Cambodia · Grade 12 · Practice Sheet 47

1. 1.

   Two masses 2,100 kg and 820 kg are 4 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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2. 2.

   ៛ 1,400 is invested at 5% compound interest per annum for 2 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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3. 3.

   Find the population standard deviation of: 15, 18, 6, 12, 7 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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4. 4.

   Find the momentum of a 22 kg object moving at 12 m/s.

   Formula:Momentum

   $p = mv$

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5. 5.

   A current of 3.2 A flows through a 12 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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6. 6.

   A 35 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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7. 7.

   A cone has base radius 5 cm and height 12 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.

   Find the momentum of a 6 kg object moving at 19 m/s.

   Formula:Momentum

   $p = mv$

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9. 9.

   Find the population standard deviation of: 3, 7, 3, 17, 14 (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 2.8 A flows through a 59 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 4 terms of a geometric series with first term a = 1 and common ratio r = 4.

    Formula:Sum of a Geometric Series

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

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12. 12.

    Find the population standard deviation of: 6, 10, 5, 4, 17 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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13. 13.

    A device runs at 127 V drawing 9 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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14. 14.

    Find the sum of the first 17 terms of an arithmetic series with first term a = 3 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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15. 15.

    A force of 121 N acts on an area of 7.4 m². Find the pressure.

    Formula:Pressure

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

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16. 16.

    A current of 4.3 A flows through a 4 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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17. 17.

    Find the sum of the first 3 terms of a geometric series with first term a = 4 and common ratio r = 2.

    Formula:Sum of a Geometric Series

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

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18. 18.

    An object with initial velocity 2 m/s accelerates at 4.3 m/s² for 8 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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19. 19.

    A current of 5.5 A flows through a 13 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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20. 20.

    An object with initial velocity 3 m/s accelerates at 2.9 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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