Order of operations
Work out expressions in the correct order: Brackets, Indices, Division/Multiplication, Addition/Subtraction.
BIDMAS: Brackets → Indices → Divide/Multiply → Add/Subtract Cambridge Lower Secondary 2026
🧮 Cambridge Lower Secondary Maths Formula Sheet
Essential formulas for number, algebra, geometry and measure, and statistics and probability across Grades 6-8.
Number & Algebra Geometry & Measure Statistics & Probability
Our formula sheets are free to download — save this one as PDF for offline revision.
Aligned with the latest 2026 syllabus and board specifications. This sheet is prepared to match your exam board’s official specifications for the 2026 exam series.
Build Strong Mathematical Foundations
This formula sheet covers the key relationships from Grades 6 through 8 — most schools don't sit the optional Cambridge Checkpoint exam, but this is exactly the content every student needs before starting Cambridge IGCSE.
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Number skills
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Algebra essentials
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Geometry formulas
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Statistics basics
Number
Order of operations, place value, factors and fractions
The core number skills built up across Grades 6–8, from order of operations through to standard form.
Factors, multiples and primes
A factor divides exactly into a number; a multiple is in its times table; a prime number has exactly 2 factors (1 and itself).
HCF
Highest Common Factor — the largest number that divides into two numbers exactly LCM
Lowest Common Multiple — the smallest number that both numbers divide into exactly Powers and roots
A power multiplies a number by itself; a root reverses this.
Square
n² = n × n Cube
n³ = n × n × n Square root
√n — the number that, squared, gives n Fractions, decimals and percentages
The same value written three ways — convert between them to compare or calculate.
Fraction → decimal
numerator ÷ denominator Decimal → percentage
× 100 Percentage of an amount
(percentage ÷ 100) × amount Ratio and proportion
A ratio compares two quantities; divide a total in a given ratio by splitting it into equal parts.
To share an amount in the ratio a : b, divide by (a + b), then multiply by a and by b Standard form
A way of writing very large or very small numbers compactly (Grade 8).
n is positive for large numbers, negative for numbers between 0 and 1.
a × 10ⁿ, where 1 ≤ a < 10 Algebra
Expressions, equations, sequences and graphs
Building algebraic fluency from simplifying expressions through to plotting straight-line graphs.
Simplifying expressions
Collect like terms — terms with exactly the same letters and powers — by adding or subtracting their coefficients.
3x + 5x = 8x (but 3x + 5y cannot be simplified further) Substitution
Replace each letter in a formula with its given value, then calculate.
If a = 2 and b = 5, then 3a + b = (3 × 2) + 5 = 11 Expanding and factorising
Expanding multiplies out a bracket; factorising is the reverse — pulling out a common factor.
Expand
a(b + c) = ab + ac Factorise
ab + ac = a(b + c) Solving linear equations
Do the same operation to both sides until the unknown is on its own.
e.g. 2x + 3 = 11 → 2x = 8 → x = 4 Sequences
The nth term rule lets you find any term in a sequence without listing every term before it.
e.g. for 5, 8, 11, 14 … the common difference is 3, so the nth term is 3n + 2.
nth term = (common difference × n) + (first term − common difference) Linear functions and graphs
A straight-line graph has a constant gradient (steepness) and a fixed y-intercept.
y = mx + c, where m = gradient, c = y-intercept Geometry and Measure
Angles, shapes, perimeter, area and volume
Angle facts and the key perimeter, area and volume formulas used throughout Grades 6–8.
Angle facts
The core angle rules used to find missing angles.
On a straight line
sum = 180° Around a point
sum = 360° In a triangle
sum = 180° In a quadrilateral
sum = 360° Perimeter and circumference
Perimeter is the distance around a shape; circumference is the perimeter of a circle.
Rectangle
P = 2(length + width) Circle
C = πd = 2πr Area
The space covered by a 2D shape.
Rectangle
A = length × width Triangle
A = ½ × base × height Parallelogram
A = base × height Circle
A = πr² Volume and surface area
Volume is the space inside a 3D shape; surface area is the total area of all its faces.
Cuboid volume
V = length × width × height Prism volume
V = cross-sectional area × length Transformations
Ways to move or resize a shape without changing its properties (except size, for enlargement).
Translation
moves a shape without turning or resizing it Reflection
flips a shape over a mirror line Rotation
turns a shape around a fixed point Enlargement
resizes a shape by a scale factor from a centre point Rate of change
How one quantity changes in relation to another over time (Grade 7–8).
rate = change in quantity ÷ time taken Statistics and Probability
Averages, data representation and probability
Summarising data with averages and describing the likelihood of events.
Averages and range
Three ways to find a 'typical' value in a data set, plus a measure of spread.
Mean
sum of all values ÷ number of values Median
the middle value when data is placed in order Mode
the most frequently occurring value Range
highest value − lowest value Data representation
Bar charts, pie charts and frequency tables each summarise data visually in different ways.
Pie chart sector angle = (frequency ÷ total frequency) × 360°.
Collecting and organising data
A tally chart records raw data as it's collected; a frequency table then summarises the totals.
Probability
Probability measures how likely an event is, on a scale from 0 (impossible) to 1 (certain).
P(event) = number of favourable outcomes ÷ total number of possible outcomes How to Use This Formula Sheet
Boost your Cambridge exam confidence with these proven study strategies from our tutoring experts.
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Practice, Don't Just Memorise
Apply each formula to a few practice questions. Understanding when and why to use a formula matters more than reciting it.
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Show Your Working
Write out each step when substituting into a formula — it makes mistakes easier to spot and marks easier to earn.
Formula Sheet FAQ
Quick answers about this free PDF and how to use it for exam revision and active recall.
Is the Cambridge Lower Secondary Maths Formula Sheet 2026 free to download as a PDF?
Yes. This Tutopiya formula sheet is free to use and you can download it as a PDF from this page for offline revision. There is no payment or account required for the PDF download.
What Mathematics topics and equations does this formula sheet cover?
This page groups key Mathematics formulas in one place for revision. Essential Cambridge Lower Secondary Mathematics formulas for Grades 6-8 (ages 11-14): number, algebra, geometry and measure, statistics and probability — the content every student needs before starting Cambridge IGCSE. Always cross-check with your official syllabus and past papers for your exam session.
Can I use this instead of the official exam formula booklet in the exam?
No. In the exam you must follow only what your exam board allows in the hall—usually the official formula booklet or data sheet where provided. This page is a revision and teaching aid, not a replacement for board-issued materials.
Who is this formula sheet for (Middle School)?
It is written for students preparing for assessments at Middle School in Mathematics, including classroom revision, homework support, and independent study. Teachers and tutors can also share it as a quick reference.
How should I revise with this formula sheet?
Work through past paper questions, quote the correct formula before substituting values, and check units and notation every time. Pair this sheet with timed practice and mark schemes so you see how examiners expect working to be set out.
Where can I get more help with Mathematics revision?
Explore Tutopiya’s study tools, past paper finder, and revision checklists linked from our tools hub, or book a trial lesson with a subject specialist for personalised support alongside this formula reference.
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Formulas align with the Cambridge Lower Secondary Mathematics framework for Grades 6-8.
Always show your working and include units in your final answers.