# QCE Mathematical Methods – Calculus and Further Functions

2.1 Exponential Functions

2.2 Logarithmic Functions

2.3 Trigonometric Functions

2.4 Differentiation

2.5 Discrete Random Variables

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

- Exponential Functions 2
- Logarithmic Functions 1
- Trigonometric Functions 1
- Introduction to Differential Calculus
- Further Differentiation and Applications 1
- Discrete Random Variables 1

Exponential graphs are examined, and their applications in various settings are explored. Logarithms are introduced, and the basic trigonometric functions are studied. Rates and average rates of change are also introduced, followed by the key concept of the derivative as an ‘instantaneous rate of change’. These concepts are reinforced numerically by calculating difference quotients both geometrically, as gradients of chords and tangents, and algebraically.

Calculus is developed to study the derivatives of polynomial and power functions, with applications of the derivative to curve sketching, calculating gradients and equations of tangents (a link to linear function assumed knowledge), determining instantaneous velocities and solving optimisation problems. Discrete random variables are introduced; this supports the development of a framework for statistical inference.

*Source – QCAA General Senior Syllabus 2025*

QCE Mathematical Methods Courses

QCE Mathematical Methods Syllabus

## Course Content

### Exponential Functions

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