Poland · Klasa 12 · Practice Sheet 3

1. 1.

   Find the population standard deviation of: 11, 9, 16, 10, 14 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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2. 2.

   A population of 3,600 grows 8% per year. Find its size after 3 years (nearest whole number).

   Formula:Exponential Growth

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

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3. 3.

   A force of 35 N moves an object 33 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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4. 4.

   Find the sum of the first 3 terms of a geometric series with first term a = 5 and common ratio r = 4.

   Formula:Sum of a Geometric Series

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

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5. 5.

   Find the force needed to accelerate a 7 kg mass at 6.4 m/s².

   Formula:Newton's Second Law

   $F = ma$

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6. 6.

   A population of 3,700 grows 8% per year. Find its size after 4 years (nearest whole number).

   Formula:Exponential Growth

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

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7. 7.

   A current of 1.6 A flows through a 35 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 36 kg object moving at 26 m/s.

   Formula:Momentum

   $p = mv$

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9. 9.

   A device runs at 167 V drawing 8.6 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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10. 10.

    Find the population standard deviation of: 17, 11, 3, 2, 16 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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11. 11.

    Solve using the quadratic formula: x² − 1x − 12 = 0.

    Formula:Quadratic Formula

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

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12. 12.

    A current of 7.2 A flows through a 24 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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13. 13.

    A device runs at 25 V drawing 0.3 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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14. 14.

    A body starts at 5 m/s and accelerates at 1.7 m/s² for 11 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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15. 15.

    Find the population standard deviation of: 12, 12, 11, 19, 3 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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16. 16.

    A population of 7,600 grows 3% per year. Find its size after 3 years (nearest whole number).

    Formula:Exponential Growth

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

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17. 17.

    A device runs at 117 V drawing 3.8 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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18. 18.

    A force of 53 N moves an object 11 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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19. 19.

    Find the population standard deviation of: 11, 2, 20, 2, 14 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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20. 20.

    A population of 7,700 grows 8% per year. Find its size after 7 years (nearest whole number).

    Formula:Exponential Growth

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

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