Additional Mathematics for OCR (Heftet (myke permer))

Val Hanrahan has been Head of Maths at an Independent school. She has also written several Pure Maths A/AS texts. Roger Porkess has written and edited books for GCSE, A/AS level and Key Stage 3.

The content of the course covers four areas from Pure Mathematics - algebra, coordinate geometry, trigonometry and calculus and three areas from Applied Mathematics - statistics, mechanics and decision and discrete maths. This course is ideal preparation for all students going on to either AS/A2 Mathematics or Further Mathematics courses. Not only will it give a taster of work to come it may accelerate students' progress in their next course.

1 Algebra: review Linear expressions Solving linear equations Changing the subject of an equation Quadratic expressions Solving a quadratic equation that factorises Completing the square Simultaneous equations 2 Algebra: techniques Linear inequalities Solving quadratic inequalities Manipulating algebraic fractions Solving equations involving fractions Simplifying expressions containing square roots 3 Algebra: polynomials Operations with polynomials The Factor Theorem The Remainder Theorem 4 Algebra: applications The binomial expansion The binomial distribution 5 Co-ordinate geometry I Co-ordinates The gradient of a line Parallel and perpendicular lines The distance between two points Midpoint of a line joining two points The equation of a straight line Drawing a line given its equation Finding the equation of a line Intersection of two lines The circle 6 Co-ordinate geometry II, applications Inequalities Using inequalities for problem solving 7 Trigonometry I Using trigonometry in right angled triangles Trigonometrical functions for angles of any size Solving trigonometrical equations Identities involving sintheta, costheta, and tantheta The area of a triangle The Sine and Cosine rules 8 Trigonometry II -- Applications Applications of the Sine and Cosine rules in 2-D Height and distance problems in 3-D 3-D problems involving solids 9 Calculus I - Differentiation Finding the gradient of a curve Differentiating by using standard results Tangents and normals Stationary points Curve sketching 10 Calculus II - Integration Reversing differentiation Using integration to find areas 11 Calculus III - Applications to kinematics Variable acceleration problems The formulae for constant acceleration