QCE Specialist Mathematics – Combinatorics, Vectors and Proof Course Image

QCE Specialist Mathematics – Combinatorics, Vectors and Proof

1.1 Counting Techniques
1.2 Vectors
1,3 Nature of Proof
1.4 Number
1.5 Circle Geometry

42 Lessons

In this course, students will develop the mathematical understanding and skills to solve problems relating to:

  • Combinatorics
  • Vectors in the Plane
  • Introduction to Proof

Combinatorics provides techniques that are useful in many areas of mathematics, including probability and algebra. Vectors in the plane provide new perspectives for working with two-dimensional space and introduce techniques extending to three-dimensional space in QCE Specialist Mathematics – Mathematical Induction, Further Vectors, Further Matrices and Further Complex Numbers. Introduction to proof provides the opportunity to summarise and extend students’ studies in deductive Euclidean geometry. Studying other topics in the course, including vectors and complex numbers, is greatly beneficial.

These three topics considerably broaden students’ mathematical experience and enhance their awareness of the breadth and utility of the subject. They contain procedures and processes that will be required for later topics. All these topics develop students’ ability to construct mathematical arguments and enable students to increase their mathematical flexibility and versatility.

Source – QCAA General Senior Syllabus 2019




Permutations Involving Restrictions

Arrangements in a Circle


Applications of Counting Techniques


Vectors and Scalars

Vector Equality

Position Vector

Vector Addition

Vector Subtraction

Basic Vector Equations

Scalar Multiplication

Vectors in the Plane

Length of a Vector

Operations with Plane Vectors

Vectors between Two Points

Vectors in Space

Operations with Vectors in Space



Implication of Propositions

Converse of Statements

Equivalence of Statements


Contrapositive of Propositions

Logical Equivalence


Deductive Proof

Proofs of Inequalities


Circle Definitions

Angles in Centre and Circumference

Angles in Same Segment

Angles in Semi Circle

Cyclic Quadrilateral and Angles in a Circle

Alternate Segment

Chords and Tangents in Circles

Intersecting Chords

Tangents and Secants