Maths

Vector methods with projectiles

Theory

Exercises

Learning Goals

Variable acceleration in one dimension

Theory

Exercises

Learning Goals

Differentiating vectors

Theory

Exercises

Learning Goals

Integrating vectors

Theory

Exercises

Learning Goals

Study Tips

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Application of forces

Friction with static particles

Static particles

Theory

Exercises

Learning Goals

Modelling with statics

Theory

Exercises

Learning Goals

Theory

Exercises

Learning Goals

Statics of rigid bodies

Theory

Exercises

Learning Goals

Dynamics and inclined planes

Theory

Exercises

Learning Goals

Connected particles

Theory

Exercises

Learning Goals

Projectiles

Projectiles: Horizontal and vertical components

Horizontal projection

Theory

Exercises

Learning Goals

Theory

Exercises

Learning Goals

Projection at any angle

Theory

Exercises

Learning Goals

Equation of the trajectory of a projectile

Theory

Exercises

Learning Goals

Forces and friction

Resolving forces

Theory

Exercises

Learning Goals

Inclined planes

Theory

Exercises

Learning Goals

The coefficient of friction

Theory

Exercises

Learning Goals

Moments

Moments

Theory

Exercises

Learning Goals

Resultant moments

Theory

Exercises

Learning Goals

Equilibrium

Theory

Exercises

Learning Goals

Centre of mass

Theory

Exercises

Learning Goals

Tilting

Theory

Exercises

Learning Goals

Laminas

Theory

Exercises

Learning Goals

Forces and motion

Force diagrams

Theory

Exercises

Learning Goals

Forces as vectors

Theory

Exercises

Learning Goals

Forces and acceleration

Theory

Exercises

Learning Goals

Motion in two dimensions

Theory

Exercises

Learning Goals

Connected particles

Theory

Exercises

Learning Goals

Pulleys

Theory

Exercises

Learning Goals

Variable acceleration

Functions of time: Displacement, velocity, acceleration

Theory

Exercises

Learning Goals

Using differentiation to find velocity and acceleration

Theory

Exercises

Learning Goals

Maxima and minima problems

Theory

Exercises

Learning Goals

Using integration to find velocity and displacement

Theory

Exercises

Learning Goals

Constant acceleration formulae

Theory

Exercises

Learning Goals

Constant acceleration

Constant acceleration: Deriving formulae

Displacement-time graphs

Theory

Exercises

Learning Goals

Velocity-time graphs

Theory

Exercises

Learning Goals

Theory

Exercises

Learning Goals

Constant acceleration formulae: SUVAT

Theory

Exercises

Learning Goals

Vertical motion under gravity

Theory

Exercises

Learning Goals

Modelling in mechanics

Modelling assumptions

Theory

Exercises

Learning Goals

Quantities and units in mechanics

Theory

Exercises

Learning Goals

Working with vectors

Theory

Exercises

Learning Goals

Normal distribution

The normal distribution: Finding probabilities

The normal distribution

Theory

Exercises

Learning Goals

Theory

Exercises

Learning Goals

The inverse normal distribution function

Theory

Exercises

Learning Goals

The standard normal distribution

Theory

Exercises

Learning Goals

Finding the mean and standard deviation

Theory

Exercises

Learning Goals

Normal approximation to the binomial distribution

Theory

Exercises

Learning Goals

Hypothesis testing with the normal distribution

Theory

Exercises

Learning Goals

Conditional probability

Conditional probability in Venn diagrams

Set notation

Theory

Exercises

Learning Goals

Conditional probability

Theory

Exercises

Learning Goals

Theory

Exercises

Learning Goals

Probability formulae

Theory

Exercises

Learning Goals

Conditional probability: Tree diagrams

Theory

Exercises

Learning Goals

Correlation and hypothesis testing

Exponential models

Theory

Exercises

Learning Goals

Measuring correlation

Theory

Exercises

Learning Goals

Hypothesis testing for zero correlation

Theory

Exercises

Learning Goals

Hypothesis testing I

Hypothesis testing: Finding critical values

Hypothesis testing

Theory

Exercises

Learning Goals

Theory

Exercises

Learning Goals

One-tailed tests

Theory

Exercises

Learning Goals

Two-tailed tests

Theory

Exercises

Learning Goals

Binomial distribution

Probability distributions

Theory

Exercises

Learning Goals

The binomial distribution

Theory

Exercises

Learning Goals

Cumulative probabilities

Theory

Exercises

Learning Goals

Probability

