Zambia · Grade 12 · Practice Sheet 16

1. 1.

   Two masses 5,800 kg and 420 kg are 15 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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2. 2.

   Find the momentum of a 56 kg object moving at 19 m/s.

   Formula:Momentum

   $p = mv$

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3. 3.

   Find the force needed to accelerate a 11 kg mass at 8.4 m/s².

   Formula:Newton's Second Law

   $F = ma$

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4. 4.

   Find the sum of the first 12 terms of an arithmetic series with first term a = 5 and common difference d = 6.

   Formula:Sum of an Arithmetic Series

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

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5. 5.

   A population of 1,800 grows 10% per year. Find its size after 4 years (nearest whole number).

   Formula:Exponential Growth

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

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6. 6.

   Solve using the quadratic formula: x² − 1x − 2 = 0.

   Formula:Quadratic Formula

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

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7. 7.

   In a triangle, a = 5, b = 7 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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8. 8.

   Find the population standard deviation of: 2, 17, 13, 4, 3 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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9. 9.

   A device runs at 127 V drawing 4.1 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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10. 10.

    A wave has frequency 445 Hz and wavelength 1.39 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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11. 11.

    A current of 7.3 A flows through a 56 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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12. 12.

    Find the sum of the first 7 terms of a geometric series with first term a = 3 and common ratio r = 4.

    Formula:Sum of a Geometric Series

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

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13. 13.

    Two masses 1,400 kg and 510 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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14. 14.

    Find the momentum of a 53 kg object moving at 15 m/s.

    Formula:Momentum

    $p = mv$

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15. 15.

    Find the sum of the first 16 terms of an arithmetic series with first term a = 1 and common difference d = 1.

    Formula:Sum of an Arithmetic Series

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

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16. 16.

    A 28 kg object moves at 2 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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17. 17.

    Two masses 4,800 kg and 850 kg are 5 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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18. 18.

    Find the momentum of a 53 kg object moving at 7 m/s.

    Formula:Momentum

    $p = mv$

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19. 19.

    A force of 342 N acts on an area of 8.1 m². Find the pressure.

    Formula:Pressure

    $P = \dfrac{F}{A}$

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20. 20.

    Find the momentum of a 9 kg object moving at 17 m/s.

    Formula:Momentum

    $p = mv$

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