Core Math 1 (Edexcel AS and A level Modular Math)

1. Algebra and functions

1.1 Simplifying expressions by collecting like terms

1.2 The rules of indices

1.3 Expanding an expression

1.4 Factorising expressions

1.5 Factorising quadratic expressions

1.6 The rules of indices for all rational exponents

1.7 The use and manipulation of surds

1.8 Rationalising the denominator of a fraction when it is a surd

Chapter 1 summary of key points

2. Quadratic functions

2.1 Plotting the graphs of quadratic functions

2.2 Solving quadratic equations by factorisation

2.3 Completing the square

2.4 Solving quadratic equations by completing the square

2.5 Solving quadratic equations by using the formula

2.6 Sketching graphs of quadratic equations

Chapter 2 summary of key points

3. Equations and inequalities

3.1 Solving simultaneous linear equations by elimination

3.2 Solving simultaneous linear equations by substitution

3.3 Using substitution when one equation is linear and the other is quadratic

3.4 Solving linear inequalities

3.5 Solving quadratic inequalities

Chapter 3 summary of key points

4. Sketching curves

4.1 Sketching the graphs of cubic functions

4.2 Interpreting graphs of cubic functions

4.3 Sketching the reciprocal function

4.4 Using the intersection points of graphs of functions to solve equations

4.5 The effect of the transformations $f(x+a)$, $f(x-a)$ and $f(x)+a$

4.6 The effect of the transformations $f(ax)$ and $af(x)$

4.7 Performing transformations on the sketches of curves

Chapter 4 summary of key points

Review Exercise 1

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

5.1 The equation of a straight line in the form $y=mx+c$ or $ax+by+c=0$

5.2 The gradient of a straight line

5.3 The equation of a straight line of the form $y-y_1=m(x-x_1)$

5.4 The formula for finding the equation of a straight line

5.5 The conditions for two straight lines to be parallel or perpendicular

Chapter 5 summary of key points

6. Sequences and series

6.1 Introduction to sequences

6.2 The $n$th term of a sequence

6.3 Sequences generated by a recurrence relationship

6.4 Arithmetic sequences

6.5 Arithmetic series

6.6 The sum to $n$ of an arithmetic series

6.7 Using $\Sigma$ notation

Chapter 6 summary of key points

7. Differentiation

7.1 The derivative of $f(x)$ as the gradient of the tangent to the graph $y=f(x)$

7.2 Finding the formula for the gradient of $x^n$

7.3 Finding the gradient formula of simple functions

7.4 The gradient formula for a function where the powers of $x$ are real numbers

7.5 Expanding or simplifying functions to make them easier to differentiate

7.6 Finding second order derivatives

7.7 Finding the rate of change of a function at a particular point

7.8 Finding the equation of the tangent and normal to a curve at a point

Chapter 7 summary of key points

8. Integration

8.1 Integrating $x^n$

8.2 Integrating simple expressions

8.3 Using the integral sign

8.4 Simplifying expressions before integrating

8.5 Finding the constant of integration

Chapter 8 summary of key points

Review Exercise 2

Practice paper

Examination style paper

Formulae you need to remember

Lists of symbols and notation

Index