Egypt · Grade 12 · Practice Sheet 2

1. 1.

   A force of 278 N acts on an area of 0.8 m². Find the pressure.

   Formula:Pressure

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

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2. 2.

   Find the population standard deviation of: 20, 4, 19, 18, 20 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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3. 3.

   A wave has frequency 725 Hz and wavelength 1.09 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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4. 4.

   A population of 9,000 grows 5% per year. Find its size after 5 years (nearest whole number).

   Formula:Exponential Growth

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

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5. 5.

   Find the population standard deviation of: 19, 17, 20, 7, 12 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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6. 6.

   A triangle has sides a = 9 cm and b = 17 cm with an included angle C = 60°. 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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7. 7.

   A population of 5,500 grows 3% per year. Find its size after 7 years (nearest whole number).

   Formula:Exponential Growth

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

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8. 8.

   A triangle has sides a = 11 cm and b = 11 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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9. 9.

   Find the sum of the first 6 terms of a geometric series with first term a = 2 and common ratio r = 4.

   Formula:Sum of a Geometric Series

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

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10. 10.

    A force of 491 N acts on an area of 3.3 m². Find the pressure.

    Formula:Pressure

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

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11. 11.

    E£ 1,200 is invested at 6% 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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12. 12.

    A 10 kg object moves at 13 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

    $KE = \tfrac{1}{2} m v^2$

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13. 13.

    A current of 3.8 A flows through a 6 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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14. 14.

    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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15. 15.

    A 13 kg object moves at 12 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

    $KE = \tfrac{1}{2} m v^2$

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16. 16.

    Find the momentum of a 6 kg object moving at 20 m/s.

    Formula:Momentum

    $p = mv$

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17. 17.

    A force of 60 N acts on an area of 7.2 m². Find the pressure.

    Formula:Pressure

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

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18. 18.

    A device runs at 202 V drawing 4.6 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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19. 19.

    A force of 37 N moves an object 36 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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20. 20.

    Two masses 2,500 kg and 320 kg are 11 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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