Patterns
Find patterns that repeat or grow, and say what comes next.
- Patterns that repeat
- Making your own patterns
- Number patterns
- Patterns that grow
- Patterns in sums
5 chapters planned
Algebra
Every book on this topic, lowest level first. Each one builds on the book above it. If a book feels hard, go back up the ladder to the one before.
NextYou are here Patterns and rules
Find the rule behind a pattern and use it to say what comes next.
- Number sequences
- Growing shape patterns
- Number machines
- Missing numbers
- Odd and even rules
- Square and triangle numbers
- Jumping far ahead
7 chapters
NextYou are here Letters for numbers and simple equations
Use letters to stand for numbers, tidy up expressions, and solve simple equations.
- Letters for unknown numbers
- Putting numbers in
- Collecting like terms
- Brackets
- Solving equations in one step
- Solving equations in two steps
- Writing your own equations
- Sequences and the nth term
8 chapters
NextYou are here Coordinates and straight lines
Plot points on a grid and draw the straight lines that rules make.
- Coordinates
- All four quarters of the grid
- Shapes on a grid
- From a rule to a line
- Lines like x = 3 and y = −2
- Steepness: the gradient
- The equation y = mx + c
- Graphs from real life
8 chapters
Linear and simultaneous equations
Solve linear equations and inequalities, and find two unknowns at once.
- Harder linear equations
- Changing the subject
- Inequalities
- Equations of straight lines
- Two equations: adding or taking away
- Two equations: substitution
- Two equations on a graph
- Word problems and regions
8 chapters planned
Quadratics
Expand, factorise and solve quadratic equations, and draw their curved graphs.
- Expanding two brackets
- Factorising quadratics
- Using factorising
- Completing the square
- The quadratic formula
- Graphs of quadratics
- Quadratic sequences
- A line and a curve
8 chapters planned
Functions and graphs
Use function notation, learn the shapes of the main graphs, and move them about.
- Function notation
- Composite and inverse functions
- Cubic, reciprocal and circle graphs
- Exponential graphs
- Graphs of sin, cos and tan
- Moving graphs
- Gradients and areas under graphs
- Solving with graphs and trials
8 chapters planned
Functions, polynomials and the binomial
Work with polynomials, use the factor theorem, and expand brackets raised to any power.
- Domain, range and inverses
- The modulus function
- Dividing polynomials
- The factor theorem
- Partial fractions
- Pascal's triangle and choosing
- The binomial expansion
7 chapters planned
Exponentials and logarithms
Use the number e and logarithms to model growth and to solve equations where the unknown is a power.
- Exponential functions
- Logarithms
- Laws of logarithms
- Equations with powers
- The number e and natural logs
- Growth and decay models
- Straight lines from logs
7 chapters planned
Differentiation
Find how fast things change, and use it to find the highest and lowest points of curves.
- The gradient of a curve
- Differentiating powers
- Tangents and normals
- Turning points
- Biggest and smallest
- Exponentials, logs and trig functions
- Chain, product and quotient rules
- Connected rates and implicit curves
8 chapters planned
Integration
Undo differentiation to find areas under curves and totals from rates.
- Undoing differentiation
- Definite integrals and area
- Area between curves
- More functions to integrate
- Substitution and integration by parts
- Estimating areas
- Differential equations
- Motion and totals
8 chapters planned
Proof, sequences and series
Learn to prove things for certain, and work with sequences and their sums.
- What a proof is
- Proof by contradiction
- Sequences
- Sigma notation
- Arithmetic series
- Geometric series
- Proof by induction
- Limits and series that settle
8 chapters planned