Pure mathematics Year 1

1. ALGEBRAIC EXPRESSIONS

1.1 Index laws

1.2 Expanding brackets

1.3 Factorising

1.4 Negative and fractional indices

1.5 Surds

1.6 Rationalising denominators

1.7 Mixed exercise 1

1.8 Review exercise for chapter 1

 

2. QUADRATICS

2.1 Solving quadratic equations

2.2 Completing the square

2.3 Functions

2.4 Quadratic graphs

2.5 The discriminant

2.6 Modelling with quadratics

2.7 Mixed exercise 2

2.8 Review exercise for chapter 2

 

3. EQUATIONS AND INEQUALITIES

3.1 Linear simultaneous equations

3.2 Quadratic simultaneous equations

3.3 Simultaneous equations on graphs

3.4 Linear inequalities

3.5 Quadratic inequalities

3.6 Inequalities on graphs

3.7 Regions

3.8 Mixed exercise 3

3.9 Review exercise for chapter 3

 

4. GRAPHS AND TRANSFORMATIONS

4.1 Cubic graphs

4.2 Quartic graphs

4.3 Reciprocal graphs

4.4 Points of intersection

4.5 Translating graphs

4.6 Stretching graphs

4.7 Transforming functions

4.8 Mixed exercise 4

4.9 Review exercise for chapter 4

 

5. STRAIGHT LINE GRAPHS

5.1 $y=mx+c$

5.2 Equations of straight lines

5.3 Parallel and perpendicular lines

5.4 Length and area

5.5 Modelling with straight lines

5.6 Mixed exercise 5

5.7 Review exercise for chapter 5

 

6. CIRCLES

6.1 Mid-points and perpendicular bisectors

6.2 Equations of a circle

6.3 Intersections of straight lines and circles

6.4 Use tangent and chord properties

6.5 Circles and triangles

6.6 Mixed exercise 6

6.7 Review exercise for chapter 6

 

7. ALGEBRAIC METHODS

7.1 Algebraic fractions

7.2 Dividing polynomials

7.3 The factor theorem

7.4 Mathematical proof

7.5 Methods of proof

7.6 Mixed exercise 7

7.7 Review exercise for chapter 7

 

8. THE BINOMIAL EXPANSION

8.1 Pascal’s triangle

8.2 Factorial notation

8.3 The binomial expansion

8.4 Solving binomial problems

8.5 Binomial estimation

8.6 Mixed exercise 8

8.7 Review exercise for chapter 8

 

9. TRIGONOMETRIC RATIOS

9.1 The cosine rule

9.2 The sine rule

9.3 Areas of triangles

9.4 Solving triangle problems

9.5 Graphs of sine, cosine and tangent

9.6 Transforming trigonometric graphs

9.7 Mixed exercise 9

9.8 Review exercise for chapter 9

 

10. TRIGONOMETRIC IDENTITIES AND EQUATIONS

10.1 Angles in all four quadrants

10.2 Exact values of trigonometric ratios

10.3 Trigonometric identities

10.4 Simple trigonometric equations

10.5 Harder trigonometric equations

10.6 Equations and identities

10.7 Mixed exercise 10

10.8 Review exercise for chapter 10

 

11. VECTORS

11.1 Vectors

11.2 Representing vectors

11.3 Magnitude and direction

11.4 Position vectors

11.5 Solving geometric problems

11.6 Modelling with vectors

11.7 Mixed exercise 11

11.8 Review exercise for chapter 11

 

12. DIFFERENTIATION

12.1 Gradients of curves

12.2 Finding the derivative

12.3 Differentiating $x^n$

12.4 Differentiating quadratics

12.5 Differentiating functions with two or more terms

12.6 Gradients, tangents and normal

12.7 Increasing and decreasing functions

12.8 Second order derivatives

12.9 Stationary points

12.10 Sketching gradient functions

12.11 Modelling with differentiation

12.12 Mixed exercise 12

12.13 Review exercise for chapter 12

 

13. INTEGRATION

13.1 Integrating $x^n$

13.2 Indefinite integrals

13.3 Finding functions

13.4 Definite integrals

13.5 Areas under curves

13.6 Areas under the x-axis

13.7 Areas between curves and lines

13.8 Mixed exercise 13

13.9 Review exercise for chapter 13

 

14. EXPONENTIALS AND LOGARITHMS

14.1 Exponential functions

14.2 $y=\textrm{e}^x$

14.3 Exponential modelling

14.4 Logarithms

14.5 Laws of logarithms

14.6 Solving equations using logarithms

14.7 Working with natural logarithms

14.8 Logarithms and non-linear data

14.9 Mixed exercise 14

14.10 Review exercise for chapter 14

블로그 한눈에 보기 - 목차(Contents)