Ghana · Grade 12 · Practice Sheet 21

1. 1.

   A population of 6,800 grows 10% per year. Find its size after 4 years (nearest whole number).

   Formula:Exponential Growth

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

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2. 2.

   A force of 7 N moves an object 17 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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3. 3.

   A current of 3.4 A flows through a 38 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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4. 4.

   Find the momentum of a 37 kg object moving at 2 m/s.

   Formula:Momentum

   $p = mv$

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5. 5.

   Find the population standard deviation of: 2, 11, 19, 3, 15 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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6. 6.

   Find the gravitational potential energy of a 19 kg object raised 39 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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7. 7.

   In a triangle, a = 11, b = 16 and the included angle C = 80°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

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8. 8.

   A 28 kg object moves at 23 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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9. 9.

   An object with initial velocity 13 m/s accelerates at 4.2 m/s² for 6 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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10. 10.

    Find the momentum of a 23 kg object moving at 21 m/s.

    Formula:Momentum

    $p = mv$

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11. 11.

    Find the sum of the first 4 terms of a geometric series with first term a = 3 and common ratio r = 3.

    Formula:Sum of a Geometric Series

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

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12. 12.

    Find the force needed to accelerate a 14 kg mass at 7 m/s².

    Formula:Newton's Second Law

    $F = ma$

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13. 13.

    A force of 83 N moves an object 30 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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14. 14.

    An object with initial velocity 3 m/s accelerates at 4 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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15. 15.

    A body starts at 12 m/s and accelerates at 1.2 m/s² for 8 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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16. 16.

    Find the sum of the first 19 terms of an arithmetic series with first term a = 3 and common difference d = 8.

    Formula:Sum of an Arithmetic Series

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

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17. 17.

    A device runs at 32 V drawing 1.3 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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18. 18.

    Find the population standard deviation of: 20, 16, 9, 12, 6 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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19. 19.

    A 23 kg object moves at 23 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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20. 20.

    A population of 6,600 grows 5% per year. Find its size after 2 years (nearest whole number).

    Formula:Exponential Growth

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

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