Core Math 2 (Edexcel AS and A level Modular Math)

1. Algebra and functions

1.1 Simplifying algebraic fractions by division

1.2 Dividing a polynomial by $(x-p)$

1.3 Factorising a polynomial using the factor theorem

1.4 Using the remainder theorem

Chapter 1 summary of key points

2. The sine and cosine rule

2.1 Using the sine rule to find missing sides

2.2 Using the sine rule to find unknown angles

2.3 The rule and finding two solutions for a missing angle

2.4 Using the cosine rule to find an unknown side

2.5 Using the cosine rule to find a missing angle

2.6 Using the sine rule, the cosine rule and Pythagoras’ Theorem

2.7 Calculating the area of a triangle using sine

Chapter 2 summary of key points

3. Exponentials and logarithms

3.1 The function $y=a^x$

3.2 Writing expressions as a logarithm

3.3 Calculating using logarithms to base 10

3.4 Laws of logarithms

3.5 Solving equations of the form $a^x=b$

3.6 Changing the base of logarithms

Chapter 3 summary of key points

4. Coordinate geometry in the $(x,y)$ plane

4.1 The mid-point of a line

4.2 The distance between two points on a line

4.3 The equation of a circle

Chapter 4 summary of key points

Review Exercise 1

5. The binomial expansion

5.1 Pascal’s triangle

5.2 Combinations and factorial notation

5.3 Using $\binom{n}{r}$ in the binomial expansion

5.4 Expanding $(a+bx)^n$ using the binomial expansion

Chapter 5 summary of key points

6. Radian measure and its applications

6.1 Using radians to measure angles

6.2 The length of the arc of a circle

6.3 The area of a sector of a circle

6.4 The area of a segment of a circle

Chapter 6 summary of key points

7. Geometric sequences and series

7.1 Geometric sequences

7.2 Geometric progressions and the $n$th term

7.3 Using geometric sequences to solve problems

7.4 The sum of a geometric series

7.5 The sum to infinity of a geometric series

Chapter 7 summary of key points

8. Graphs of trigonometric functions

8.1 Sine, cosine and tangent functions

8.2 The values of trigonometric functions in the four quadrants

8.3 Exact values and surds for trigonometrical functions

8.4 Graphs of $\sin\theta$, $\cos\theta$ and $\tan\theta$

8.5 Simple transformations of $\sin\theta$, $\cos\theta$ and $\tan\theta$

Chapter 8 summary of key points

Review Exercise 2

9. Differentiation

9.1 Increasing and decreasing functions

9.2 Stationary points, maximum, minimum and points of inflexion

9.3 Using turning points to solve problems

Chapter 9 summary of key points

10. Trigonometrical identities and simple equations

10.1 Simple trigonometrical identities

10.2 Solving simple trigonometrical equations

10.3 Solving equations of the form $\sin(n\theta+a)=k$, $\cos(n\theta+a)=k$ and $\tan(n\theta+a)=k$

10.4 Solving quadratic trigonometrical equations

Chapter 10 summary of key points

11. Integration

11.1 Simple definite integration

11.2 Area under a curve

11.3 Area under a curve that gives negative values

11.4 Area between a straight line and a curve

11.5 The trapezium rule

Chapter 11 summary of key points

Review Exercise 3

Practice paper

Examination style paper

Formulae you need to remember

Lists of symbols and notation

Index