Rounding & Bounds
Lower bound
Value − ½ × degree of accuracy Upper bound
Value + ½ × degree of accuracy Compound bounds
For a × b: max = UBₐ × UB_b; min = LBₐ × LB_b. For a ÷ b: max = UBₐ ÷ LB_b; min = LBₐ ÷ UB_b OCR GCSE Mathematics J560
📐 OCR GCSE Mathematics Formula Sheet 2026
All the essential J560 Higher tier formulas in one place — number, algebra, ratio & rates, geometry & trigonometry, probability and statistics.
Number & Algebra Geometry & Trigonometry Probability Statistics
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.
Every OCR GCSE Maths Higher Formula in One Sheet
OCR GCSE Mathematics (J560 Higher) requires fluency with formulas you'll need to recall — many are no longer provided in the exam. This sheet brings together every key formula, identity and method across the six syllabus strands so you can revise efficiently for the 2026 papers.
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Number, indices, surds and standard form
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Quadratics, simultaneous equations and sequences
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Pythagoras, trigonometry, sine & cosine rules
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Probability, conditional probability and statistics
Number — Higher Essentials
Foundations that thread through every paper.
Indices
Multiplication
aᵐ × aⁿ = aᵐ⁺ⁿ Division
aᵐ ÷ aⁿ = aᵐ⁻ⁿ Power of power
(aᵐ)ⁿ = aᵐⁿ Negative & fractional
a⁻ⁿ = 1 ÷ aⁿ; a^(1/n) = ⁿ√a; a^(m/n) = (ⁿ√a)ᵐ Surds
√(a × b) = √a × √b | √a × √a = a | Rationalise: multiply numerator and denominator by the conjugate Standard Form
a × 10ⁿ where 1 ≤ a < 10 — useful for very large or very small numbers; multiply/divide by adding/subtracting indices Algebra — Higher Tier Tools
Manipulation, equations, sequences and functions.
Quadratic Equations
Quadratic formula
x = (−b ± √(b² − 4ac)) ÷ 2a Factorising
Find two numbers multiplying to ac and summing to b — works for monic or non-monic quadratics Completing the square
x² + bx + c = (x + b/2)² − (b/2)² + c — finds turning point at (−b/2, c − (b/2)²) Simultaneous Equations
Linear-linear: elimination or substitution Linear-quadratic: substitute the linear equation into the quadratic, solve for one variable, back-substitute Sequences
Arithmetic nth term
uₙ = a + (n − 1)d Geometric nth term
uₙ = a × rⁿ⁻¹ Quadratic sequence
Second difference is 2a — gives nth term of form an² + bn + c Functions & Iteration
Composite
(fg)(x) = f(g(x)) — apply g first Inverse
Swap x and y in y = f(x), then rearrange for y Iteration
xₙ₊₁ = g(xₙ) — repeat until consecutive values agree to required accuracy Ratio, Proportion & Rates
Compound measures and growth/decay.
Direct & Inverse Proportion
Direct: y = kx | Square: y = kx² | Cube: y = kx³ | Inverse: y = k/x Compound Measures
Speed
Speed = Distance ÷ Time Density
Density = Mass ÷ Volume Pressure
Pressure = Force ÷ Area Growth & Decay
Compound growth
Final = Initial × (1 + r)ⁿ where r is decimal rate per period Compound decay
Final = Initial × (1 − r)ⁿ Use this for compound interest, depreciation and population models.
Geometry & Trigonometry
All the formulas you need for length, angle and shape questions.
Pythagoras & SOHCAHTOA
Pythagoras
a² + b² = c² (right-angled triangles) SOH
sin θ = Opposite ÷ Hypotenuse CAH
cos θ = Adjacent ÷ Hypotenuse TOA
tan θ = Opposite ÷ Adjacent Sine, Cosine & Area Rules
Sine rule
a ÷ sin A = b ÷ sin B = c ÷ sin C Cosine rule
a² = b² + c² − 2bc·cos A Area of triangle
Area = ½ab·sin C Circle Theorems
1) Angle at centre = 2 × angle at circumference (same arc) 2) Angle in a semicircle = 90° 3) Angles in same segment are equal 4) Opposite angles in a cyclic quadrilateral sum to 180° 5) Tangent ⟂ radius at point of contact 6) Tangents from external point are equal in length 7) Alternate segment theorem — angle between tangent and chord = angle in alternate segment 8) Perpendicular from centre to chord bisects the chord Congruence & Vectors
Congruent triangle conditions
SSS | SAS | ASA | AAS | RHS Vectors
AB → vector from A to B; column vector (x, y); magnitude = √(x² + y²); parallel vectors are scalar multiples Probability
Combined events, conditional probability and tree diagrams.
Probability Rules
Addition rule
P(A or B) = P(A) + P(B) − P(A and B) Multiplication
P(A and B) = P(A) × P(B|A) — independent if P(B|A) = P(B) Complement
P(not A) = 1 − P(A) Conditional Probability
Definition
P(B|A) = P(A and B) ÷ P(A) Use tree diagrams for two-stage events; multiply along branches, add between branches Set Notation
A ∪ B = union | A ∩ B = intersection | A' = complement | ξ = universal set | ⊂ = subset Statistics
Summarising and representing grouped data.
Averages & Spread
Mean (grouped)
Mean ≈ Σfx ÷ Σf using midpoints Median class
Class containing the (n + 1) ÷ 2 value Range & IQR
Range = max − min; IQR = Q₃ − Q₁ Cumulative Frequency & Box Plots
Cumulative frequency: plot at upper class boundary; read off median, Q₁, Q₃ Box plots show min, Q₁, median, Q₃, max — useful for comparing distributions Histograms
Frequency density
Frequency density = Frequency ÷ Class width Area of bar = frequency; useful for unequal class widths How to Use This Formula Sheet
Boost your Cambridge exam confidence with these proven study strategies from our tutoring experts.
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Recall, Don't Look Up
Many OCR formulas are no longer given in the exam. Test recall daily using flashcards for trig rules, quadratic formula and circle theorems.
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Show Every Step
Method marks are awarded even when answers are wrong — write out the formula, substitute carefully, and label units.
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Draw the Diagram
For trig, vectors and circle theorems, sketching first prevents errors. Always mark known angles and lengths on the diagram.
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Practise Past Papers
Work through OCR J560 Higher past papers under timed conditions and use the mark scheme to refine your method.
Formula Sheet FAQ
Quick answers about this free PDF and how to use it for exam revision and active recall.
Is the OCR GCSE Mathematics 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. Master OCR GCSE Mathematics (J560 Higher) with this 2026 formula sheet. Covers number, algebra, ratio & rates, geometry, trigonometry, probability and statistics — all key formulas in one place. 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 (Secondary)?
It is written for students preparing for assessments at Secondary 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.
Need Help with OCR GCSE Maths?
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This formula sheet aligns with OCR GCSE Mathematics (J560) Higher tier 2026 syllabus content.
Always include working — OCR's mark schemes credit method even where the final answer is incorrect.