High School Mathematics

Elementary (Key Stage 3)

Algebra

Collecting Terms

Number

Arithmetic

Skill - addition (1)

Skill - addition (2)

Skill - addition with negatives (1)

Skill - subtraction (1)

Skill - subtraction into negatives (1)

Skill - subtraction with negatives (1)

Skill - multiplication (1)

Skill - multiplication (2)

Skill - multiplication with negatives (1)

Skill - division (1)

Skill - division (2)

Skill - division_with_negatives (1)

Fractions

Skill - fractions addition (same denominator) (1)

Skill - fractions subtraction (same denominator) (1)

Skill - fractions multiplication (1)

Skill - fractions division (1)

Percentages

Skill - convert percentages to decimals and fractions (1)

Skill - given a percentage of an amount, find 100% of that amount (1)

Skill - increase by a percentage (multiples of 5%) (1)

Skill - decrease by a percentage (multiples of 5%) (1)

Ratio

Skill - simplify a ratio (1)

Skill - simplify an algebraic ratio (1)

Skill - simplify a ratio of time units (1)

Skill - simplify a ratio of length units (1)

Powers and Roots

Skill - evaluating squares and cubes (1)

Skill - evaluating square roots and cube roots (1)

Skill - evaluating powers and roots (1)

Geometry

Probability and Statistics

Averages

Skill - find the mode (1)

Skill - find the median (1)

Skill - find the mean (1)

Junior (Key Stage 4)

Algebra

Algebraic Fractions

Skill - simplifying (1)

Skill - simplifying (2)

Worked Examples (quartet) - simplifying

Worked Examples (quartet) - add, subtract, simplify

Collecting Terms

Skill - collecting like terms (1)

Skill - collecting like terms (2)

Equation Identity Formula

Quiz - equation, identity, formula

Expanding Brackets

Skill - expanding double brackets (1)

Skill - expanding double brackets (2)

Skill - expanding double brackets (3)

Worked Examples (quartet) - expanding single brackets

Worked Examples (quartet) - expanding double brackets

Factorising

Skill - factorising (1)

Skill - factorising (2)

Skill - factorising (3)

Skill - factorising difference of squares (1)

Skill - factorising difference of squares (2)

Skill - factorising monic quadratics (1)

Skill - factorising non-monic quadratics (1)

Skill - factorising non-monic quadratics (2)

Linear Equations

Skill - linear equations (1)

Skill - linear equations (2)

Problem solving - linear equations (1)

Problem solving - linear equations(2)

Quiz - equation of a line (parallel,perpedicular,skew) (1)

Quiz - equation of a line (parallel,perpedicular,skew) (2)

Equation of a Line

Gapfill - equation of a line (1)

Gapfill - equation of a line (2)

Gapfill - equation of a line (3)

Proportion

Quadratics

Skill - solving difference of squares

Skill - solving by the quadratic formula

Skill - solving monic quadratics

Skill - solving non-monic quadratics

Skill - completing the square (1)

Problem solving - with quadratics (1)

Problem solving - with quadratics (2)

Worked Examples (quartet) - rearranging quadratics and solving

Worked Examples (quartet) - solving quadratics

Quiz - roots of a quadratic

Rearranging

Skill - rearranging (1)

Sequences

Skill - nth term of an arithmetic sequence (1)

Skill - nth term of an arithmetic sequence (2)

Simultaneous Equations

Worked Examples (quartet) - simultaneous equations (1)

Worked Examples (quartet) - simultaneous equations (2)

Problem solving - with simultaneous equations (1)

Problem solving - with simultaneous equations (2)

Quiz - simultaneous equations

Number

Fractions

Skill - addition of fractions (1)

Skill - subtraction of fractions (1)

Skill - multiplication of fractions (1)

Skill - division of fractions (1)

Indices

Skill - indices with multiplication (1)

Skill - indices with multiplication (2)

Skill - indices with division (1)

Skill - indices with exponent (1)

Skill - indices with multiplication, division and exponent

Skill - positive fractional indices (1)

Standard Form

Skill - standard form with multiplication (1)

Skill - standard form with division (1)

Skill - standard form from ordinary number

Skill - standard form to ordinary number

Surds

Skill - collect and simplify (1)

Skill - collect and simplify (2)

Skill - divide and simplify

Skill - multiply and simplify (1)

Skill - multiply and simplify (2)

Skill - single brackets

Skill - double brackets

Skill - rationalise denominator

Geometry

Circle Theorems

Diagram - angles subtended by the same arc

Diagram - angles subtended by the diameter

Diagram - angle at the centre and at the circumference

Diagram - opposite angles of a cyclic quadrilateral

Diagram - alternate segment

Diagram - tangent meets radius at 90 degrees

Diagram - tangents from the same point ouside the circle are of equal length

Pythagoras

Worked Examples (quartet) - using Pythagorean triples (one)

