Russia · Grade 12 · Practice Sheet 11

1. 1.

   A device runs at 135 V drawing 7.9 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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2. 2.

   Find the population standard deviation of: 7, 7, 15, 5, 2 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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3. 3.

   Find the momentum of a 36 kg object moving at 17 m/s.

   Formula:Momentum

   $p = mv$

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4. 4.

   Find the sum of the first 6 terms of a geometric series with first term a = 6 and common ratio r = 2.

   Formula:Sum of a Geometric Series

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

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5. 5.

   Two masses 7,400 kg and 260 kg are 12 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.

   Solve using the quadratic formula: x² − 1x − 2 = 0.

   Formula:Quadratic Formula

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

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7. 7.

   A force of 72 N acts on an area of 6.1 m². Find the pressure.

   Formula:Pressure

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

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8. 8.

   A cone has base radius 4 cm and height 4 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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9. 9.

   Find the sum of the first 5 terms of an arithmetic series with first term a = 8 and common difference d = 2.

   Formula:Sum of an Arithmetic Series

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

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10. 10.

    A body starts at 6 m/s and accelerates at 2.2 m/s² for 5 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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11. 11.

    A force of 91 N moves an object 23 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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12. 12.

    A force of 280 N acts on an area of 7.9 m². Find the pressure.

    Formula:Pressure

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

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13. 13.

    A force of 86 N moves an object 2 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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14. 14.

    A force of 25 N acts on an area of 3.7 m². Find the pressure.

    Formula:Pressure

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

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15. 15.

    Two masses 8,200 kg and 730 kg are 20 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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16. 16.

    A device runs at 192 V drawing 1 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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17. 17.

    A population of 7,100 grows 10% per year. Find its size after 6 years (nearest whole number).

    Formula:Exponential Growth

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

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18. 18.

    A current of 1.6 A flows through a 40 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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19. 19.

    Find the population standard deviation of: 12, 3, 11, 15, 12 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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20. 20.

    Solve using the quadratic formula: x² + 7x + 6 = 0.

    Formula:Quadratic Formula

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

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