LEARN · EXPLAIN · REVISE

Compulsory volume 1

Read the idea, work independently, then explain what changed.

Each section contains concept explanations, three worked examples, ten graded exercises and teacher preparation.

1.1

Concept of a set

Build understanding of concept of a set through definitions, contrasting cases and justified applications.

1.2

Basic relations between sets

Build understanding of basic relations between sets through definitions, contrasting cases and justified applications.

1.3

Basic operations on sets

Build understanding of basic operations on sets through definitions, contrasting cases and justified applications.

1.4

Sufficient and necessary conditions

Build understanding of sufficient and necessary conditions through definitions, contrasting cases and justified applications.

1.5

Universal and existential quantifiers

Build understanding of universal and existential quantifiers through definitions, contrasting cases and justified applications.

2.1

Properties of equalities and inequalities

Build understanding of properties of equalities and inequalities through definitions, contrasting cases and justified applications.

2.2

Basic inequality: AM–GM

Build understanding of basic inequality: am–gm through definitions, contrasting cases and justified applications.

2.3

Quadratic functions, equations and inequalities

Build understanding of quadratic functions, equations and inequalities through definitions, contrasting cases and justified applications.

3.1

Function concept and representations

Build understanding of function concept and representations through definitions, contrasting cases and justified applications.

3.2

Basic properties of functions

Build understanding of basic properties of functions through definitions, contrasting cases and justified applications.

3.3

Power functions

Build understanding of power functions through definitions, contrasting cases and justified applications.

3.4

Applications of functions I

Build understanding of applications of functions i through definitions, contrasting cases and justified applications.

4.1

Exponents

Build understanding of exponents through definitions, contrasting cases and justified applications.

4.2

Exponential functions

Build understanding of exponential functions through definitions, contrasting cases and justified applications.

4.3

Logarithms

Build understanding of logarithms through definitions, contrasting cases and justified applications.

4.4

Logarithmic functions

Build understanding of logarithmic functions through definitions, contrasting cases and justified applications.

4.5

Applications of functions II

Build understanding of applications of functions ii through definitions, contrasting cases and justified applications.

5.1

General angles and radian measure

Build understanding of general angles and radian measure through definitions, contrasting cases and justified applications.

5.2

Concept of trigonometric functions

Build understanding of concept of trigonometric functions through definitions, contrasting cases and justified applications.

5.3

Reduction formulas

Build understanding of reduction formulas through definitions, contrasting cases and justified applications.

5.4

Graphs and properties of trigonometric functions

Build understanding of graphs and properties of trigonometric functions through definitions, contrasting cases and justified applications.

5.5

Trigonometric identities and transformations

Build understanding of trigonometric identities and transformations through definitions, contrasting cases and justified applications.

5.6

The function y=A sin(ωx+φ)

Build understanding of the function y=a sin(ωx+φ) through definitions, contrasting cases and justified applications.

5.7

Applications of trigonometric functions

Build understanding of applications of trigonometric functions through definitions, contrasting cases and justified applications.