Tanzania · Grade 12 · Practice Sheet 4

1. 1.

   Find the momentum of a 13 kg object moving at 19 m/s.

   Formula:Momentum

   $p = mv$

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2. 2.

   A cone has base radius 3 cm and height 8 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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3. 3.

   TSh 3,600 is invested at 8% 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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4. 4.

   A current of 3 A flows through a 37 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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5. 5.

   Two masses 4,800 kg and 890 kg are 2 m apart. Find the gravitational force between them. (G = 6.674×10⁻¹¹)

   Formula:Newton’s Law of Gravitation

   $F = G\dfrac{m_1 m_2}{r^2}$

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6. 6.

   Find the force needed to accelerate a 10 kg mass at 3.8 m/s².

   Formula:Newton's Second Law

   $F = ma$

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7. 7.

   A wave has frequency 648 Hz and wavelength 4.41 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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8. 8.

   A 38 kg object moves at 9 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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9. 9.

   Two masses 6,800 kg and 800 kg are 12 m apart. Find the gravitational force between them. (G = 6.674×10⁻¹¹)

   Formula:Newton’s Law of Gravitation

   $F = G\dfrac{m_1 m_2}{r^2}$

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10. 10.

    Find the sum of the first 18 terms of an arithmetic series with first term a = 7 and common difference d = 2.

    Formula:Sum of an Arithmetic Series

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

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11. 11.

    Find the momentum of a 44 kg object moving at 11 m/s.

    Formula:Momentum

    $p = mv$

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12. 12.

    Find the volume of a sphere of radius 8 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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13. 13.

    Find the gravitational potential energy of a 4 kg object raised 19 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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14. 14.

    Find the momentum of a 13 kg object moving at 10 m/s.

    Formula:Momentum

    $p = mv$

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15. 15.

    A device runs at 106 V drawing 8.1 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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16. 16.

    Find the force needed to accelerate a 40 kg mass at 3.4 m/s².

    Formula:Newton's Second Law

    $F = ma$

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17. 17.

    Find the population standard deviation of: 19, 2, 9, 11, 15 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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18. 18.

    A wave has frequency 379 Hz and wavelength 4.57 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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19. 19.

    A force of 69 N moves an object 11 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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20. 20.

    Find the population standard deviation of: 7, 4, 19, 8, 18 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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