Japan · Grade 12 · Practice Sheet 2

1. 1.

   A 8 kg object moves at 8 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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2. 2.

   A force of 286 N acts on an area of 2.6 m². Find the pressure.

   Formula:Pressure

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

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3. 3.

   Two masses 6,200 kg and 130 kg are 8 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.

   Solve using the quadratic formula: x² + 6x + 5 = 0.

   Formula:Quadratic Formula

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

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5. 5.

   A force of 115 N moves an object 28 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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6. 6.

   A wave has frequency 866 Hz and wavelength 4.53 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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7. 7.

   Find the momentum of a 4 kg object moving at 5 m/s.

   Formula:Momentum

   $p = mv$

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8. 8.

   A force of 87 N moves an object 5 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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9. 9.

   A current of 6.8 A flows through a 4 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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10. 10.

    An object with initial velocity 7 m/s accelerates at 3.5 m/s² for 9 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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11. 11.

    Find the sum of the first 14 terms of an arithmetic series with first term a = 11 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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12. 12.

    Solve using the quadratic formula: x² + 5x + 6 = 0.

    Formula:Quadratic Formula

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

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13. 13.

    Find the sum of the first 18 terms of an arithmetic series with first term a = 9 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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14. 14.

    A triangle has sides a = 17 cm and b = 12 cm with an included angle C = 45°. Find its area (to 2 d.p.).

    Formula:Area of a Triangle (Sine Rule)

    $A = \tfrac{1}{2} ab\sin C$

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15. 15.

    A force of 138 N acts on an area of 5.9 m². Find the pressure.

    Formula:Pressure

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

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16. 16.

    A 15 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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17. 17.

    Two masses 6,200 kg and 160 kg are 7 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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18. 18.

    Find the sum of the first 10 terms of an arithmetic series with first term a = 4 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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19. 19.

    Find the population standard deviation of: 15, 14, 16, 9, 20 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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20. 20.

    Find the momentum of a 54 kg object moving at 26 m/s.

    Formula:Momentum

    $p = mv$

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