Jacaranda Maths Quest 11 Specialist Mathematics Units 1 and 2 for Queensland, 2e learnON & Print

1 Combinatorics

1.1 Overview

1.2 Counting techniques

1.3 Factorials and permutations

1.4 Permutations with restrictions

1.5 Combinations

1.6 Applications of permutations and combinations

1.7 Review

2 Introduction to proof

2.1 Overview

2.2 Number systems and writing propositions

2.3 Direct proofs using Euclidean geometry

2.4 Indirect methods of proof

2.5 Proofs with rational and irrational numbers

2.6 Review

3 Vectors in the plane

3.1 Overview

3.2 Vectors and scalars

3.3 Vectors in two dimensions

3.4 Review

4 Algebra of vectors in two dimensions

4.1 Overview

4.2 Vector representations

4.3 Scalar (dot) product and the projection of vectors - scalar and vector resolutes

4.4 Operations with vectors

4.5 Applications of vectors in two dimensions

4.6 Review

5 Matrices

5.1 Overview

5.2 Matrix definition and notation

5.3 Addition, subtraction and scalar multiplication of matrices

5.4 Matrix multiplication

5.5 Determinants and inverses

5.6 Matrix algebra

5.7 Matrix equations

5.8 Review

6 Complex numbers

6.1 Overview

6.2 Introduction to complex numbers

6.3 Basic operations on complex numbers

6.4 Complex conjugates and division of complex numbers

6.5 The complex plane (the Argand plane)

6.6 Conjugates and multiplication in the complex plane

6.7 Review

7 Complex arithmetic and algebra

7.1 Overview

7.2 Complex numbers in polar form

7.3 Operations on complex numbers in polar form

7.4 Geometric interpretations of multiplication and division of complex numbers in polar form

7.5 Subsets of the complex plane

7.6 Roots of equations

7.7 Review

8 Circle and geometric proofs

8.1 Overview

8.2 Congruent triangles and angle relationships

8.3 Circle properties 1 - angles in a circle and chords

8.4 Circle properties 2 - tangents, secants and segments

8.5 Circle properties 3 - cyclic quadrilaterals

8.6 Geometric proofs using vectors

8.7 Review

9 Trigonometry and functions

9.1 Overview

9.2 Sketching graphs

9.3 Reciprocal trigonometric functions

9.4 Pythagorean identities

9.5 Compound angle identities

9.6 Product identities

9.7 Applications of trigonometric identities

9.8 Review

10 Matrices and transformations

10.1 Overview

10.2 Translations

10.3 Reflections and rotations

10.4 Dilations

10.5 Combinations of transformations

10.6 Review