Switzerland · Grade 11 · Practice Sheet 30

1. 1.

   A population of 4,900 grows 2% per year. Find its size after 3 years (nearest whole number).

   Formula:Exponential Growth

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

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2. 2.

   A force of 98 N moves an object 37 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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3. 3.

   Two masses 4,500 kg and 290 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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4. 4.

   Find the momentum of a 49 kg object moving at 29 m/s.

   Formula:Momentum

   $p = mv$

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5. 5.

   A population of 8,400 grows 8% 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: 3, 6, 13, 11, 13 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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7. 7.

   A cone has base radius 5 cm and height 7 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.

   A wave has frequency 654 Hz and wavelength 2.61 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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9. 9.

   A current of 1.6 A flows through a 11 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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10. 10.

    Find the volume of a sphere of radius 12 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

    $V = \tfrac{4}{3} \pi r^3$

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11. 11.

    A right-angled triangle has legs of 5 cm and 12 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

    $c = \sqrt{a^2 + b^2}$

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12. 12.

    A force of 97 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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13. 13.

    Find the volume of a sphere of radius 12 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

    $V = \tfrac{4}{3} \pi r^3$

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14. 14.

    An object has mass 146.2 g and volume 43 cm³. Find its density.

    Formula:Density

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

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15. 15.

    A right-angled triangle has legs of 10 cm and 19 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

    $c = \sqrt{a^2 + b^2}$

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16. 16.

    Find the momentum of a 25 kg object moving at 20 m/s.

    Formula:Momentum

    $p = mv$

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17. 17.

    A population of 1,200 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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18. 18.

    A cylinder has radius 12 cm and height 15 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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19. 19.

    A cone has base radius 12 cm and height 24 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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20. 20.

    A wave has frequency 481 Hz and wavelength 2.42 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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