Evaluating: Challenge & Extension
Mathematics
Year 9
15 questions
~30 mins
1 views0 downloads
About This Worksheet
A worksheet focused on evaluating expressions involving negative indices, designed to challenge and extend Year 9 students' understanding.
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Evaluating: Challenge & Extension
Subject: MathematicsGrade: Year 9
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Date:
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Untitled Worksheet
Grade Year 9
A
Fluency & Practice
Answer all questions. Show your working in the grid spaces provided.
1.
Evaluate: 2^{-3}
[2 marks]2.
Calculate: (3^{-2}) imes 3^{4}
[3 marks]3.
Simplify: 5^{-1} + 5^{0}
[2 marks]4.
Evaluate: (2^{-2})^3
[2 marks]B
Problem Solving & Reasoning
Answer the questions with detailed working and explanations.
1.
Evaluate: rac{1}{2^{-2} imes 4^{-1}} and explain each step.
[4 marks]2.
Determine the value of: (x^{-2} imes x^{3}) / x^{-1}, for x ≠ 0. Show your reasoning.
[4 marks]3.
If 4^{-k} = rac{1}{16}, find the value of k and explain your process.
[3 marks]C
Real-world Applications
Solve the following word problems involving negative indices.
1.
A scientist measures the decay of a substance where the amount remaining after t hours is given by A = A_0 imes 2^{-t/3}. If an initial amount A_0 = 16 grams, how much remains after 3 hours? Show all steps.
[4 marks]2.
A digital storage device has a failure rate modeled by ext{failure rate} = k imes 10^{-n}, where n is the number of years. If after 5 years, the failure rate is 0.0001, find the value of n.
[4 marks]D
Challenge & Extension
Attempt these challenging questions. Show detailed working.
1.
Solve for x: (x^{-3})^2 = 8, and explain your steps.
[4 marks]2.
Construct an expression involving negative indices that equals 16, using integers. Provide your expression and reasoning.
[4 marks]E
Mixed Review
Answer these questions covering various aspects of evaluating negative indices.
1.
Simplify: (6^{-2})(6^{3})
[2 marks]2.
Evaluate: (x^{-1} + x^{-2}) when x=2.
[2 marks]F
Error Analysis
Identify the mistake in the student's working and correct it.
1.
A student evaluates 2^{-3} as 8. Find the mistake and provide the correct evaluation.
[3 marks]2.
A student simplifies (3^{-2}) imes 3^{4} as 3^{2}. Explain the error and correct it.
[3 marks]Quick Actions
What is Remix?
Create a new worksheet based on this one. Change the grade level, topic, number of questions, or difficulty - then generate a fresh version.
- • Change grade level (Grade 6 → Grade 7)
- • Swap topics (Harry Potter → Macbeth)
- • Add more questions (10 → 15)
- • Adjust difficulty
Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet