Denmark · Grade 11 · Practice Sheet 36

1. 1.

   Find the population standard deviation of: 6, 3, 8, 6, 4 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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2. 2.

   An object has mass 75.6 g and volume 36 cm³. Find its density.

   Formula:Density

   $\rho = \dfrac{m}{V}$

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3. 3.

   A wave has frequency 409 Hz and wavelength 4.96 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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4. 4.

   Find the sum of the first 9 terms of an arithmetic series with first term a = 8 and common difference d = 6.

   Formula:Sum of an Arithmetic Series

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

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5. 5.

   A population of 5,800 grows 5% per year. Find its size after 5 years (nearest whole number).

   Formula:Exponential Growth

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

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6. 6.

   Find the population standard deviation of: 18, 19, 16, 2, 19 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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7. 7.

   Find the momentum of a 54 kg object moving at 15 m/s.

   Formula:Momentum

   $p = mv$

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8. 8.

   A 27 kg object moves at 10 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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9. 9.

   A population of 1,100 grows 2% per year. Find its size after 5 years (nearest whole number).

   Formula:Exponential Growth

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

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10. 10.

    kr 500 is invested at 6% compound interest per annum for 4 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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11. 11.

    A force of 51 N moves an object 38 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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12. 12.

    A device runs at 128 V drawing 5.4 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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13. 13.

    Solve using the quadratic formula: x² + 3x + 2 = 0.

    Formula:Quadratic Formula

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

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14. 14.

    Two masses 5,300 kg and 370 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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15. 15.

    A device runs at 49 V drawing 8.7 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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16. 16.

    A triangle has sides a = 15 cm and b = 5 cm with an included angle C = 90°. 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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17. 17.

    A wave has frequency 383 Hz and wavelength 2.42 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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18. 18.

    Solve using the quadratic formula: x² + 3x − 10 = 0.

    Formula:Quadratic Formula

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

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19. 19.

    Find the momentum of a 6 kg object moving at 2 m/s.

    Formula:Momentum

    $p = mv$

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20. 20.

    A device runs at 40 V drawing 2.9 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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