China · Grade 12 · Practice Sheet 42

1. 1.

   ¥700 is invested at 4% compound interest per annum for 3 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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2. 2.

   Solve using the quadratic formula: x² − 2x − 15 = 0.

   Formula:Quadratic Formula

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

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3. 3.

   Two masses 8,500 kg and 300 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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4. 4.

   A population of 7,900 grows 8% per year. Find its size after 6 years (nearest whole number).

   Formula:Exponential Growth

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

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5. 5.

   Find the volume of a sphere of radius 11 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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6. 6.

   Two masses 1,100 kg and 590 kg are 18 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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7. 7.

   A force of 309 N acts on an area of 8.5 m². Find the pressure.

   Formula:Pressure

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

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8. 8.

   A force of 95 N moves an object 20 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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9. 9.

   Find the population standard deviation of: 8, 5, 4, 7, 10 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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10. 10.

    A device runs at 218 V drawing 0.9 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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11. 11.

    A force of 91 N moves an object 23 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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12. 12.

    Find the volume of a sphere of radius 9 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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13. 13.

    Find the population standard deviation of: 11, 5, 9, 2, 20 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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14. 14.

    A device runs at 195 V drawing 6.6 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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15. 15.

    In a triangle, a = 17, b = 11 and the included angle C = 70°. 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.

    Find the gravitational potential energy of a 17 kg object raised 30 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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17. 17.

    A 31 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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18. 18.

    Find the momentum of a 18 kg object moving at 11 m/s.

    Formula:Momentum

    $p = mv$

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19. 19.

    A wave has frequency 897 Hz and wavelength 4.55 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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20. 20.

    Find the force needed to accelerate a 50 kg mass at 2.5 m/s².

    Formula:Newton's Second Law

    $F = ma$

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