Lebanon · Grade 12 · Practice Sheet 8

1. 1.

   Find the population standard deviation of: 16, 18, 14, 15, 13 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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2. 2.

   A wave has frequency 721 Hz and wavelength 2.84 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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3. 3.

   Find the momentum of a 17 kg object moving at 10 m/s.

   Formula:Momentum

   $p = mv$

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4. 4.

   A force of 349 N acts on an area of 6.1 m². Find the pressure.

   Formula:Pressure

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

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5. 5.

   Solve using the quadratic formula: x² + 3x + 2 = 0.

   Formula:Quadratic Formula

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

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6. 6.

   Two masses 2,400 kg and 690 kg are 20 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 cone has base radius 4 cm and height 24 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

   $V = \tfrac{1}{3} \pi r^2 h$

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8. 8.

   A triangle has sides a = 14 cm and b = 12 cm with an included angle C = 30°. 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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9. 9.

   In a triangle, a = 13, b = 10 and the included angle C = 60°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

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10. 10.

    Find the momentum of a 36 kg object moving at 27 m/s.

    Formula:Momentum

    $p = mv$

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11. 11.

    Find the gravitational potential energy of a 10 kg object raised 22 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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12. 12.

    A force of 225 N acts on an area of 2.6 m². Find the pressure.

    Formula:Pressure

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

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13. 13.

    Find the gravitational potential energy of a 47 kg object raised 17 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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14. 14.

    LL 600 is invested at 8% 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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15. 15.

    A force of 44 N moves an object 14 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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16. 16.

    Solve using the quadratic formula: x² − 4x − 12 = 0.

    Formula:Quadratic Formula

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

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17. 17.

    A triangle has sides a = 17 cm and b = 17 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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18. 18.

    A population of 1,800 grows 3% per year. Find its size after 8 years (nearest whole number).

    Formula:Exponential Growth

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

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19. 19.

    A wave has frequency 89 Hz and wavelength 0.97 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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20. 20.

    A device runs at 109 V drawing 2.9 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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