Israel · Grade 12 · Practice Sheet 3

1. 1.

   A force of 10 N moves an object 4 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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2. 2.

   Find the sum of the first 16 terms of an arithmetic series with first term a = 11 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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3. 3.

   Find the population standard deviation of: 3, 16, 14, 4, 2 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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4. 4.

   Solve using the quadratic formula: x² + 4x + 0 = 0.

   Formula:Quadratic Formula

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

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5. 5.

   Two masses 5,400 kg and 480 kg are 2 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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6. 6.

   A cone has base radius 8 cm and height 8 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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7. 7.

   A current of 4.6 A flows through a 20 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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8. 8.

   Find the momentum of a 32 kg object moving at 12 m/s.

   Formula:Momentum

   $p = mv$

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9. 9.

   Find the population standard deviation of: 19, 9, 7, 10, 18 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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10. 10.

    A current of 1.5 A flows through a 11 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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11. 11.

    Find the sum of the first 6 terms of an arithmetic series with first term a = 5 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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12. 12.

    A 36 kg object moves at 5 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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13. 13.

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

    Formula:Sum of an Arithmetic Series

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

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14. 14.

    A force of 47 N acts on an area of 8.4 m². Find the pressure.

    Formula:Pressure

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

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15. 15.

    A current of 5 A flows through a 25 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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16. 16.

    A cone has base radius 6 cm and height 16 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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17. 17.

    Find the force needed to accelerate a 24 kg mass at 2.8 m/s².

    Formula:Newton's Second Law

    $F = ma$

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18. 18.

    Find the gravitational potential energy of a 31 kg object raised 4 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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19. 19.

    An object with initial velocity 3 m/s accelerates at 1.1 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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20. 20.

    Find the momentum of a 57 kg object moving at 11 m/s.

    Formula:Momentum

    $p = mv$

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