Singapore · Grade 12 · Practice Sheet 23

1. 1.

   A force of 49 N moves an object 7 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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2. 2.

   A population of 2,100 grows 5% per year. Find its size after 8 years (nearest whole number).

   Formula:Exponential Growth

   $N = N_0 (1 + r)^{t}$

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3. 3.

   Find the sum of the first 5 terms of a geometric series with first term a = 7 and common ratio r = 3.

   Formula:Sum of a Geometric Series

   $S_n = \dfrac{a(r^{n} - 1)}{r - 1}$

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4. 4.

   Solve using the quadratic formula: x² − 2x − 15 = 0.

   Formula:Quadratic Formula

   $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

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5. 5.

   A wave has frequency 725 Hz and wavelength 0.88 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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6. 6.

   Find the sum of the first 3 terms of a geometric series with first term a = 2 and common ratio r = 3.

   Formula:Sum of a Geometric Series

   $S_n = \dfrac{a(r^{n} - 1)}{r - 1}$

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7. 7.

   Find the momentum of a 7 kg object moving at 28 m/s.

   Formula:Momentum

   $p = mv$

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8. 8.

   Find the population standard deviation of: 7, 19, 8, 19, 9 (to 2 d.p.).

   Formula:Standard Deviation (Population)

   $\sigma = \sqrt{\dfrac{\sum (x - \bar{x})^2}{n}}$

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9. 9.

   A current of 6.1 A flows through a 22 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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10. 10.

    A cone has base radius 4 cm and height 16 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

    $V = \tfrac{1}{3} \pi r^2 h$

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11. 11.

    $600 is invested at 5% compound interest per annum for 5 years. Find the final amount (to 2 d.p.).

    Formula:Compound Interest

    $A = P\left(1 + \dfrac{r}{100}\right)^{t}$

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12. 12.

    A wave has frequency 232 Hz and wavelength 4.41 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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13. 13.

    A triangle has sides a = 5 cm and b = 16 cm with an included angle C = 120°. Find its area (to 2 d.p.).

    Formula:Area of a Triangle (Sine Rule)

    $A = \tfrac{1}{2} ab\sin C$

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14. 14.

    In a triangle, a = 6, b = 12 and the included angle C = 110°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

    $c = \sqrt{a^2 + b^2 - 2ab\cos C}$

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15. 15.

    Find the population standard deviation of: 13, 17, 9, 12, 12 (to 2 d.p.).

    Formula:Standard Deviation (Population)

    $\sigma = \sqrt{\dfrac{\sum (x - \bar{x})^2}{n}}$

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16. 16.

    A current of 2 A flows through a 55 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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17. 17.

    A device runs at 93 V drawing 0.7 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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18. 18.

    A current of 1.7 A flows through a 40 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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19. 19.

    Find the sum of the first 5 terms of a geometric series with first term a = 1 and common ratio r = 3.

    Formula:Sum of a Geometric Series

    $S_n = \dfrac{a(r^{n} - 1)}{r - 1}$

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20. 20.

    Solve using the quadratic formula: x² − 8x + 15 = 0.

    Formula:Quadratic Formula

    $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

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