Maths Extension 1 Year 11 - Module 1 - Lesson 15

Exam Technique & Review

Use this worksheet after reading the lesson to practise the key ideas and prove you can meet the success criteria.

Name

Date

Class

1. Lesson focus

Exam review: inequalities and function graphs. Choose a method from the structure: sign charts for inequalities, inverse checks by composition, and domain conditions for transformed graphs.

Success criteria

Apply the lesson method accurately in a routine example.
Show each algebraic or domain step and check the result.
Explain why the method and restrictions fit the question.

2. Worked practice

1. Solve x²−9<0.

2. Find the inverse of f(x)=5−2x.

3. State the domain of y=1/(x²−1).

3. Challenge

For y=√(x+2), give the domain and x-intercept.

4. Multiple choice

For the inequality (x−1)(x+2)>0, which is the solution?

A. −2<x<1

B. x<−2 or x>1

C. x≤−2 or x≥1

D. all real x

Worked answer key

Compare each step with your working. Keep stated intervals, domains and restrictions in your final answer.

1. Solve x²−9<0.

(x−3)(x+3)<0; solution −3<x<3.

2. Find the inverse of f(x)=5−2x.

y=5−2x ⇒ x=(5−y)/2; f⁻¹(x)=(5−x)/2.

3. State the domain of y=1/(x²−1).

Denominator non-zero: x≠−1 and x≠1.

Challenge. For y=√(x+2), give the domain and x-intercept.

Domain x≥−2; x-intercept when x+2=0, so (−2,0).

Multiple choice. For the inequality (x−1)(x+2)>0, which is the solution?

Correct answer: B. The upward quadratic is positive outside its roots −2 and 1; strict inequality excludes both roots.

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