Providing complete syllabus support (9709), this stretching and practice-focused course builds the advanced skills needed for the latest Cambridge assessments and the transition to higher education. Engaging, real world examples make mathematics relevant to real life.
Providing complete syllabus support (9709), this stretching and practice-focused course builds the advanced skills needed for the latest Cambridge assessments and the transition to higher education. Engaging, real world examples make mathematics relevant to real life.
* Syllabus matching grid * 1 Algebra * 1.1: The modulus function * 1.2: Division of polynomials * 1.3: The remainder theorem * 1.4: The factor theorem * 2 Logarithms and exponential functions * 2.1: Continuous exponential growth and decay * 2.2: The logarithmic function * 2.3: ex and logarithms to base e * 2.4: Equations and inequalities using logarithms * 2.5: Using logarithms to reduce equations to linear form * 3 Trigonometry * 3.1: Secant, cosecant, and cotangent * 3.2: Further trigonometric identities * 3.3: Addition formulae * 3.4: Double angle formulae * 3.5: Expressing a sin + b cos in the form R sin( ± a) or R cos( ± a) * Review exercise A - Pure 2 * Review exercise A - Pure 3 * Maths in real-life: Predicting tidal behaviour * 4 Differentiation * 4.1: Differentiating the exponential function * 4.2: Differentiating the natural logarithmic function * 4.3: Differentiating products * 4.4: Differentiating quotients * 4.5: Differentiating sin x, cos x, and tan x * 4.6: Implicit differentiation * 4.7: Parametric differentiation * 5 Integration * 5.1: Integration of eax+b * 5.2: Integration of 1 x + b * 5.3: Integration of sin (ax + b), cos (ax + b), ec2 (ax + b) * 5.4: Extending integration of trigonometric functions * 5.5: Numerical integration using the trapezium rule * 6 Numerical solution of equations * 6.1: Finding approximate roots by change of sign or graphical methods * 6.2: Finding roots using iterative relationships * 6.3: Convergence behaviour of iterative functions * Review exercise B - Pure 2 * Review exercise B - Pure 3 * Maths in real-life: Nature of Mathematics * 7 Further algebra * 7.1: Partial fractions * 7.2: Binomial expansions of the form (1 + x)n when n is not a positive integer * 7.3: Binomial expansions of the form (a + x)n where n is not a positive integer * 7.4: Binomial expansions and partial fractions * 8 Further integration * 8.1: Integration using partial fractions * 8.2: Integration of f(x) f (x) * 8.3: Integration by parts * 8.4: Integration using substitution * Review exercise C - Pure 3 * 9 Vectors * 9.1: The equation of a straight line * 9.2: Intersecting lines * 9.3: The angle between two straight lines * 9.4: The equation of a plane * 9.5: Configurations of a line and a plane * 9.6: Configurations of two planes * 9.7: The distance from a point to a plane or line * 10 Differential equations * 10.1: Forming simple differential equations (DEs) * 10.2: Solving first-order differential equations with separable variables * 10.3: Finding particular solutions to differential equations * 10.4: Modelling with differential equations * 11 Complex numbers * 11.1: Introducing complex numbers * 11.2: Calculating with complex numbers * 11.3: Solving equations involving complex numbers * 11.4: Representing complex numbers geometrically * 11.5: Polar form and exponential form * 11.6: Loci in the Argand diagram * Review exercise D - Pure 3 * Maths in real-life: Electrifying, magnetic and damp: how complex mathematics makes life simpler * Exam-style paper A - Pure 2 * Exam-style paper B - Pure 2 * Exam-style paper C - Pure 3 * Exam-style paper D - Pure 3 * Answers * Glossary of terms * Index
* Syllabus matching grid * 1 Algebra * 1.1: The modulus function * 1.2: Division of polynomials * 1.3: The remainder theorem * 1.4: The factor theorem * 2 Logarithms and exponential functions * 2.1: Continuous exponential growth and decay * 2.2: The logarithmic function * 2.3: ex and logarithms to base e * 2.4: Equations and inequalities using logarithms * 2.5: Using logarithms to reduce equations to linear form * 3 Trigonometry * 3.1: Secant, cosecant, and cotangent * 3.2: Further trigonometric identities * 3.3: Addition formulae * 3.4: Double angle formulae * 3.5: Expressing a sin + b cos in the form R sin( ± a) or R cos( ± a) * Review exercise A - Pure 2 * Review exercise A - Pure 3 * Maths in real-life: Predicting tidal behaviour * 4 Differentiation * 4.1: Differentiating the exponential function * 4.2: Differentiating the natural logarithmic function * 4.3: Differentiating products * 4.4: Differentiating quotients * 4.5: Differentiating sin x, cos x, and tan x * 4.6: Implicit differentiation * 4.7: Parametric differentiation * 5 Integration * 5.1: Integration of eax+b * 5.2: Integration of 1 x + b * 5.3: Integration of sin (ax + b), cos (ax + b), ec2 (ax + b) * 5.4: Extending integration of trigonometric functions * 5.5: Numerical integration using the trapezium rule * 6 Numerical solution of equations * 6.1: Finding approximate roots by change of sign or graphical methods * 6.2: Finding roots using iterative relationships * 6.3: Convergence behaviour of iterative functions * Review exercise B - Pure 2 * Review exercise B - Pure 3 * Maths in real-life: Nature of Mathematics * 7 Further algebra * 7.1: Partial fractions * 7.2: Binomial expansions of the form (1 + x)n when n is not a positive integer * 7.3: Binomial expansions of the form (a + x)n where n is not a positive integer * 7.4: Binomial expansions and partial fractions * 8 Further integration * 8.1: Integration using partial fractions * 8.2: Integration of f(x) f (x) * 8.3: Integration by parts * 8.4: Integration using substitution * Review exercise C - Pure 3 * 9 Vectors * 9.1: The equation of a straight line * 9.2: Intersecting lines * 9.3: The angle between two straight lines * 9.4: The equation of a plane * 9.5: Configurations of a line and a plane * 9.6: Configurations of two planes * 9.7: The distance from a point to a plane or line * 10 Differential equations * 10.1: Forming simple differential equations (DEs) * 10.2: Solving first-order differential equations with separable variables * 10.3: Finding particular solutions to differential equations * 10.4: Modelling with differential equations * 11 Complex numbers * 11.1: Introducing complex numbers * 11.2: Calculating with complex numbers * 11.3: Solving equations involving complex numbers * 11.4: Representing complex numbers geometrically * 11.5: Polar form and exponential form * 11.6: Loci in the Argand diagram * Review exercise D - Pure 3 * Maths in real-life: Electrifying, magnetic and damp: how complex mathematics makes life simpler * Exam-style paper A - Pure 2 * Exam-style paper B - Pure 2 * Exam-style paper C - Pure 3 * Exam-style paper D - Pure 3 * Answers * Glossary of terms * Index
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