Hong Kong · Grade 12 · Practice Sheet 22

1. 1.

   Find the force needed to accelerate a 32 kg mass at 3 m/s².

   Formula:Newton's Second Law

   $F = ma$

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2. 2.

   Find the volume of a sphere of radius 3 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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3. 3.

   Find the gravitational potential energy of a 44 kg object raised 3 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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4. 4.

   Find the momentum of a 39 kg object moving at 5 m/s.

   Formula:Momentum

   $p = mv$

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5. 5.

   Find the force needed to accelerate a 15 kg mass at 5.7 m/s².

   Formula:Newton's Second Law

   $F = ma$

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6. 6.

   A wave has frequency 830 Hz and wavelength 0.74 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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7. 7.

   Two masses 9,000 kg and 500 kg are 7 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 wave has frequency 364 Hz and wavelength 2.97 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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9. 9.

   A triangle has sides a = 14 cm and b = 12 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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10. 10.

    A device runs at 60 V drawing 3.4 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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11. 11.

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

    Formula:Quadratic Formula

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

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12. 12.

    Find the sum of the first 7 terms of a geometric series with first term a = 5 and common ratio r = 2.

    Formula:Sum of a Geometric Series

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

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13. 13.

    Solve using the quadratic formula: x² − 8x + 12 = 0.

    Formula:Quadratic Formula

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

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14. 14.

    Find the sum of the first 8 terms of a geometric series with first term a = 8 and common ratio r = 4.

    Formula:Sum of a Geometric Series

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

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15. 15.

    In a triangle, a = 8, b = 15 and the included angle C = 80°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

    $c = \sqrt{a^2 + b^2 - 2ab\cos C}$

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16. 16.

    A current of 6.3 A flows through a 40 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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17. 17.

    An object with initial velocity 1 m/s accelerates at 1.8 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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18. 18.

    Find the sum of the first 6 terms of an arithmetic series with first term a = 9 and common difference d = 7.

    Formula:Sum of an Arithmetic Series

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

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19. 19.

    Find the momentum of a 35 kg object moving at 7 m/s.

    Formula:Momentum

    $p = mv$

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20. 20.

    A force of 100 N moves an object 21 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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