Unit 1: Number and Algebra

Topic 1.5: Introduction to Exponents and Logarithms Questions

Practice 20 exam-style questions for IB Math AI SL Topic 1.5. Review the question stems below, then unlock the full Question Bank to access markschemes, model answers, and AI grading.

1State1 mark
2026Aimnova original
Simplify 7^0.
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2Evaluate2 marks
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Evaluate log 10000.
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3Expand2 marks
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Expand log(16/y).
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4Simplify2 marks
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Simplify (a^3)(a^5).
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5Rewrite2 marks
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Rewrite 5^3 = 125 in logarithmic form.
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6Evaluate2 marks
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Evaluate log_7 49.
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7State1 mark
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Which is correct for multiplying powers with the same base?
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8State1 mark
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Simplify x^6 ÷ x^2.
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9State1 mark
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What is a^-3 equal to?
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10State1 mark
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Simplify (y^2)^4.
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11Simplify2 marks
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Simplify (2x)^3.
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12Expand2 marks
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Expand log(a^4).
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13Rewrite2 marks
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Rewrite x^-4 without a negative exponent.
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14State1 mark
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What is log_10 1000?
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15State1 mark
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Rewrite 2^5 = 32 in logarithmic form.
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16State1 mark
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What is log_4 1?
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17State1 mark
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In calculator notation, log 100 means:
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18State1 mark
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A logarithm gives you:
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19Evaluate2 marks
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Evaluate log_3 81.
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20State1 mark
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Expand log(xy).
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