Malaysia · Year 12 · Practice Sheet 37

1. 1.

   Find the sum of the first 7 terms of an arithmetic series with first term a = 2 and common difference d = 4.

   Formula:Sum of an Arithmetic Series

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

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2. 2.

   Find the population standard deviation of: 5, 9, 13, 3, 19 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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3. 3.

   Two masses 4,500 kg and 490 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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4. 4.

   A wave has frequency 881 Hz and wavelength 1.98 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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5. 5.

   Find the population standard deviation of: 17, 13, 15, 10, 15 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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6. 6.

   Find the momentum of a 58 kg object moving at 9 m/s.

   Formula:Momentum

   $p = mv$

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7. 7.

   A population of 4,500 grows 5% per year. Find its size after 6 years (nearest whole number).

   Formula:Exponential Growth

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

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8. 8.

   A body starts at 1 m/s and accelerates at 1.7 m/s² for 12 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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9. 9.

   A 16 kg object moves at 8 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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10. 10.

    A population of 5,100 grows 8% per year. Find its size after 6 years (nearest whole number).

    Formula:Exponential Growth

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

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11. 11.

    A current of 4 A flows through a 36 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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12. 12.

    Two masses 6,600 kg and 250 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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13. 13.

    Find the gravitational potential energy of a 46 kg object raised 27 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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14. 14.

    A 35 kg object moves at 15 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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15. 15.

    A device runs at 120 V drawing 6.7 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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16. 16.

    A current of 2.3 A flows through a 16 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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17. 17.

    Find the gravitational potential energy of a 8 kg object raised 25 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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18. 18.

    A device runs at 151 V drawing 2.4 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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19. 19.

    Find the population standard deviation of: 14, 7, 14, 9, 7 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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20. 20.

    An object with initial velocity 6 m/s accelerates at 3 m/s² for 4 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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