QCE Mathematical Methods – Further Calculus Course Image

QCE Mathematical Methods – Further Calculus

3.1 Logarithmic Functions
3.2 Differentiation
3.3 Integration

37 Lessons

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

  • Logarithmic Functions 2
  • Further Differential and Applications 2
  • Integrals

Logarithmic laws and definitions are developed and used. Logarithmic functions are explored graphically and algebraically. The calculus study continues with the derivatives of exponential, logarithmic and trigonometric functions and their applications, together with some differentiation techniques and applications to optimisation problems and graph sketching. Integration is introduced as a process that reverses differentiation and as a way of calculating areas and the fundamental theorem of calculus.

Source – QCAA General Senior Syllabus 2019


Logarithmic Laws

Logarithmic Equations

Exponential Equations using Logarithms

Logarithm Change of Base Rule

Graphing Logarithmic Functions


Limits at Constants

Limits at Infinity

Natural Exponential

Evaluating Exponential Functions

Derivatives of Exponential Functions

Exponential Growth

Exponential Decay

Derivatives of Logarithmic Functions

Derivative of Sine Functions

Derivatives of Cosine Functions

Derivatives of Tangent Functions


Integration of Exponential Functions

Integration of Sine and Cosine

Integrating Trigonometric Functions by Recognition

Basic Integration Rules

Basic Integration Rules involving Algebra

Integration of Power Functions

Particular Values

Indefinite Integration by Recognition

Upper and Lower Rectangles

Definite Integrals

Problem Solving by Integration

Definite Integration of Power Functions

Area Under a Curve

Signed Areas

Area between Two Functions

Area between Two Functions involving Signed Areas

Area under Trigonometric Curves

Trapezoidal Rule