Oxford International AQA Examinations: International A2 Level Mathematics Pure and Mechanics
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Description
Contents
Reviews
Language
English
ISBN
9780198411413
Front Cover
Title Page
Contents
About this book
1 Functions
1.1 Functions
1.2 Composite functions
1.3 Inverse functions
1.4 Modulus functions
1.5 Combinations of transformations
1.6 Simplification of rational functions
1.7 Algebraic division
1.8 Partial fractions
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Assessment
2 Binomial Series
2.1 The binomial series for any value of n
2.2 Approximations
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3 Trigonometric Functions and Formulae
3.1 The inverse trigonometric functions
3.2 The reciprocal trigonometric functions
3.3 Trigonometric formulae
3.4 Compound angle formulae
3.5 Expressions of the formf(θ) = a cos θ + b sin θ
3.6 Double angle formulae
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Assessment
4 Exponential and Logarithmic Functions
4.1 Exponential growth and decay
4.2 The exponential function
4.3 Natural logarithms
4.4 The logarithmic function
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5 Differentiation
5.1 The derivative of ex
5.2 The derivative of ln x
5.3 The derivatives of sin x and cos x
5.4 Differentiating products, quotients and composite functions
5.5 Implicit functions
5.6 Parametric equations
5.7 Finding dy/dx using parametric equations
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Assessment
6 Integration
6.1 Standard integrals
6.2 Integrating products by substitution
6.3 Integration by parts
6.4 Integrating fractions
6.5 Special techniques for integrating some trigonometric functions
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7 Differential Equations
7.1 First order differential equations with separable variables
7.2 Natural occurrence of differential equations
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8 Numerical Methods
8.1 Approximately locating the roots of an equation
8.2 Using the iteration xn + 1 = g(xn)
8.3 Rules to find the approximate value of an area under a curve
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9 Vectors
9.1 Properties of vectors
9.2 Position vectors
9.3 The location of a point in space
9.4 Operations on cartesian vectors
9.5 Properties of a line joining two points
9.6 The equation of a straight line
9.7 Pairs of lines
9.8 The scalar product
9.9 The coordinates of the foot of the perpendicular from a point to a line
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10 Mathematical Modelling and Kinematics
10.1 Mathematical modelling
10.2 Vectors and kinematics
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11 Forces in Equilibrium, Friction and Moments
11.1 Types of force and drawing diagrams
11.2 The resultant of coplanar forces
11.3 Concurrent forces in equilibrium
11.4 Moments and rigid objects in equilibrium
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12 Centres of Mass
12.1 Definition of centre of mass
12.2 The centre of mass of a system of particles
12.3 The centre of mass of a composite lamina
12.4 Suspended bodies
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13 Motion in One, Two and Three Dimensions
13.1 Linear motion with constant acceleration
13.2 Newton’s Law applied to motionwith variable acceleration in two or three dimensions
13.3 Projectiles
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14 Work, Power and Energy
14.1 Work
14.2 Power
14.3 Energy
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15 Uniform Circular Motion
15.1 Angular velocity and acceleration
15.2 Motion in a horizontal circle
15.3 The conical pendulum
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Glossary
Answers
Index
Index
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