Year 11 Mathematical Methods Unit 1

Revision Worksheet

Name: Class: Date:

Show clear working. Give exact answers unless a decimal approximation is requested. Label all graph features carefully.

Part A: Function Language

For $f (x) = \frac{3}{x - 2} + 1$ , state the maximal domain, vertical asymptote, horizontal asymptote, and intercepts.
Sketch the graph, labelling all key features.
Write the function in full function notation.

Part B: Circular Functions

Solve $2 \sin (x) - 1 = 0$ for $0 \leq x \leq 2 π$ .
Sketch $y = 2 \cos (3 x) - 1$ for one full cycle.
State the amplitude, period, maximum value, and minimum value.

Part C: Quadratics and Inverses

Find the rule of a quadratic with turning point $(- 2, 7)$ passing through $(1, - 2)$ .
For $g : [4, \infty) \to R$ , $g (x) = \sqrt{x - 4} + 2$ , find $g^{- 1}$ .
State the domain and range of both functions.

Part D: Piecewise Modelling

Create a piecewise function with exactly three pieces: one linear, one quadratic, and one circular function.
Use adjacent domains that do not overlap.
Sketch the full graph and label each endpoint clearly.

Part E: Probability

A trial has success probability $0.4$ and is repeated three times independently. Draw a tree diagram.
Find the probability of exactly two successes.
Find the probability of at least one success.
Explain which calculation could be done using the complement.

Reflection

One topic I can do confidently:
One topic I need to practise again:
One mistake I will check for next time: