Secondary 3 E-Maths sample questions with answers

Numbers and their Operations

1. 1Evaluate 49^(-1/2).

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   Answer: 1/7

   1. 49^(-1/2) = 1 / 49^(1/2)
   2. 49^(1/2) = sqrt(49) = 7, so the value is 1/7

2. 2Write the fourth root of y^3 as a power of y.

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   Answer: y^(3/4)

   1. The fourth root is the index 1/4.
   2. (y^3)^(1/4) = y^(3/4)

3. 3Express 0.000 038 5 in standard form.

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   Answer: 3.85 × 10^(-5)

   1. Move the decimal point 5 places to the right to get 3.85.
   2. 0.000 038 5 = 3.85 × 10^(-5)

4. 4A music video was watched 26.4 million times. Write this number in standard form.

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   Answer: 2.64 × 10^7

   1. 26.4 million = 26.4 × 10^6
   2. 26.4 × 10^6 = 2.64 × 10^7

5. 5Simplify 4m^5n^2 × 3m^(-2)n^4.

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   Answer: 12m^3n^6

   1. Numbers: 4 × 3 = 12
   2. Powers of m: 5 + (-2) = 3
   3. Powers of n: 2 + 4 = 6

6. 6The wavelength of a red light is 6.8 × 10^(-7) m. Express this wavelength in nanometres.

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   Answer: 680 nm

   1. 6.8 × 10^(-7) m = 680 × 10^(-9) m
   2. 1 nm = 10^(-9) m, so the wavelength is 680 nm

7. 7Without using a calculator, (a) write 4.7 × 10^120 in the form k × 10^121, (b) hence find 4.7 × 10^120 + 3.2 × 10^121, giving your answer in standard form.

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   Answer: (a) 0.47 × 10^121 (b) 3.67 × 10^121

   1. (a) 4.7 × 10^120 = 0.47 × 10^121
   2. (b) 0.47 × 10^121 + 3.2 × 10^121 = 3.67 × 10^121

8. 8Evaluate (2/3)^(-3) + 5^0, giving your answer as a mixed number.

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   Answer: 4 3/8

   1. (2/3)^(-3) = (3/2)^3 = 27/8
   2. 5^0 = 1
   3. 27/8 + 1 = 4 3/8

9. 9Simplify (125p^9 / q^(-6))^(-1/3), giving your answer in positive index form.

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   Answer: 1 / (5p^3q^2)

   1. 125^(-1/3) = 1/5
   2. (p^9)^(-1/3) = p^(-3) and (q^(-6))^(-1/3) = q^2, which sits in the denominator
   3. q^(-2) / (5p^3) = 1 / (5p^3q^2)

10. 10Simplify (16x^(-8) / (9y^4))^(-3/2), giving your answer in positive index form.

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    Answer: 27x^12y^6 / 64

    1. Turn the fraction over: (9y^4 / (16x^(-8)))^(3/2)
    2. = 27y^6 / (64x^(-12))
    3. = 27x^12y^6 / 64

11. 11Simplify the cube root of (-8a^6b^(-9)), giving your answer in positive index form.

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    Answer: -2a^2 / b^3

    1. (-8)^(1/3) = -2, (a^6)^(1/3) = a^2 and (b^(-9))^(1/3) = b^(-3)
    2. -2a^2b^(-3) = -2a^2 / b^3

12. 12Evaluate 4^(-2) + 3^0 × (1/2)^(-3).

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    Answer: 8 1/16

    1. 4^(-2) = 1/4^2 = 1/16
    2. 3^0 = 1
    3. (1/2)^(-3) = 2^3 = 8
    4. 1/16 + 1 × 8 = 8 1/16