KS4 GCSE Mathematics


Progress Leader: Miss A Sharples
Teaching Staff: Mrs A Scarborough, Mrs E Merritt, Mr A Taylor, Mr D Hurst, Miss A Barton, Mrs M Tyler
Link Governor: Mr J Lyon


Mathematics is a creative and interconnected discipline. It is essential to everyday life, critical to science, technology and engineering, and necessary for financial literacy and most forms of employment.
GCSE Mathematics builds on the KS3 curriculum furthering students’ ability to;
• Develop conceptual understanding using concrete, pictorial and abstract representations.
• Develop fluency, and the ability to recall and apply knowledge accurately.
• An ability to link different aspects of mathematics to other topic areas, and across the wider curriculum.
• An opportunity to reason mathematically, developing justifications and proof, and making generalisations.
• The ability to communicate their ideas effectively using appropriate vocabulary and mathematical symbols
• Develop the confidence to apply knowledge, skills and reasoning to standard and non-standard problems.


The aims and objectives of Level 1/Level 2 GCSE (9–1) in Mathematics are to enable students to:
• develop fluent knowledge, skills and understanding of mathematical methods and concepts
• acquire, select and apply mathematical techniques to solve problems
• reason mathematically, make deductions and inferences, and draw conclusions
• comprehend, interpret and communicate mathematical information in a variety of forms appropriate to the information and context.
Students will be assessed on: number; algebra; ratio, proportion and rates of change; geometry and measures and statistics.


All students will sit 3 papers at either Higher or Foundation tier: Paper 1 – Non-Calculator / Paper 2 – Calculator / Paper 3 – Calculator.

The assessments will cover the following content headings:

Foundation proportionHigher Proportion
1 Number28%


2 Algebra23%33%
3 Ratio, proportion and rates of change28%23%
4 Geometry and measures
5 Statistics & Probability



Unit 1 – Number

Unit 2 – Algebra

Unit 3 – Statistics

Unit 4 – Number

Spec Ref: N2, N3, N5, N6, N7, N8, N9, N14, N15
Calculations, checking and rounding
Indices, roots, reciprocals and hierarchy of operations
Factors, multiples, primes, standard form and surds

Spec Ref: N1, N3, N8, A1, A2, A3, A4, A5, A6, A7, A17, A20, A21, A23, A24, A25
Algebra: the basics, setting up, rearranging and solving equations

Spec Ref: G14, S2, S3, S4, S5, S6
Averages and range
Representing and interpreting data and scatter graphs

Spec Ref: N1, N2, N3, N8, N10, N11, N12, N13, R3, R2, R3, R4, R5, R6, R7, R8, R9, R10
Fractions and percentages 12 b Ratio and proportion


Unit 5 – Geometry

Unit 6 – Graphs

Unit 7 – Perimeter, are and volume

Unit 8 – Transformations

Spec Ref: G1, G3, G4, G6, G11, N7, N8, N15, A4, A5, R12, G6, G20, G21
Polygons, angles and parallel lines 6 b Pythagoras’ Theorem and trigonometry

Spec Ref: N13, A8, A9, A10, A11, A12, A14, A15, A16, A17, A18, R1, R10, R11, R14
Graphs: the basics and real-life graphs
Linear graphs and coordinate geometry
Quadratic, cubic and other graphs

Spec Ref: N8, N14, N15, N16, A5, R1, G1, G9, G12, G13, G14, G16, G17, G18
Perimeter, area and circles
3D forms and volume, cylinders, cones and spheres Accuracy and bounds

Spec Ref: R2, G2, G3, R6, G5, G7, G8, G12, G13, G15, G24, G25
Constructions, loci and bearings


Unit 9 – Algebra

Unit 10 – Probability

Unit 11 – Multiplicative reasoning

Unit 12 – Similarity and Congruence

Spec Ref: N1, N8, A4, A5, A9, A11, A18, A19, A21, A22
Solving quadratic and simultaneous equations

Spec Ref: N1, P1, P2, P3, P4, P5, P6, P7, P8, P9

Spec Ref: N3, N12, N13, R1, R6, R8, R10, R11, R13, R14, R16
Multiplicative reasoning

Spec Ref: R6, R12, G5, G6, G17, G19
Similarity and congruence in 2D and 3D


Unit 1 – Number

Unit 2 – Algebra

Unit 3 – Statistics

Unit 4 – Number

Unit 5 – Algebra

Spec Ref: N1, N2, N3, N4, N6, N7, N14, N15
Integers and place value, Decimals, Indices, powers and roots. Factors, multiples and primes.

Spec Ref: N1, N3, A1, A2 A3, A4, A5, A6, A7, A21
Algebra: the basics. Expressions and substitution into formula.

Spec Ref: G2, G14, G15 S2, S4, S5, S6
Tables, charts and graphs, Pie charts, Scatter graphs

Spec Ref: N1, N2, N3, N8, N10, N12, N13, R3, R9, S2
Fractions, decimals and percentages

Spec Ref: N1, N15, N16, A2, A3, A5, A7, A17, A21, A22
Equations and inequalities. Sequences


Unit 6 – Geometry

Unit 7 – Statistics

Unit 8 – Geometry

Unit 9 – Graphs

Unit 10 – Transformations

Spec Ref: G1, G3, G4, G6, G11, G15, A8
Properties of shapes, parallel lines and angle facts
Interior and exterior angles of polygons

Spec Ref: S1, S2, S4
Statistics, sampling and the averages

Spec Ref: N14, A5, R1, G11, G12, G14, G15, G16, G17
Perimeter, area and volume

Spec Ref: N13, A7, A8, A9, A10, A12, A14, A17, R1, R11, R14, G11, G14)
Real-life graphs, coordinates, Straight-line graphs

