Ghana · Grade 12 · Practice Sheet 1

1. 1.

   Find the force needed to accelerate a 24 kg mass at 6 m/s².

   Formula:Newton's Second Law

   $F = ma$

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2. 2.

   Find the volume of a sphere of radius 4 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

   $V = \tfrac{4}{3} \pi r^3$

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3. 3.

   Two masses 4,900 kg and 160 kg are 6 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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4. 4.

   A current of 3.3 A flows through a 9 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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5. 5.

   Find the gravitational potential energy of a 35 kg object raised 14 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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6. 6.

   Find the population standard deviation of: 12, 6, 15, 19, 7 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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7. 7.

   A cone has base radius 8 cm and height 20 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 device runs at 40 V drawing 0.9 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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9. 9.

   Solve using the quadratic formula: x² + 8x + 12 = 0.

   Formula:Quadratic Formula

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

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10. 10.

    Find the gravitational potential energy of a 7 kg object raised 15 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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11. 11.

    An object with initial velocity 13 m/s accelerates at 4.2 m/s² for 3 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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12. 12.

    Find the force needed to accelerate a 16 kg mass at 4.1 m/s².

    Formula:Newton's Second Law

    $F = ma$

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13. 13.

    Find the population standard deviation of: 13, 16, 3, 8, 15 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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14. 14.

    GH₵ 2,900 is invested at 5% 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 body starts at 0 m/s and accelerates at 3.1 m/s² for 4 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 11 terms of an arithmetic series with first term a = 5 and common difference d = 1.

    Formula:Sum of an Arithmetic Series

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

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17. 17.

    Find the force needed to accelerate a 29 kg mass at 1.7 m/s².

    Formula:Newton's Second Law

    $F = ma$

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18. 18.

    A current of 7.7 A flows through a 5 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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19. 19.

    A device runs at 100 V drawing 3.3 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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20. 20.

    A 33 kg object moves at 25 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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