Calculating probabilities

Theory

Exercises

Learning Goals

Venn diagrams

Theory

Exercises

Learning Goals

Probability: Mutually exclusive and independent events

Theory

Exercises

Learning Goals

Probability: Tree diagrams

Theory

Exercises

Learning Goals

Representation of data

Measures of location and spread

Outliers

Theory

Exercises

Learning Goals

Box plots

Theory

Exercises

Learning Goals

Cumulative frequency

Theory

Exercises

Learning Goals

Histograms

Theory

Exercises

Learning Goals

Comparing data sets

Theory

Exercises

Learning Goals

Correlation

Theory

Exercises

Learning Goals

Linear regression

Theory

Exercises

Learning Goals

Measures of central tendency: Mean, median, mode

Theory

Exercises

Learning Goals

Measures of spread: Range

Theory

Exercises

Learning Goals

Variance and standard deviation

Theory

Exercises

Learning Goals

Data collection

Population and samples

Theory

Exercises

Learning Goals

Sampling techniques

Theory

Exercises

Learning Goals

Types of data

Theory

Exercises

Learning Goals

Vectors II

Solving geometric problems

3D coordinates

Theory

Exercises

Learning Goals

Vectors in 3D

Theory

Exercises

Learning Goals

Theory

Exercises

Learning Goals

Applications to mechanics: 3D vectors

Theory

Exercises

Learning Goals

Numerical methods

Staircase and cobweb diagrams

Locating roots

Theory

Exercises

Learning Goals

Iteration

Theory

Exercises

Learning Goals

Theory

Exercises

Learning Goals

Newton-Raphson method

Theory

Exercises

Learning Goals

Numerical methods: Applications to modelling

Theory

Exercises

Learning Goals

Integration II

See All (11)

Integrating standard functions

Theory

Exercises

Learning Goals

Integrating f(ax + b)

Theory

Exercises

Learning Goals

Integration with trigonometric identities

Theory

Exercises

Learning Goals

Reverse chain rule

Theory

Exercises

Learning Goals

Integration by substitution

Theory

Exercises

Learning Goals

Integration by parts

Theory

Exercises

Learning Goals

$Integration using partial fractions$

Integration using partial fractions

Theory

Exercises

Learning Goals

Finding areas using integration

Theory

Exercises

Learning Goals

The trapezium rule

Theory

Exercises

Learning Goals

Solving differential equations

Theory

Exercises

Learning Goals

Modelling with differential equations

Theory

Exercises

Learning Goals

Differentiation II

See All (11)

Differentiating sin x and cos x

Theory

Exercises

Learning Goals

Differentiating exponentials and logarithmic functions

Theory

Exercises

Learning Goals

The chain rule

Theory

Exercises

Learning Goals

The product rule

Theory

Exercises

Learning Goals

The quotient rule

Theory

Exercises

Learning Goals

Differentiating inverse functions

Theory

Exercises

Learning Goals

Differentiating trigonometric functions

Theory

Exercises

Learning Goals

Parametric differentiation

Theory

Exercises

Learning Goals

Implicit differentiation

Theory

Exercises

Learning Goals

Second derivatives: Concave and convex functions

Theory

Exercises

Learning Goals

Connected rates of change

Theory

Exercises

Learning Goals

Trigonometry and modelling

Using the angle addition formulae

Addition formulae

Theory

Exercises

Learning Goals

Theory

Exercises

Learning Goals

Double angle formulae

Theory

Exercises

Learning Goals

Solving trigonometric equations: Double angle formula

Theory

Exercises

Learning Goals

Simplifying a cos x + b sin x

Theory

Exercises

Learning Goals

Proving trigonometric identities

Theory

Exercises

Learning Goals

Modelling with trigonometric functions

Theory

Exercises

Learning Goals

Trigonometric functions

Secant, cosecant and cotangent

Theory

Exercises

Learning Goals

Graphs of sec x, cosec x and cot x

Theory

Exercises

Learning Goals

Solving equations with sec x, cosec x and cot x

Theory

Exercises

Learning Goals

Further trigonometric identities

Theory

Exercises

Learning Goals

Inverse trigonometric functions

Theory

Exercises

Learning Goals

Radians

Areas of sectors and segments

Radian measure

Theory

Exercises

Learning Goals

Arc length

Theory

Exercises

Learning Goals

Theory

Exercises

Learning Goals

Solving trigonometric equations

Theory

Exercises

Learning Goals

Small angle approximations

Theory

Exercises

Learning Goals

Sequences and series

See All (8)

