Denmark · Grade 11 · Practice Sheet 2

1. 1.

   A cone has base radius 10 cm and height 12 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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2. 2.

   A force of 249 N acts on an area of 4.6 m². Find the pressure.

   Formula:Pressure

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

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3. 3.

   A population of 7,800 grows 2% per year. Find its size after 4 years (nearest whole number).

   Formula:Exponential Growth

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

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4. 4.

   A cylinder has radius 6 cm and height 5 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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5. 5.

   An object has mass 112.5 g and volume 15 cm³. Find its density.

   Formula:Density

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

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6. 6.

   A force of 109 N moves an object 25 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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7. 7.

   A cylinder has radius 7 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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8. 8.

   Find the force needed to accelerate a 36 kg mass at 0.9 m/s².

   Formula:Newton's Second Law

   $F = ma$

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9. 9.

   A cone has base radius 10 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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10. 10.

    A force of 42 N moves an object 36 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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11. 11.

    A device runs at 175 V drawing 5.9 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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12. 12.

    A force of 402 N acts on an area of 2 m². Find the pressure.

    Formula:Pressure

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

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13. 13.

    A wave has frequency 780 Hz and wavelength 2.39 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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14. 14.

    Two masses 1,600 kg and 590 kg are 15 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.

    Find the sum of the first 8 terms of an arithmetic series with first term a = 4 and common difference d = 4.

    Formula:Sum of an Arithmetic Series

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

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16. 16.

    Find the population standard deviation of: 7, 5, 4, 5, 3 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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17. 17.

    A cylinder has radius 14 cm and height 18 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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18. 18.

    Solve using the quadratic formula: x² − 5x + 0 = 0.

    Formula:Quadratic Formula

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

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19. 19.

    A wave has frequency 694 Hz and wavelength 2.6 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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20. 20.

    A 13 kg object moves at 14 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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