Spec Ref: R6, R12, G1, G7, G24
Reflections, rotations, translations, enlargements


Unit 11 – Ratio and proportion

Unit 12 – Trigonometry

Unit 13 – Probability

Unit 14 – Multiplicative reasoning

Spec Ref: N11, N13, R1, R2, R3, R4, R5, R6, R7, R8, R10, R13, R14
Ratio and proportion

Spec Ref: N7, N15, A4, A5, R12, G6, G20, G21
Pythagoras theorem and Trigonometry

Spec Ref: N5, P1, P2, P3, P4, P5, P6, P7, P8

Spec Ref: N12, N13, A5, R1, R9, R10, R11, R13, R16, G14
Multiplicative reasoning: more percentages, rates of change, compound measures




Unit 13 – Trigonometry 2

Unit 14 - Data

Unit 15 - Algebra

Unit 16 – Circle theorems

Unit 17 - Algebra

Spec Ref: A8, A12, A13, G21
Spec Ref N16, A5, A8, G11, G20, G22, G23
Graphs of trigonometric functions.
Further trigonometry.

Spec Ref: S1 S3, S4, S5
Sampling, cumulative frequency, box plots and histograms

Spec Ref: N8, A4, A11, A12, A18, A19, A20, A21,
Quadratics, expanding more than two brackets, sketching graphs, graphs of circles, cubes and quadratics.

Spec Ref: G9, G10, A16
Circle theorems. Circle geometry

Spec Ref: N8, A4, A5, A6, A7, A18
Changing the subject of formulae (more complex), algebraic fractions, solving equations arising from algebraic fractions, rationalising surds, proof.


Unit 18 - Vectors

Unit 19 - Reciprocal and exponential graphs. Direct and inverse proportion.

Spec Ref G25
Vectors and geometric proof.

Spec Ref: R11, R14, R15, R16, A7, A12, A13, A14, A15 Reciprocal and exponential graphs; Gradient and area under graphs.
Spec Ref: A21, R7, R10, R11, R14
Direct and inverse proportion.


Course complete

Revision using question level analysis from mock exams



Unit 15 – Geometry

Unit 16 - Algebra - Quadratic equations

Unit 17 – Geometry/Circles

Unit 18 - Number

Spec Ref: G1, G2, G9, G12, G13, G15, R2, G2, G5, G15
Plans and elevations. Constructions, loci and bearings.

Spec Ref: A4, A11, A18, A11, A12, A14, A18
Expanding and factorising. Quadratic equations: graphs.

Spec Ref: N8, N14, N15, A5, G9, G16, G17, G18
Perimeter, area and volume 2: circles, cylinders, cones and spheres.

Spec Ref: N2, N3, N8, 18b, N7, N9
Fractions. Indices and standard form.


Unit 19 – Geometry

Unit 20 - Algebra

Spec Ref: R6, R12, G5, G6, G7, G19, 19b, G24, G25
Similarity and congruence in 2D.

Spec ref: N1, A3, A5, A6, A9, A10, A12, A14, A19, A21, A22, R10, R14
Rearranging equations, graphs of cubic and reciprocal functions and simultaneous equations.


Course Complete

Revision using question level analysis from mock exams


UKMT Senior challenge – Years 10/11
Runshaw Maths challenge – Year 11
St John Rigby Maths challenge – Year 10
College taster days – Year 11


Most courses require a GCSE grade 4 or above in Mathematics. Students will be required to re-sit GCSE Maths if they fail to reach this standard.
Requirements to study A Level Mathematics can vary dependent on College. Most would require a GCSE Mathematics grade of 6 or higher.
Requirements to study A Level Sciences are generally dependent on achieving a Grade 5 or 6 in GCSE Mathematics.


There are lots of pressure on students during KS4, but below are some simple tips to help.
• Ensure they feel supported regardless of results
• Assist them in drawing up a realistic revision timetable or flashcards with key facts
• Encourage them to use apps and websites provided by school
• Complete past papers
• Maths Revision guides/flashcards
Below are links to blogs that have further suggestions for support you can offer;


Manchester museum of science and industry
Bletchley Park, Buckinghamshire the once top-secret home of the World War Two Code-breakers is now a vibrant heritage attraction, popular with schools for its specific focus on Mathematics, History and Computing.
Bank of England Museum, London offers a range of one hour talks for a multitude of ages, which are also free but must be booked in advance.
The Royal Observatory, Greenwich
Woolsthorpe Manor – Isaac Newton changed the world here


Corbett Maths videos - https://corbettmaths.com/contents/
BBC Maths podcasts - http://www.bbc.co.uk/radio4/features/collections/mathematics/
Think like a mathematician -https://www.bbc.co.uk/bitesize/topics/zfxhfg8/resources/1
Films to see:
Hidden Figures
A Beautiful Mind
The Imitation Game
Good Will Hunting
A Brilliant young Mind


The Monty Hall Problem: Beyond Closed Doors by Rob Deaves - Age 14+
The Language of Mathematics by Keith Devlin - Age 14+
How Not to Be Wrong: The Hidden Maths of Everyday Life – Jordan Ellenberg


Maths watch - https://vle.mathswatch.co.uk/vle/
Corbett Maths – https://corbettmaths.com/
Maths genie - https://www.mathsgenie.co.uk/
BBC Bitesize - https://www.bbc.co.uk/bitesize
PIXL maths app - https://mathsapp.pixl.org.uk/PMA.html


Mathematics can help students looking for a career in areas such as engineering, accountancy, medicine, science and research. Mathematics is also seen as being an important qualification by employers and further education providers.

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