Hong Kong · Grade 12 · Practice Sheet 33

1. 1.

   Find the population standard deviation of: 17, 9, 20, 2, 18 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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2. 2.

   An object with initial velocity 15 m/s accelerates at 2.4 m/s² for 7 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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3. 3.

   A body starts at 2 m/s and accelerates at 2.6 m/s² for 6 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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4. 4.

   Find the population standard deviation of: 2, 17, 12, 13, 11 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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5. 5.

   Find the force needed to accelerate a 22 kg mass at 8.8 m/s².

   Formula:Newton's Second Law

   $F = ma$

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6. 6.

   A body starts at 18 m/s and accelerates at 4 m/s² for 4 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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7. 7.

   An object with initial velocity 6 m/s accelerates at 1.9 m/s² for 2 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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8. 8.

   A population of 4,000 grows 5% per year. Find its size after 3 years (nearest whole number).

   Formula:Exponential Growth

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

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9. 9.

   A device runs at 70 V drawing 8.5 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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10. 10.

    A force of 131 N acts on an area of 4.4 m². Find the pressure.

    Formula:Pressure

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

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11. 11.

    A wave has frequency 732 Hz and wavelength 2.24 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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12. 12.

    Find the force needed to accelerate a 45 kg mass at 2.3 m/s².

    Formula:Newton's Second Law

    $F = ma$

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13. 13.

    A force of 86 N moves an object 37 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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14. 14.

    Find the gravitational potential energy of a 25 kg object raised 27 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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15. 15.

    A 3 kg object moves at 13 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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16. 16.

    Solve using the quadratic formula: x² − 6x + 5 = 0.

    Formula:Quadratic Formula

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

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17. 17.

    A triangle has sides a = 19 cm and b = 20 cm with an included angle C = 90°. Find its area (to 2 d.p.).

    Formula:Area of a Triangle (Sine Rule)

    $A = \tfrac{1}{2} ab\sin C$

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18. 18.

    A population of 4,800 grows 5% per year. Find its size after 2 years (nearest whole number).

    Formula:Exponential Growth

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

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19. 19.

    A force of 52 N moves an object 26 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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20. 20.

    A 25 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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