit 16: Algebra: quadratic equations and graphs

• solve simultaneous equations algebraically

/ Solve these simultaneous equations:
3x – y = 23
2x + y = 7 / Foundation Unit 20: Rearranging equations, graphs of cubic and reciprocal functions and simultaneous equations
UNIT 16: Circle theorems and circle geometry

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