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Complete Pure Mathematics 2 & 3 for Cambridge International AS & A Level
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Develop advanced mathematical skills with a real-world focus

Table of Contents

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 *C + b cos *C in the form R sin(*C ± a) or R cos(*C ± 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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