1.1 The use of brackets in algebraic expressions 1.2. Simplifying algebraic expressions 1.3 The solution of linear equations 1.4 Changing the subject of an algebraic expression 1.5 The solution of simple linear simultaneous equations 1.6 Use and manipulation of surds

Topic 2: Manipulation of algebraic expressions

2.1 Completing the square 2.2 The solution of quadratic equations (factorisation, the use of the formula and by completing the square 2.3 The discriminant of a quadratic equation 2.4 Sketching a quadratic function Topic 3: The remainder and factor theorems and solving cubic equations

3.1 Finding the remainder of a polynomial 3.2 Finding the linear factors of a polynomial 3.3 Solving a cubic equation by factorisation

Topic 4: Problem solving and inequalities

4.1 Setting up and solving problems 4.2 Manipulating inequalities 4.3 Solving linear and quadratic inequalities algebraically 4.4 Solving linear and quadratic inequalities graphically

Topic 5: The binomial expansion and probability

5.1 The binomial expansion of (a + b) ^{n} 5.2 Probability situations giving rise to the binomial distribution 5.3 Calculating probabilities using the binomial distribution

Section 2: Coordinate geometry

Topic 6: Coordinate geometry of straight lines

6.1 The gradient of a line 6.2 Calculating the distance between two points 6.3 Proving two lines are the same length using vectors 6.4 Finding the mid-point of a straight line joining two points 6.5 The equation of a straight line graph 6.6 Finding the gradient and the intercept on the y-axis from the equation of a straight line 6.7 Equations of vertical and horizontal lines 6.8 Finding the equation of a straight line 6.9 Condition for two straight lines to be parallel to each other 6.10 Condition for two straight lines to be perpendicular to each other 6.11 Determining the equation of a line that is parallel to another line 6.12 A quicker way to determine the equation of a line through a point that is parallel to another line 6.13 Proving that a point (x, y) lies on a line 6.14 Finding the coordinates of the point of intersection of two straight lines

Topic 7: Coordinate geometry of the circle

7.1 The equation of a circle 7.2 Finding the equation of a tangent to a circle 7.3 Finding where a circle and straight line intersect or meet

Topic 8: Inequalities and linear programming

8.1 Drawing lines and regions representing inequalities 8.2 Expressing real situations as linear inequalities 8.3 Maximisation and minimisation problems 8.4 Use of the objective function

Section 3: Trigonometry

Topic 9: Trigonometric ratios and the graphs of sine, cosine and tangent

9.1 Sine, cosine and tangent functions 9.2 Finding angles using the CAST method 9.3 Finding angles using trigonometric graphs 9.4 The sine and cosine rules Topic 10: Trigonometric identities and solving trigonometric equations

10.1 The trigonometric identities
tan𝜃=sin𝜃cos𝜃and cos𝜃 plus sin2𝜃=1 10.2 Solution of simple trigonometric equations in a given interval 10.3 Applying trigonometry to 2 and 3 dimensional problems

Section 4: Calculus

Topic 11: Differentiation

11.1 Differentiation of kxn and related sums 11.2 The gradient (i.e.dydx) of a curve and as a measure of rate of change 11.3 Gradients of tangents and normals, and their equations 11.4 Stationary points 11.5 Determining the nature of stationary points 11.6 Sketching a curve with known stationary points Topic 12: Integration

12.1 Integration as the reverse process of differentiation 12.2 Integration of kxn and related sums 12.3 Finding the constant of integration 12.4 Finding the equation of a curve, given its gradient function and one point

Topic 13: Definite integration

13.1 The difference between indefinite and definite integrals 13.2 Evaluation of definite integrals 13.3 Finding the area between a curve, two ordinates and the x-axis 13.4 Finding the area between two curves

Topic 14: Application of calculus to kinematics

14.1 Using differentiation and integration with respect to time to solve simple problems involving acceleration 14.2 Use of constant acceleration formulae where appropriate 14.3 Solving problems using the constant acceleration formulae

About the author:

Stephen Doyle is an experienced Mathematics teacher, examiner and bestselling author. He has taught in a variety of schools and colleges and has written and contributed to numerous books and other learning resources. He has written all of Illuminate's WJEC A Level Mathematics Study and Revision Guides as well as Mathematics for A Level Chemistry.