Maths

Vector methods with projectiles

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Variable acceleration in one dimension

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Differentiating vectors

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Integrating vectors

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Study Tips

Boost your skills with our essential study tips!

Application of forces

Static particles

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Modelling with statics

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Friction with static particles

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Statics of rigid bodies

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Dynamics and inclined planes

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Connected particles

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Projectiles

Horizontal projection

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Projectiles: Horizontal and vertical components

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Projection at any angle

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Equation of the trajectory of a projectile

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Forces and friction

Resolving forces

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Inclined planes

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The coefficient of friction

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Moments

Moments

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Resultant moments

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Equilibrium

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Centre of mass

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Tilting

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Laminas

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Forces and motion

Force diagrams

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Forces as vectors

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Forces and acceleration

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Motion in two dimensions

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Connected particles

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Pulleys

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Variable acceleration

Functions of time: Displacement, velocity, acceleration

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Using differentiation to find velocity and acceleration

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Maxima and minima problems

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Using integration to find velocity and displacement

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Constant acceleration formulae

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Constant acceleration

Displacement-time graphs

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Velocity-time graphs

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Constant acceleration: Deriving formulae

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Constant acceleration formulae: SUVAT

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Vertical motion under gravity

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Modelling in mechanics

Modelling assumptions

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Quantities and units in mechanics

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Working with vectors

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Normal distribution

The normal distribution

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The normal distribution: Finding probabilities

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The inverse normal distribution function

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The standard normal distribution

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Finding the mean and standard deviation

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Normal approximation to the binomial distribution

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Hypothesis testing with the normal distribution

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Conditional probability

Set notation

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Conditional probability

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Conditional probability in Venn diagrams

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Probability formulae

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Conditional probability: Tree diagrams

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Correlation and hypothesis testing

Exponential models

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Measuring correlation

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Hypothesis testing for zero correlation

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Hypothesis testing I

Hypothesis testing

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Hypothesis testing: Finding critical values

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One-tailed tests

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Two-tailed tests

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Probability distributions

Binomial distribution

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The binomial distribution

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Cumulative probabilities

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Probability

Calculating probabilities

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Venn diagrams

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Probability: Mutually exclusive and independent events

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Probability: Tree diagrams

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Representation of data

Outliers

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Box plots

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Cumulative frequency

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Histograms

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Comparing data sets

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Correlation

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Linear regression

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Measures of central tendency: Mean, median, mode

Measures of location and spread

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Measures of spread: Range

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Variance and standard deviation

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Data collection

Population and samples

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Sampling techniques

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Types of data

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Vectors II

3D coordinates

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Vectors in 3D

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Solving geometric problems

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Applications to mechanics: 3D vectors

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Numerical methods

Locating roots

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Iteration

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Staircase and cobweb diagrams

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Newton-Raphson method

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Numerical methods: Applications to modelling

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Integrating standard functions

Integration II

See All (11)

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Integrating f(ax + b)

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Integration with trigonometric identities

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Reverse chain rule

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Integration by substitution

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Integration by parts

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Integration using partial fractions

$Integration using partial fractions$

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Finding areas using integration

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The trapezium rule

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Solving differential equations

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Modelling with differential equations

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Differentiating sin x and cos x

Differentiation II

See All (11)

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Differentiating exponentials and logarithmic functions

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The chain rule

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The product rule

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The quotient rule

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Differentiating inverse functions

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Differentiating trigonometric functions

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Parametric differentiation

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Implicit differentiation

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Second derivatives: Concave and convex functions

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Connected rates of change

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Trigonometry and modelling

Addition formulae

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Using the angle addition formulae

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Double angle formulae

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Solving trigonometric equations: Double angle formula

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Simplifying a cos x + b sin x

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Proving trigonometric identities

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Modelling with trigonometric functions

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Trigonometric functions

Secant, cosecant and cotangent

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Graphs of sec x, cosec x and cot x

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Solving equations with sec x, cosec x and cot x

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Further trigonometric identities

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Inverse trigonometric functions

