United States · Grade 12 · Practice Sheet 10

1. 1.

   In a triangle, a = 17, b = 13 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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2. 2.

   A 5 kg object moves at 11 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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3. 3.

   A wave has frequency 730 Hz and wavelength 0.41 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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4. 4.

   A current of 4 A flows through a 40 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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5. 5.

   Find the gravitational potential energy of a 29 kg object raised 34 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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6. 6.

   Two masses 2,000 kg and 430 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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7. 7.

   A 29 kg object moves at 11 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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8. 8.

   Find the gravitational potential energy of a 6 kg object raised 11 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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9. 9.

   A population of 4,000 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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10. 10.

    A 40 kg object moves at 21 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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11. 11.

    Find the momentum of a 49 kg object moving at 5 m/s.

    Formula:Momentum

    $p = mv$

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12. 12.

    Find the gravitational potential energy of a 9 kg object raised 25 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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13. 13.

    Find the momentum of a 51 kg object moving at 25 m/s.

    Formula:Momentum

    $p = mv$

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14. 14.

    A population of 7,000 grows 2% per year. Find its size after 2 years (nearest whole number).

    Formula:Exponential Growth

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

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15. 15.

    A force of 82 N moves an object 9 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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16. 16.

    A population of 7,900 grows 3% per year. Find its size after 7 years (nearest whole number).

    Formula:Exponential Growth

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

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17. 17.

    A device runs at 70 V drawing 10 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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18. 18.

    Find the population standard deviation of: 18, 2, 15, 20, 3 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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19. 19.

    Find the momentum of a 49 kg object moving at 12 m/s.

    Formula:Momentum

    $p = mv$

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20. 20.

    A device runs at 109 V drawing 4.2 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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