Core Math 3 (Edexcel AS and A level Modular Math)

1. Algebraic fractions

1.1 Simplify algebraic fractions by cancelling common factors

1.2 Multiplying and dividing algebraic fractions

1.3 Adding and subtracting algebraic fractions

1.4 Dividing algebraic fractions and the remainder theorem

2. Functions

2.1 Mapping diagrams and graphs of operations

2.2 Functions and function notation

2.3 Range, mapping diagrams, graphs and definitions of functions

2.4 Using composite functions

2.5 Finding and using inverse functions

3. The exponential and log functions

3.1 Introducing exponential functions of the form $y=a^x$

3.2 Graphs of exponential functions and modelling using $y=e^x$

3.3 Using $e^x$ and the inverse of the exponential function $\log_e x$

4. Numerical methods

4.1 Finding approximate roots of $f(x)=0$ graphically

4.2 Using iterative and algebraic methods to find approximate roots of $f(x)=0$

Review Exercise 1

5. Transforming graphs of functions

5.1 Sketching graphs of the modulus function $y=\lvert f(x)\rvert$

5.2 Sketching graphs of the function $y=f(\lvert x\rvert)$

5.3 Solving equations involving a modulus

5.4 Applying a combination of transformations to sketch curves

5.5 Sketching transformations and labelling the coordinates of given point

6. Trigonometry

6.1 The functions secant $\theta$, cosecant $\theta$, and cotangent $\theta$

6.2 The graphs of secant $\theta$, cosecant $\theta$, and cotangent $\theta$

6.3 Simplifying expressions, proving identities and solving equations using $\sec\theta$, $\csc\theta$ and $\cot\theta$

6.4 Using the identities $1+\tan^2\theta=\sec^2\theta$ and $1+\cot^2\theta=\csc^2\theta$

6.5 Using inverse trigonometrical functions and their graphs

7. Further trigonometric identities and their applications

7.1 Using the addition trigonometrical formulae

7.2 Using double angle trigonometrical formulae

7.3 Solving equations and proving identities using double angle formulae

7.4 Using the form $a\cos\theta+b\sin\theta$ in solving trigonometrical problems

7.5 The factor formulae

8. Differentiation

8.1 Differentiating using the chain rule

8.2 Differentiating using the product rule

8.3 Differentiating using the quotient rule

8.4 Differentiating the exponential function

8.5 Finding the differential of the logarithmic function

8.6 Differentiating $\sin x$

8.7 Differentiating $\cos x$

8.8 Differentiating $\tan x$

8.9 Differentiating further trigonometric functions

8.10 Differentiating functions formed by combining trigonometrical, exponential, logarithmic and polynomial functions

Review Exercise 2

Practice paper

Examination style paper

Formulae you need to remember

List of symbols and notation

Answers

Index