Sequences revision

Theory

Exercises

Learning Goals

Arithmetic sequences

Theory

Exercises

Learning Goals

Arithmetic series

Theory

Exercises

Learning Goals

Geometric sequences

Theory

Exercises

Learning Goals

Geometric series

Theory

Exercises

Learning Goals

Sum to infinity

Theory

Exercises

Learning Goals

Sigma notation

Theory

Exercises

Learning Goals

Modelling with sequences and series

Theory

Exercises

Learning Goals

Binomial expansion II

Binomial expansion: (1+x)^n

Theory

Exercises

Learning Goals

Binomial expansion: (a+bx)^n

Theory

Exercises

Learning Goals

$Binomial expansion with partial fractions$

Binomial expansion with partial fractions

Theory

Exercises

Learning Goals

Binomial expansion of compound expressions

Theory

Exercises

Learning Goals

Parametric equations

Using trigonometric identities

Parametric equations

Theory

Exercises

Learning Goals

Theory

Exercises

Learning Goals

Sketching parametric curves

Theory

Exercises

Learning Goals

Points of intersection of parametric curves

Theory

Exercises

Learning Goals

Modelling with parametric equations

Theory

Exercises

Learning Goals

Functions

See All (8)

Functions and mappings

Theory

Exercises

Learning Goals

Composite functions

Theory

Exercises

Learning Goals

Inverse functions

Theory

Exercises

Learning Goals

The modulus function

Theory

Exercises

Learning Goals

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

Theory

Exercises

Learning Goals

Combining transformations

Theory

Exercises

Learning Goals

Solving modulus equations

Theory

Exercises

Learning Goals

Modulus inequalities

Theory

Exercises

Learning Goals

Algebraic fractions

Operations with algebraic fractions

$Operations with algebraic fractions$

Theory

Exercises

Learning Goals

$Partial fractions$

Partial fractions

Theory

Exercises

Learning Goals

Repeated factors

Theory

Exercises

Learning Goals

Algebraic division

Theory

Exercises

Learning Goals

Proof II

Proof by contradiction

Theory

Exercises

Learning Goals

Criticising proofs

Theory

Exercises

Learning Goals

Vectors I

Magnitude and direction of a vector

Vectors

Theory

Exercises

Learning Goals

Representing vectors

Theory

Exercises

Learning Goals

Theory

Exercises

Learning Goals

Position vectors and displacement vectors

Theory

Exercises

Learning Goals

Solving geometric problems

Theory

Exercises

Learning Goals

Modelling with vectors

Theory

Exercises

Learning Goals

Integration I

Finding functions by integrating

Integrating x^n

Theory

Exercises

Learning Goals

Indefinite integrals

Theory

Exercises

Learning Goals

Theory

Exercises

Learning Goals

Definite integrals

Theory

Exercises

Learning Goals

Area under a curve

Theory

Exercises

Learning Goals

Area under the x-axis

Theory

Exercises

Learning Goals

Area between a curve and a line

Theory

Exercises

Learning Goals

Differentiation I

See All (10)

Finding the gradient of a curve

Theory

Exercises

Learning Goals

Differentiation from first principles

Theory

Exercises

Learning Goals

Differentiating x^n

Theory

Exercises

Learning Goals

Differentiating functions with multiple terms

Theory

Exercises

Learning Goals

Gradients, tangents and normals

Theory

Exercises

Learning Goals

Increasing and decreasing functions

Theory

Exercises

Learning Goals

Second order derivatives

Theory

Exercises

Learning Goals

Stationary points

Theory

Exercises

Learning Goals

Sketching gradient functions

Theory

Exercises

Learning Goals

Modelling with differentiation

Theory

Exercises

Learning Goals

Exponentials and logarithms

See All (9)

