Qatar · Grade 12 · Practice Sheet 38

1. 1.

   Find the gravitational potential energy of a 42 kg object raised 23 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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2. 2.

   Find the population standard deviation of: 3, 5, 4, 2, 15 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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3. 3.

   Find the sum of the first 5 terms of a geometric series with first term a = 5 and common ratio r = 4.

   Formula:Sum of a Geometric Series

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

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4. 4.

   A force of 81 N acts on an area of 3.8 m². Find the pressure.

   Formula:Pressure

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

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5. 5.

   A wave has frequency 795 Hz and wavelength 4.71 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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6. 6.

   A force of 385 N acts on an area of 9.5 m². Find the pressure.

   Formula:Pressure

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

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7. 7.

   A wave has frequency 90 Hz and wavelength 2.67 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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8. 8.

   Find the gravitational potential energy of a 44 kg object raised 20 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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9. 9.

   A current of 7.9 A flows through a 5 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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10. 10.

    A population of 9,000 grows 3% per year. Find its size after 2 years (nearest whole number).

    Formula:Exponential Growth

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

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11. 11.

    Find the population standard deviation of: 5, 13, 6, 12, 15 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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12. 12.

    A body starts at 1 m/s and accelerates at 4.8 m/s² for 4 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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13. 13.

    Find the force needed to accelerate a 54 kg mass at 1.3 m/s².

    Formula:Newton's Second Law

    $F = ma$

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14. 14.

    A device runs at 61 V drawing 7.3 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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15. 15.

    Find the sum of the first 6 terms of a geometric series with first term a = 8 and common ratio r = 2.

    Formula:Sum of a Geometric Series

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

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16. 16.

    Find the gravitational potential energy of a 18 kg object raised 15 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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17. 17.

    A 11 kg object moves at 4 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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18. 18.

    A wave has frequency 136 Hz and wavelength 4.67 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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19. 19.

    Solve using the quadratic formula: x² − 8x + 15 = 0.

    Formula:Quadratic Formula

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

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20. 20.

    A cone has base radius 5 cm and height 5 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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