Mongolia · Grade 11 · Practice Sheet 50

1. 1.

   A wave has frequency 114 Hz and wavelength 2.15 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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2. 2.

   Two masses 2,000 kg and 500 kg are 18 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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3. 3.

   Find the population standard deviation of: 12, 18, 9, 5, 5 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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4. 4.

   A wave has frequency 394 Hz and wavelength 1.83 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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5. 5.

   A right-angled triangle has legs of 11 cm and 9 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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6. 6.

   Find the force needed to accelerate a 18 kg mass at 0.7 m/s².

   Formula:Newton's Second Law

   $F = ma$

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7. 7.

   A force of 114 N moves an object 16 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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8. 8.

   A cone has base radius 12 cm and height 16 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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9. 9.

   Find the volume of a sphere of radius 6 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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10. 10.

    A wave has frequency 362 Hz and wavelength 2.12 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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11. 11.

    An object has mass 66 g and volume 44 cm³. Find its density.

    Formula:Density

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

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12. 12.

    A 3 kg object moves at 24 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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13. 13.

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

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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14. 14.

    An object has mass 123.2 g and volume 14 cm³. Find its density.

    Formula:Density

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

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15. 15.

    A body starts at 16 m/s and accelerates at 5.8 m/s² for 11 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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16. 16.

    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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17. 17.

    A device runs at 188 V drawing 7.2 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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18. 18.

    A force of 129 N acts on an area of 3.6 m². Find the pressure.

    Formula:Pressure

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

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19. 19.

    Solve using the quadratic formula: x² − 6x + 0 = 0.

    Formula:Quadratic Formula

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

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20. 20.

    A device runs at 236 V drawing 9 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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