Exponential functions

Theory

Exercises

Learning Goals

y = e^x

Theory

Exercises

Learning Goals

Exponential modelling

Theory

Exercises

Learning Goals

Logarithms

Theory

Exercises

Learning Goals

Laws of logarithms

Theory

Exercises

Learning Goals

Solving equations using logarithms

Theory

Exercises

Learning Goals

Natural logarithms

Theory

Exercises

Learning Goals

Logarithms and non-linear data

Theory

Exercises

Learning Goals

Harder exponential modelling

Theory

Exercises

Learning Goals

Trigonometric equations

Angles in all four quadrants

Theory

Exercises

Learning Goals

Exact trigonometric values

Theory

Exercises

Learning Goals

Trigonometric identities

Theory

Exercises

Learning Goals

Simple trigonometric equations

Theory

Exercises

Learning Goals

Harder trigonometric equations

Theory

Exercises

Learning Goals

Equations and identities

Theory

Exercises

Learning Goals

Trigonometry

Solving triangle problems

The cosine rule

Theory

Exercises

Learning Goals

The sine rule

Theory

Exercises

Learning Goals

Area of a triangle

Theory

Exercises

Learning Goals

Theory

Exercises

Learning Goals

Trig graphs: sin x, cos x, tan x

Theory

Exercises

Learning Goals

Transforming trigonometric graphs

Theory

Exercises

Learning Goals

Binomial expansion I

Solving binomial problems

Pascal's triangle

Theory

Exercises

Learning Goals

Factorial notation

Theory

Exercises

Learning Goals

Binomial expansion

Theory

Exercises

Learning Goals

Theory

Exercises

Learning Goals

Binomial estimation

Theory

Exercises

Learning Goals

Circles

Midpoints and perpendicular bisectors

Theory

Exercises

Learning Goals

Equation of a circle

Theory

Exercises

Learning Goals

Intersection of straight lines and circles

Theory

Exercises

Learning Goals

Using tangent and chord properties

Theory

Exercises

Learning Goals

Circles and triangles

Theory

Exercises

Learning Goals

Intersection of two circles

Theory

Exercises

Learning Goals

Straight line graphs

Equations of straight lines

y = mx + c

Theory

Exercises

Learning Goals

Theory

Exercises

Learning Goals

Parallel and perpendicular lines

Theory

Exercises

Learning Goals

Length and area

Theory

Exercises

Learning Goals

Modelling with straight lines

Theory

Exercises

Learning Goals

Transformations

Translating graphs

Theory

Exercises

Learning Goals

Stretching and reflecting graphs

Theory

Exercises

Learning Goals

Transforming graphs

Theory

Exercises

Learning Goals

Sketching graphs

Direct and inverse proportion

Cubic graphs

Theory

Exercises

Learning Goals

Quartic graphs

Theory

Exercises

Learning Goals

Reciprocal graphs

Theory

Exercises

Learning Goals

Points of intersection

Theory

Exercises

Learning Goals

Using the discriminant

Theory

Exercises

Learning Goals

Theory

Exercises

Learning Goals

Polynomials

Simplifying algebraic fractions

Functions

Theory

Exercises

Learning Goals

Expanding brackets

Theory

Exercises

Learning Goals

Factorising

Theory

Exercises

Learning Goals

$Simplifying algebraic fractions$

Theory

Exercises

Learning Goals

Polynomial division

Theory

Exercises

Learning Goals

The factor theorem

Theory

Exercises

Learning Goals

Equations and inequalities

Linear simultaneous equations

Theory

Exercises

Learning Goals

Quadratic simultaneous equations

Theory

Exercises

Learning Goals

Set notation and interval notation

Theory

Exercises

Learning Goals

Linear inequalities

Theory

Exercises

Learning Goals

Quadratic inequalities

Theory

Exercises

Learning Goals

Inequalities on graphs

Theory

Exercises

Learning Goals

Inequality regions

Theory

Exercises

Learning Goals

Quadratics

Solving quadratic equations

Theory

Exercises

Learning Goals

Completing the square

Theory

Exercises

Learning Goals

Quadratic graphs

Theory

Exercises

Learning Goals

Identifying the discriminant

Theory

Exercises

Learning Goals

Solving disguised quadratics

Theory

Exercises

Learning Goals

Indices and surds

Negative and fractional indices

Laws of indices

Theory

Exercises

Learning Goals

$Negative and fractional indices$

Theory

Exercises

Learning Goals

Surds

Theory

Exercises

Learning Goals

Rationalising the denominator

Theory

Exercises

Learning Goals

Proof I