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SA 1: w.b. 20th October

SA 2: w.b. 15th December

SA 3: w.b. 23rd February

SA 4: w.b. 15th June (End of year exams)

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Knowledge that students will be taught:

ALL students will be able to:

classify data sets as discrete or continuous data

draw and complete a grouped frequency table

draw a bar chart or equal histogram

draw a frequency polygon

draw scatter graphs

draw time-series graphs

In addition, Higher Tier students will be able to:

calculate frequency densities

draw unequal histograms

draw cumulative frequency graphs and boxplots

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Knowledge that students will be taught:

ALL students will be able to:

identify the number of edges, faces and vertices of a 3D shape

name different types of 3D shapes

draw the net of a 3D shape

draw the plan and elevations of a 3D shape

draw a sketch of a 3D shape from its plan and elevation views

calculate the volume and surface area of a simple 3D shape made with cubes

recall the formulae to calculate the volume and surface area of a prism, pyramid, cone, cylinder, and sphere.

In addition, Higher Tier students will be able to:

identify a frustum

describe how a frustum is formed

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Knowledge that students will be taught:

ALL students will be able to:

draw straight-line graphs

find the equation of a horizontal or vertical line

identify the key properties of the straight-line equation y = mx + c

find the equation of a straight-line graph

recognise equations of parallel lines

draw distance-time graphs

calculate the distance that an object has travelled

calculate the acceleration of an object

draw speed-time graphs

In addition, Higher Tier students will be able to:

recognise equations of perpendicular lines

draw graphs of quadratic functions

draw velocity-time graphs

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Knowledge that students will be taught:

ALL students will be able to:

list factors, multiples, prime numbers, square numbers, square roots, cube numbers, and cube roots

define what a highest common factor (HCF) or lowest common multiple (LCM) of a pair of numbers is

define what a prime factor is

write numbers using index notation

In addition, Higher Tier students will be able to:

rewrite the power of a given number as a power of a different number e.g. finding the value of a such that 2¹² = 4a

simplify surds

rationalise surds using a single term or by expanding brackets with conjugates

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Knowledge that students will be taught:

ALL students will be able to:

write a proportion of a whole using fractions, decimals, or percentages

simplify a ratio with the same units or with different units

write a ratio in the form 1:n or n:1

divide amounts into a given ratio

calculate key percentages of amounts without a calculator e.g. 50%, 25%, 10%, 1%

state the decimal multiplier that is required to calculate a percentage change with a calculator

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Knowledge that students will be taught:

ALL students will be able to:

name the different parts of a circle

recall the formulae to calculate the area and circumference of a circle

recall the formulae to calculate the area and arc length of a sector of a circle

use a protractor and a pair of compasses correctly

define what a perpendicular bisector is

In addition, Higher Tier students will be able to:

recall and define a variety of circle theorems

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Knowledge that students will be taught:

ALL students will be able to:

identify inverse operations

recognise linear equations

write the factorisation of a quadratic equation

recognise simultaneous equations

recognise and use inequality notation

write inequalities using correct notation

In addition, Higher Tier students will be able to:

complete the square for a quadratic expression

recite the quadratic formula

describe the process of iteration

draw a graph to represent an inequality

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Knowledge that students will be taught:

ALL students will be able to:

round numbers to different levels of accuracy, including decimal places and significant figures

use a calculator effectively and efficiently

convert between different units of length, mass, and capacity

calculate speed, distance, and time

calculate density, mass, and volume

find upper and lower bounds of measurements

In addition, Higher Tier students will be able to:

write numbers in standard form

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Knowledge that students will be taught:

ALL students will be able to:

draw a probability scale labelled with correct mathematical vocabulary

draw a probability scale with fractions, decimals, or percentages

write a probability using words or as a fraction, decimal or percentage

describe what relative frequency is

describe what theoretical probability is

describe what expected frequency is

describe what mutually exclusive events are

describe what exhaustive means

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Knowledge that students will be taught:

ALL students will be able to:

identify different angle types

measure lines and angles accurately

calculate the area of a triangle, rectangle, parallelogram, trapezium, and compound shapes

draw a reflection, a rotation, or a translation of a shape

draw an enlargement using positive integer and fractional scale factors

construct and describe combined transformations

In addition, Higher Tier students will be able to:

construct enlargements and describe the effect of an enlargement using negative integer and fractional scale factors

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Knowledge that students will be taught:

ALL students will be able to:

use a formula to represent a real-life problem

substitute into expressions and formulae

use inverse operations in formulae

change the subject of a formula

identify an algebraic expression, formula, equation, identity, and function

expand and factorise with double brackets (including difference of two squares problems)

In addition, Higher Tier students will be able to:

use function notation

substitute into functions

find inverse functions and compound functions

solve equations involving functions

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Knowledge that students will be taught:

ALL students will be able to:

find equivalent fractions and simplify fractions

convert between mixed numbers and improper fractions

calculate fractions of an amount

calculate percentages of an amount

add, subtract, multiply and divide fractions together

convert between fractions, decimals, and percentages

In addition, Higher Tier students will be able to:

convert recurring decimals to fractions

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Knowledge that students will be taught:

ALL students will be able to:

take a random sample

recall the definition of a sample and a census

draw a data collection sheet

draw a variety of statistical diagrams, including frequency tables, stem-and-leaf diagrams, two-way tables, pictograms, bar charts, bar-line charts, dual bar charts and pie charts

define the mean, median, mode and range for a set of data

In addition, Higher Tier students will be able to:

select a stratified sample

define the lower quartile, upper quartile and interquartile range for a set of data

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Knowledge that students will be taught:

ALL students will be able to:

calculate angles on a straight line

calculate angles around a point

calculate vertically opposite angles

recognise parallel and perpendicular lines

calculate angles in parallel lines

calculate angles in triangles and quadrilaterals

measure and calculate bearings

construct accurate bearings diagrams

recognise congruent and similar shapes

calculate angles in polygons

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Website Link:

Sparx Maths - Home

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GCSE Mathematics 2025 Higher Tier Exam Aid