Worked Examples (quartet) - using Pythagorean triples (two)

Worked Examples (quartet) - with isosceles triangles

Trigonometry

Quiz - exact values (1)

Quiz - exact values (2)

Worked example (trio) - rearranging trigonometric ratios (1)

Worked example (quartet) - solving trigonometric equations (1)

Worked example - cosine rule (proof) (1)

Worked example - cosine rule (find missing side length) (1)

Worked example - cosine rule (find missing angle) (1)

Senior (Key Stage 5)

Pure

Algebraic and Partial Fractions

Worked Example (trio) - algebraic fractions (division) (1)

Worked Example (trio) - partial fractions (1)

Worked Example (pair) - partial fractions (repeated term in denominator) (1)

Worked Example (pair) - partial fractions (quadratic factor in denominator) (1)

Binomial Theorem

Skill - trinomial expansion

Worked Example (pair) - binomial expansion with positive integer index

Worked Example (pair) - binomial expansion with positive fractional index

Worked Example (pair) - binomial expansion with negative integer index

Worked Example (pair) - factoring out (binomial expansion for (a+bx)ⁿ, where n is negative or fractional)

Complex Numbers

Skill - using i

Worked Examples (quartet) - using the form bi

Worked Examples (quartet) - adding and subtracting complex numbers

Worked Examples (pair) - solving quadratics (1)

Worked Examples (pair) - solving quadratics (2)

Worked Example - deMoivre from powers

Worked Example - deMoivre to powers

Worked example - roots of complex numbers

Worked Example - roots of unity

Worked Example - z identities

Coordinate Geometry

Skill - determine centre and radius of a circle from an equation

Gapfill - equation of a line (1)

Differential Equations

Worked Example - separation of variables

Worked Example - integrating factor

General - Second Order Differential Equations

Worked Example - second order equation with two roots

Worked Example - second order equation with a repeated root

Worked Example - second order equation with complex roots

Worked Example - second order equation involving trigonometric function and a particular integral

Worked Example - coupled first-order simultaneous equations

Differentiation

Worked Example - differentiation by first principles (1)

Worked Example - differentiation by first principles (2)

Worked Example - differentiation by first principles (3)

Worked Example - chain rule

Worked Example - product rule

Worked Example - quotient rule

Worked Example - differentiating inverse trigonometric functions

Worked Example - differentiatiating inverse tan by substitution and implicitly

Exponentials and Logarithms

Proofs of Log Laws

Functions

Diagram - many to one

Diagram - one to many

Diagram - one to one

Diagram - one to none

Diagram - one to many example

Diagram - one to one example

Interactive - domain and range example (1)

Interactive - domain and range example (2)

Quartet - composite functions

Worked Example - piecewise functions (1)

Worked Example - piecewise functions (2)

Worked Example - piecewise functions (3)

Worked Example - solving piecewise functions (1)

Worked Example - solving piecewise functions (2)

Worked Example - inverse functions (1)

Worked Example - inverse functions (2)

Worked Example - inverse functions (3)

Worked Example - inverse functions (4)

Worked Example - self inverse functions

Quiz - function mappings

Quiz - piecewise functions

Quiz - possible functions

Hyperbolic Functions

Worked Example - arcosh into ln

Worked Example - arsinh into ln

Worked Example - artanh into ln

Worked Example (trio) - differentiating inverse hyperbolic functions

Integration

Standard Integrals

Skill - indefinite integration with polynomials (1)

Skill - indefinite integration with polynomials (2)

Skill - definite integration with polynomials

Worked Example - reverse chain rule (definite) (1)

Worked Example (quartet) - reverse chain rule (indefinite) (1)

Worked Example (pair) - integration by substitution (indefinite) (1)

Worked Example (pair) - integration by substitution (definite) (1)

Worked Example - integration by parts (indefinite) (1)

Worked Example - special cases (integrate lnx, cos²x, sin²x, tan²x)

Matrices

Worked Example - inverse matrices (1)

Worked Example - inverse matrices (2)

Polar Coordinates

Worked Example - converting polar coordinates

Worked Example - area bounded by a polar curve

Trigonometry

Trigonometric Identities

Formulae - addition, sum and product

Graphs - reciprocal trigonometric functions

Worked Example (pair) - solving f(nθ) = c

Worked Example - solving trigonometric equations of the form (ax+b)

Worked Example - solving trigonometric quadratics (without substitution of identities)

Worked Example - solving trigonometric quadratic (with substitution of identities)

Worked Example - solving inverse trigonometric quadratic (with substitution of identities)

Probability and Statistics

Correlation and Regression

Correlation (Table)

Uniform Distribution

Area of a circle

Area of a square

Mean and variance