Differentiation Rules
Standard differentiation formulas.
d/dx(xⁿ) = nxⁿ⁻¹ d/dx(eˣ) = eˣ d/dx(ln x) = 1/x d/dx(sin x) = cos x d/dx(cos x) = -sin x AQA A-Level 2025
🧮 AQA A-Level Mathematics Formula Sheet
Essential formulas for pure mathematics, mechanics, and statistics aligned to AQA A-Level Mathematics (7356/7357) specification.
Pure Maths Mechanics Statistics
Master A-Level Mathematics
This formula sheet covers key mathematical relationships from the AQA A-Level Mathematics specification, helping you solve complex problems and achieve top grades.
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Calculus formulas
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Mechanics equations
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Statistics formulas
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Algebra essentials
Pure Mathematics
Algebra, calculus, trigonometry, and coordinate geometry for A-Level.
Integration Rules
Standard integration formulas.
∫xⁿ dx = xⁿ⁺¹/(n+1) + C (n ≠ -1) ∫eˣ dx = eˣ + C ∫1/x dx = ln|x| + C ∫cos x dx = sin x + C ∫sin x dx = -cos x + C Quadratic Formula
Solutions for ax² + bx + c = 0 where a ≠ 0.
x = [-b ± √(b² - 4ac)] / (2a) Topic Focus
Calculus Applications
- Differentiation finds rates of change and gradients of curves.
- Integration finds areas under curves and reverses differentiation.
- Always include the constant of integration (+C) in indefinite integrals.
Mechanics
Motion, forces, and energy relationships in mechanics.
SUVAT Equations
s displacement, u initial velocity, v final velocity, a acceleration, t time.
v = u + at s = ut + ½at² v² = u² + 2as s = ½(u + v)t Force (Newton's Second Law)
F force (N), m mass (kg), a acceleration (m/s²).
F = ma Momentum
p momentum (kg m/s), m mass (kg), v velocity (m/s).
p = mv Topic Focus
Motion Equations
- SUVAT equations apply only when acceleration is constant.
- Choose the appropriate SUVAT equation based on what you know and what you need to find.
- Always define positive direction and use consistent sign conventions.
Statistics
Probability, distributions, and statistical analysis.
Mean
Average of data values.
Mean = (Sum of all values) / (Number of values) Variance
Measure of spread in data.
Variance = Σ(x - μ)² / n Standard Deviation
Square root of variance.
σ = √Variance Topic Focus
Statistical Measures
- Mean measures central tendency; standard deviation measures spread.
- Larger standard deviation means more variation in the data.
- Use appropriate statistical tests based on data type and distribution.
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 Problem-Solving
Apply formulas to A-Level problems. Understand when and why to use each formula.
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Check Units
Always verify units match before substituting values. Convert units if necessary.
Excel in AQA A-Level Mathematics
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Formulas align with AQA A-Level Mathematics specification (7356/7357) for UK students.
Always show your working and include units in your final answers.