F1.1
Working with Functions
Understand the concept of a function; use function notation; determine domain and range; work with graphs of functions.
Sample questions
- 1.State the domain and range of f(x) = √(4 − x²).
- 2.Given f(x) = 2x + 1 and g(x) = x², find f(g(3)).
Exam weighting
3–5 marks — foundational; tested throughout the paper in combination with other topics.
Common student mistakes
- ·Incorrect domain/range for composite or restricted functions
- ·Confusing f(x) with f(a) when substituting
- ·Misidentifying whether a relation is a function (vertical line test errors)
F1.2
Linear, Quadratic and Cubic Functions
Represent, interpret and model linear, quadratic and cubic functions and their graphs.
Sample questions
- 1.Sketch y = x² − 4x + 3, labelling the vertex, x-intercepts and y-intercept.
- 2.For what values of k does x² + kx + 9 = 0 have two distinct real roots?
Exam weighting
3–5 marks — graphing, completing the square, discriminant.
Common student mistakes
- ·Sign errors when completing the square
- ·Misidentifying the vertex from vertex form
- ·Forgetting to check turning point type (max vs min)
F1.3
Further Functions and Relations
Work with polynomial, absolute value, exponential, logarithmic and hyperbolic functions.
Sample questions
- 1.Sketch y = |2x − 4|, showing all intercepts.
- 2.Describe the transformation that maps y = x² to y = (x − 2)² + 3.
Exam weighting
2–4 marks.
Common student mistakes
- ·Incorrect absolute value graph — missing the reflection for negative x
- ·Confusing transformations: horizontal shifts vs vertical shifts
Other Advanced topics
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