Core pure mathematics 1

1. COMPLEX NUMBERS

1.1 Imaginary and complex numbers

1.2 Multiplying complex numbers

1.3 Complex conjugation

1.4 Roots of quadratic equations

1.5 Solving cubic and quartic equations

1.6 Mixed exercise 1

1.7 Review exercise for chapter 1

 

2. ARGAND DIAGRAMS

2.1 Argand diagrams

2.2 Modulus and argument

2.3 Modulus-argument form of complex numbers

2.4 Loci in the Argand diagram

2.5 Regions in the Argand diagram

2.6 Mixed exercise 2

2.7 Review exercise for chapter 2

 

3. SERIES

3.1 Sums of natural numbers

3.2 Sums of squares and cubes

3.3 Mixed exercise 3

3.4 Review exercise for chapter 3

 

4. ROOTS OF POLYNOMIALS

4.1 Roots of a quadratic equation

4.2 Roots of a cubic equation

4.3 Roots of a quartic equation

4.4 Expressions relating to the roots of a polynomial

4.5 Linear transformations of roots

4.6 Mixed exercise 4

4.7 Review exercise for chapter 4

 

5. VOLUMES OF REVOLUTION

5.1 Volumes of revolution around the x-axis

5.2 Volumes of revolution around the y-axis

5.3 Adding and subtracting volumes

5.4 Modelling with volumes of revolution

5.5 Mixed exercise 5

5.6 Review exercise for chapter 5

 

6. MATRICES

6.1 Introduction to matrices

6.2 Matrix multiplication

6.3 Determinants

6.4 Inverting a $2\times2$ matrix

6.5 Inverting a $3\times3$ matrix

6.6 Solving systems of equations using matrices

6.7 Mixed exercise 6

6.8 Review exercise for chapter 6

 

7. LINEAR TRANSFORMATIONS

7.1 Linear transformations in two dimensions

7.2 Reflections and rotations

7.3 Enlargements and stretches

7.4 Successive transformations

7.5 Linear transformations in three dimensions

7.6 The inverse of a linear transformation

7.7 Mixed exercise 7

7.8 Review exercise for chapter 7

 

8. PROOF BY INDUCTION

8.1 Proof by mathematical induction

8.2 Proving divisibility results

8.3 Proving statements involving matrices

8.4 Mixed exercise 8

8.5 Review exercise for chapter 8

 

9. VECTORS

9.1 Equation of a line in three dimensions

9.2 Equation of a plane in three dimensions

9.3 Scalar product

9.4 Calculating angles between lines and planes

9.5 Points of intersection

9.6 Finding perpendiculars

9.7 Mixed exercise 9

9.8 Review exercise for chapter 9

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