Netherlands · Year 11 · Practice Sheet 18

1. 1.

   A wave has frequency 93 Hz and wavelength 2.91 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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2. 2.

   A force of 43 N moves an object 22 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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3. 3.

   Find the gravitational potential energy of a 16 kg object raised 6 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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4. 4.

   Two masses 1,400 kg and 710 kg are 6 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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5. 5.

   A population of 8,200 grows 5% per year. Find its size after 6 years (nearest whole number).

   Formula:Exponential Growth

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

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6. 6.

   A device runs at 214 V drawing 1.9 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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7. 7.

   €3,100 is invested at 8% compound interest per annum for 5 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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8. 8.

   An object has mass 259.7 g and volume 49 cm³. Find its density.

   Formula:Density

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

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9. 9.

   A cylinder has radius 11 cm and height 20 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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10. 10.

    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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11. 11.

    Find the population standard deviation of: 19, 10, 9, 6, 6 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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12. 12.

    Find the gravitational potential energy of a 13 kg object raised 24 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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13. 13.

    A wave has frequency 242 Hz and wavelength 4.95 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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14. 14.

    A population of 1,300 grows 3% per year. Find its size after 2 years (nearest whole number).

    Formula:Exponential Growth

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

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15. 15.

    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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16. 16.

    A cone has base radius 6 cm and height 14 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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17. 17.

    Two masses 5,500 kg and 900 kg are 17 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.

    A population of 7,500 grows 2% per year. Find its size after 7 years (nearest whole number).

    Formula:Exponential Growth

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

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19. 19.

    A wave has frequency 478 Hz and wavelength 2.54 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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20. 20.

    A force of 20 N acts on an area of 2.1 m². Find the pressure.

    Formula:Pressure

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

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