Zambia · Grade 12 · Practice Sheet 8

1. 1.

   Find the sum of the first 15 terms of an arithmetic series with first term a = 5 and common difference d = 5.

   Formula:Sum of an Arithmetic Series

   $S_n = \tfrac{n}{2}\left(2a + (n-1)d\right)$

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2. 2.

   ZK 3,500 is invested at 4% compound interest per annum for 3 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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3. 3.

   A cone has base radius 4 cm and height 13 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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4. 4.

   A force of 37 N moves an object 12 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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5. 5.

   Find the momentum of a 55 kg object moving at 15 m/s.

   Formula:Momentum

   $p = mv$

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6. 6.

   A 6 kg object moves at 17 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

   $KE = \tfrac{1}{2} m v^2$

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7. 7.

   Find the population standard deviation of: 13, 11, 11, 16, 19 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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8. 8.

   A device runs at 235 V drawing 4.4 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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9. 9.

   A wave has frequency 586 Hz and wavelength 1.5 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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10. 10.

    Find the momentum of a 56 kg object moving at 12 m/s.

    Formula:Momentum

    $p = mv$

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11. 11.

    Solve using the quadratic formula: x² + 3x − 18 = 0.

    Formula:Quadratic Formula

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

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12. 12.

    A wave has frequency 39 Hz and wavelength 1.35 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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13. 13.

    Find the volume of a sphere of radius 12 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

    $V = \tfrac{4}{3} \pi r^3$

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14. 14.

    Find the population standard deviation of: 9, 13, 19, 18, 18 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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15. 15.

    A wave has frequency 578 Hz and wavelength 4.95 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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16. 16.

    A force of 89 N moves an object 25 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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17. 17.

    Find the momentum of a 50 kg object moving at 12 m/s.

    Formula:Momentum

    $p = mv$

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18. 18.

    A population of 1,100 grows 5% per year. Find its size after 4 years (nearest whole number).

    Formula:Exponential Growth

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

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19. 19.

    An object with initial velocity 1 m/s accelerates at 2.1 m/s² for 8 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

    $s = ut + \tfrac{1}{2}at^2$

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20. 20.

    ZK 3,800 is invested at 6% 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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