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Radians

Radian measure

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Arc length

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Areas of sectors and segments

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Solving trigonometric equations

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Small angle approximations

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Sequences and series

See All (8)

Sequences revision

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Arithmetic sequences

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Arithmetic series

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Geometric sequences

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Geometric series

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Sum to infinity

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Sigma notation

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Modelling with sequences and series

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Binomial expansion II

Binomial expansion: (1+x)^n

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Binomial expansion: (a+bx)^n

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Binomial expansion with partial fractions

$Binomial expansion with partial fractions$

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Binomial expansion of compound expressions

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Parametric equations

Parametric equations

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Using trigonometric identities

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Sketching parametric curves

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Points of intersection of parametric curves

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Modelling with parametric equations

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Functions

See All (8)

Functions and mappings

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Composite functions

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Inverse functions

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The modulus function

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y = |f(x)| and y = f(|x|)

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Combining transformations

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Solving modulus equations

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Modulus inequalities

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Algebraic fractions

Operations with algebraic fractions

$Operations with algebraic fractions$

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$Partial fractions$

Partial fractions

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Repeated factors

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Algebraic division

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Proof II

Proof by contradiction

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Criticising proofs

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Vectors I

Vectors

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Representing vectors

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Magnitude and direction of a vector

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Position vectors and displacement vectors

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Solving geometric problems

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Modelling with vectors

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Integration I

Integrating x^n

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Indefinite integrals

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Finding functions by integrating

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Definite integrals

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Area under a curve

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Area under the x-axis

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Area between a curve and a line

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Finding the gradient of a curve

Differentiation I

See All (10)

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Differentiation from first principles

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Differentiating x^n

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Differentiating functions with multiple terms

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Gradients, tangents and normals

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Increasing and decreasing functions

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Second order derivatives

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Stationary points

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Sketching gradient functions

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Modelling with differentiation

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Exponentials and logarithms

See All (9)

Exponential functions

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y = e^x

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Exponential modelling

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Logarithms

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Laws of logarithms

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Solving equations using logarithms

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Natural logarithms

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Logarithms and non-linear data

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Harder exponential modelling

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Trigonometric equations

Angles in all four quadrants

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Exact trigonometric values

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Trigonometric identities

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Simple trigonometric equations

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Harder trigonometric equations

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Equations and identities

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Trigonometry

The cosine rule

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The sine rule

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Area of a triangle

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Solving triangle problems

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Trig graphs: sin x, cos x, tan x

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Transforming trigonometric graphs

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Binomial expansion I

Pascal's triangle

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Factorial notation

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Binomial expansion

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Solving binomial problems

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Binomial estimation

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Circles

Midpoints and perpendicular bisectors

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Equation of a circle

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Intersection of straight lines and circles

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Using tangent and chord properties

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Circles and triangles

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Intersection of two circles

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Straight line graphs

y = mx + c

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Equations of straight lines

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Parallel and perpendicular lines

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Length and area

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Modelling with straight lines

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Transformations

Translating graphs

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Stretching and reflecting graphs

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Transforming graphs

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Sketching graphs

Cubic graphs

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Quartic graphs

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Reciprocal graphs

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Points of intersection

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Using the discriminant

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Direct and inverse proportion

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Polynomials

Functions

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Expanding brackets

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Factorising

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Simplifying algebraic fractions

$Simplifying algebraic fractions$

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Polynomial division

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The factor theorem

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Equations and inequalities

Linear simultaneous equations

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Quadratic simultaneous equations

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Set notation and interval notation

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Linear inequalities

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Quadratic inequalities

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Inequalities on graphs

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Inequality regions

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Quadratics

Solving quadratic equations

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Completing the square

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Quadratic graphs

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Identifying the discriminant

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Solving disguised quadratics

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Indices and surds

Laws of indices

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Negative and fractional indices

$Negative and fractional indices$

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Surds

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Rationalising the denominator

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Proof I

Mathematical structure and arguments

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Disproof by counterexample

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Proof by deduction

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