Taiwan · Grade 12 · Practice Sheet 42

1. 1.

   Find the gravitational potential energy of a 4 kg object raised 35 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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2. 2.

   A wave has frequency 224 Hz and wavelength 2.09 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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3. 3.

   Find the gravitational potential energy of a 2 kg object raised 21 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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4. 4.

   Find the population standard deviation of: 5, 20, 8, 11, 10 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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5. 5.

   A population of 7,000 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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6. 6.

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

   Formula:Sum of a Geometric Series

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

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7. 7.

   A population of 4,000 grows 3% per year. Find its size after 6 years (nearest whole number).

   Formula:Exponential Growth

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

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8. 8.

   Two masses 6,800 kg and 510 kg are 16 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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9. 9.

   A force of 156 N acts on an area of 8.2 m². Find the pressure.

   Formula:Pressure

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

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10. 10.

    Find the volume of a sphere of radius 5 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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11. 11.

    A triangle has sides a = 5 cm and b = 10 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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12. 12.

    A 6 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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13. 13.

    Find the gravitational potential energy of a 38 kg object raised 7 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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14. 14.

    Find the sum of the first 6 terms of a geometric series with first term a = 6 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.

    A wave has frequency 45 Hz and wavelength 4.3 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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16. 16.

    A force of 35 N moves an object 40 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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17. 17.

    Find the sum of the first 14 terms of an arithmetic series with first term a = 4 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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18. 18.

    Find the volume of a sphere of radius 6 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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19. 19.

    A force of 110 N moves an object 35 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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20. 20.

    A force of 488 N acts on an area of 6.5 m². Find the pressure.

    Formula:Pressure

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

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