China · Grade 12 · Practice Sheet 45

1. 1.

   A 33 kg object moves at 22 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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2. 2.

   Find the volume of a sphere of radius 11 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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3. 3.

   A device runs at 25 V drawing 8.1 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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4. 4.

   A 33 kg object moves at 22 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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5. 5.

   A body starts at 10 m/s and accelerates at 2.7 m/s² for 12 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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6. 6.

   Find the gravitational potential energy of a 33 kg object raised 14 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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7. 7.

   A device runs at 121 V drawing 6.8 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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8. 8.

   Find the force needed to accelerate a 9 kg mass at 0.9 m/s².

   Formula:Newton's Second Law

   $F = ma$

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9. 9.

   A device runs at 187 V drawing 9.8 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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10. 10.

    Find the force needed to accelerate a 54 kg mass at 0.6 m/s².

    Formula:Newton's Second Law

    $F = ma$

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11. 11.

    A 38 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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12. 12.

    Find the population standard deviation of: 14, 17, 6, 5, 13 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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13. 13.

    Find the sum of the first 5 terms of a geometric series with first term a = 4 and common ratio r = 3.

    Formula:Sum of a Geometric Series

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

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14. 14.

    A force of 80 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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15. 15.

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

    Formula:Quadratic Formula

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

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16. 16.

    A population of 1,000 grows 10% per year. Find its size after 2 years (nearest whole number).

    Formula:Exponential Growth

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

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17. 17.

    Solve using the quadratic formula: x² − 2x − 24 = 0.

    Formula:Quadratic Formula

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

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18. 18.

    A wave has frequency 255 Hz and wavelength 3.84 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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19. 19.

    A body starts at 18 m/s and accelerates at 4.9 m/s² for 7 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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20. 20.

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

    Formula:Quadratic Formula

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

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