Hong Kong · Grade 12 · Practice Sheet 26

1. 1.

   Find the gravitational potential energy of a 23 kg object raised 29 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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2. 2.

   Solve using the quadratic formula: x² + 4x + 3 = 0.

   Formula:Quadratic Formula

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

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3. 3.

   Find the sum of the first 8 terms of a geometric series with first term a = 1 and common ratio r = 3.

   Formula:Sum of a Geometric Series

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

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4. 4.

   Find the force needed to accelerate a 60 kg mass at 2.5 m/s².

   Formula:Newton's Second Law

   $F = ma$

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5. 5.

   A current of 1.1 A flows through a 58 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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6. 6.

   A device runs at 58 V drawing 3.3 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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7. 7.

   Find the sum of the first 5 terms of an arithmetic series with first term a = 9 and common difference d = 3.

   Formula:Sum of an Arithmetic Series

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

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8. 8.

   A device runs at 70 V drawing 1.3 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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9. 9.

   A wave has frequency 320 Hz and wavelength 4.49 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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10. 10.

    Find the momentum of a 56 kg object moving at 9 m/s.

    Formula:Momentum

    $p = mv$

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11. 11.

    A triangle has sides a = 6 cm and b = 18 cm with an included angle C = 120°. 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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12. 12.

    Find the sum of the first 7 terms of a geometric series with first term a = 1 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.

    Two masses 6,200 kg and 610 kg are 9 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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14. 14.

    A 3 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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15. 15.

    A device runs at 193 V drawing 5 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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16. 16.

    Find the gravitational potential energy of a 21 kg object raised 31 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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17. 17.

    Solve using the quadratic formula: x² + 1x − 20 = 0.

    Formula:Quadratic Formula

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

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18. 18.

    A device runs at 92 V drawing 5.2 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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19. 19.

    Find the sum of the first 14 terms of an arithmetic series with first term a = 2 and common difference d = 1.

    Formula:Sum of an Arithmetic Series

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

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20. 20.

    A device runs at 60 V drawing 3.2 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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