1. Pure Mathematics 1

1.1 Quadratics

1.2 Functions

1.3 Coordinate geometry

1.4 Circular measure

1.5 Trigonometry

1.6 Series

1.7 Differentiation

1.8 Integration

3. Pure Mathematics 3

3.2 Logarithmic and exponential functions

3.3 Trigonometry

3.4 Differentiation

3.5 Integration

3.5.1—Extended integration rules

3.5.2—Trig integration

3.5.3—Partial fractions

3.5.4—An integrand of the form x

3.5.5—Inverse tangent

3.5.6—Integration by substitution

3.6 Numerical solution of equations

3.8 Differential equations

3.9 Complex numbers

4. Mechanics

4.1 Forces and equilibrium

4.2 Kinematics of motion in a straight line

4.3 Momentum

4.4 Newton's laws of motion

4.5 Energy, work and power

5. Probability & Statistics 1

5.1 Representation of data

5.2 Permutations and combinations

5.3 Probability

5.4 Discrete random variables

5.5 The normal distribution

6. Probability & Statistics 2

6.1 The Poisson distribution

6.2 Linear combinations of random variables

6.3 Continuous random variables

6.4 Sampling and estimation

6.5 Hypothesis tests

A-Level CAIE Mathematics A2 3.5.6—Integration by substitution Question Bank

• use a given substitution to simplify and evaluate either a definite or an indefinite integral. e.g. to integrate sin2 2x cos x using the substitution u = sin x.

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