Each chapter keeps explanations, definitions and exam advice together—without mixing in quizzes or practice questions.
CHAPTER 1
Functions
Use domains, ranges, inverse functions, composite functions and modulus transformations.
An inverse exists only after the function is one-to-one on its stated domain.
CHAPTER 2
Quadratic functions
Use completed-square form, discriminants, graphs, roots and quadratic inequalities.
The discriminant connects the number of roots to intersections and tangency.
CHAPTER 3
Factors of polynomials
Apply remainder and factor theorems, divide polynomials and solve cubic equations.
A zero remainder proves that the corresponding linear expression is a factor.
CHAPTER 4
Equations, inequalities and graphs
Solve modulus problems, substituted equations and cubic inequalities using algebra and graphs.
Every algebraic solution must still satisfy the original equation and its restrictions.
CHAPTER 5
Simultaneous equations
Use substitution or elimination with linear, quadratic, reciprocal and product relationships.
Eliminate one variable carefully, then test every resulting pair in both equations.
CHAPTER 6
Logarithmic and exponential functions
Use logarithm laws, change of base, inverse graphs, asymptotes and exponential equations.
The argument of every real logarithm must be strictly positive.
CHAPTER 7
Straight-line graphs
Use line geometry and transform nonlinear relationships into straight-line form.
Name the plotted variables before reading the transformed gradient and intercept.
CHAPTER 8
Coordinate geometry of the circle
Work with circle equations, intersections, tangents, common chords and relative positions.
Subtracting two circle equations removes the squared terms and reveals the common chord.
CHAPTER 9
Circular measure
Use radians to calculate arcs, sectors, segments and compound circular regions.
The formulas s = rθ and A = ½r²θ require θ in radians.
CHAPTER 10
Trigonometry
Use six trigonometric functions, graphs, identities, equations and proofs.
Solve within the transformed-angle domain before converting back to the requested variable.
CHAPTER 11
Permutations and combinations
Distinguish arrangements from selections and calculate using factorial notation.
Ask whether order creates a different outcome before choosing nPr or nCr.
CHAPTER 12
Series
Use binomial expansions, arithmetic and geometric progressions, and convergent infinite series.
The general binomial term is the safest way to target one required power.
CHAPTER 13
Vectors in two dimensions
Calculate with vectors, position and unit vectors, geometry, velocity and collision models.
Two moving particles collide only when both position components agree at the same time.
CHAPTER 14
Calculus
Differentiate, integrate and apply calculus to graphs, optimisation, rates, areas and kinematics.
Connect the algebraic derivative or integral to what the quantity means in context.