Ireland · Year 11 · Practice Sheet 10

1. 1.

   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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2. 2.

   A 6 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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3. 3.

   Find the population standard deviation of: 6, 18, 11, 2, 17 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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4. 4.

   An object with initial velocity 5 m/s accelerates at 1.2 m/s² for 7 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

   $s = ut + \tfrac{1}{2}at^2$

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5. 5.

   A cylinder has radius 11 cm and height 27 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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6. 6.

   Find the momentum of a 28 kg object moving at 19 m/s.

   Formula:Momentum

   $p = mv$

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7. 7.

   A cone has base radius 2 cm and height 17 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 population of 5,500 grows 10% per year. Find its size after 8 years (nearest whole number).

   Formula:Exponential Growth

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

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9. 9.

   A device runs at 38 V drawing 7.9 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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10. 10.

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

    Formula:Sum of a Geometric Series

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

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11. 11.

    Find the force needed to accelerate a 56 kg mass at 3.5 m/s².

    Formula:Newton's Second Law

    $F = ma$

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12. 12.

    A current of 2.4 A flows through a 58 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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13. 13.

    Find the momentum of a 49 kg object moving at 28 m/s.

    Formula:Momentum

    $p = mv$

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14. 14.

    Find the sum of the first 5 terms of an arithmetic series with first term a = 9 and common difference d = 7.

    Formula:Sum of an Arithmetic Series

    $S_n = \tfrac{n}{2}\left(2a + (n-1)d\right)$

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15. 15.

    A body starts at 11 m/s and accelerates at 3.3 m/s² for 2 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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16. 16.

    Find the momentum of a 45 kg object moving at 2 m/s.

    Formula:Momentum

    $p = mv$

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17. 17.

    Find the sum of the first 7 terms of a geometric series with first term a = 1 and common ratio r = 3.

    Formula:Sum of a Geometric Series

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

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18. 18.

    Find the sum of the first 18 terms of an arithmetic series with first term a = 6 and common difference d = 4.

    Formula:Sum of an Arithmetic Series

    $S_n = \tfrac{n}{2}\left(2a + (n-1)d\right)$

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19. 19.

    A current of 1.2 A flows through a 47 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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20. 20.

    A wave has frequency 201 Hz and wavelength 1.72 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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