Hong Kong · Grade 12 · Practice Sheet 44

1. 1.

   Find the population standard deviation of: 19, 13, 16, 4, 14 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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2. 2.

   A body starts at 15 m/s and accelerates at 5 m/s² for 4 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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3. 3.

   Find the volume of a sphere of radius 10 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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4. 4.

   A device runs at 240 V drawing 0.6 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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5. 5.

   A wave has frequency 157 Hz and wavelength 2.01 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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6. 6.

   Find the gravitational potential energy of a 46 kg object raised 18 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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7. 7.

   Two masses 3,600 kg and 410 kg are 14 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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8. 8.

   A body starts at 3 m/s and accelerates at 3 m/s² for 9 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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9. 9.

   Solve using the quadratic formula: x² − 9x + 18 = 0.

   Formula:Quadratic Formula

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

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10. 10.

    A triangle has sides a = 7 cm and b = 7 cm with an included angle C = 45°. 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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11. 11.

    Find the gravitational potential energy of a 36 kg object raised 39 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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12. 12.

    A current of 1.8 A flows through a 48 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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13. 13.

    Find the gravitational potential energy of a 32 kg object raised 39 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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14. 14.

    An object with initial velocity 9 m/s accelerates at 3.6 m/s² for 3 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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15. 15.

    A 25 kg object moves at 6 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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16. 16.

    An object with initial velocity 14 m/s accelerates at 3.2 m/s² for 5 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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17. 17.

    Solve using the quadratic formula: x² + 7x + 12 = 0.

    Formula:Quadratic Formula

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

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18. 18.

    A force of 40 N acts on an area of 2.8 m². Find the pressure.

    Formula:Pressure

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

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19. 19.

    Find the gravitational potential energy of a 27 kg object raised 23 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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20. 20.

    HK$ 1,800 is invested at 6% compound interest per annum for 5 years. Find the final amount (to 2 d.p.).

    Formula:Compound Interest

    $A = P\left(1 + \dfrac{r}{100}\right)^{t}$

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