Purpose: Confirm prerequisite skills (integer exponents, square roots, fractions) before tackling exponential functions.
Prerequisite Skills
Question 1 [2 marks]
Evaluate \( 2^5 \) and \( 3^4 \) without a calculator.
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Question 2 [3 marks]
Simplify \( a^4 \cdot a^7 \) and \( \dfrac{x^9}{x^3} \).
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Question 3 [2 marks]
Evaluate \( \sqrt{49} \) and \( \sqrt[3]{27} \).
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Question 4 [3 marks]
Express \( 8 \) and \( 32 \) as powers of 2.
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Question 5 [3 marks]
Sketch the graph of \( y = 2x \). Then sketch the graph of \( y = x^2 \). State two key differences.
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Question 6 [3 marks]
Convert \( 0.04 \) and \( 1.25 \) to fractions in simplest form.
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Reflection
Question 7 [Reflection]
What feels most unfamiliar so far: rational exponents, the new graph shape (asymptote), or the laws of exponents? Be specific.
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