Ukraine · Grade 9 · Practice Sheet 27

1. 1.

   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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2. 2.

   Find the momentum of a 32 kg object moving at 7 m/s.

   Formula:Momentum

   $p = mv$

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3. 3.

   A force of 82 N moves an object 2 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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4. 4.

   Find the circumference of a circle whose radius is 25 m. (Use π ≈ 3.14159)

   Formula:Circumference of a Circle

   $C = 2\pi r$

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5. 5.

   Solve for x: 8x + 5 = 77.

   Formula:Solving a Linear Equation

   $x = \dfrac{c - b}{a}$

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6. 6.

   A wave has frequency 583 Hz and wavelength 1.46 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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7. 7.

   A circle has a radius of 13 cm. Find its area. (Use π ≈ 3.14159)

   Formula:Area of a Circle

   $A = \pi r^2$

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8. 8.

   A cone has base radius 3 cm and height 23 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.

   A bag has 17 equally likely marbles, of which 4 are red. Find the probability of drawing a red marble (to 3 d.p.).

   Formula:Simple Probability

   $P(E) = \dfrac{\text{favourable}}{\text{total}}$

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10. 10.

    Find the force needed to accelerate a 39 kg mass at 2.1 m/s².

    Formula:Newton's Second Law

    $F = ma$

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11. 11.

    An object has mass 217.5 g and volume 25 cm³. Find its density.

    Formula:Density

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

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12. 12.

    Find the gravitational potential energy of a 8 kg object raised 32 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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13. 13.

    A device runs at 145 V drawing 8.7 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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14. 14.

    An object has mass 296.4 g and volume 38 cm³. Find its density.

    Formula:Density

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

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15. 15.

    Find the force needed to accelerate a 31 kg mass at 0.6 m/s².

    Formula:Newton's Second Law

    $F = ma$

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16. 16.

    A car travels 146 km in 2 hours. Find its average speed.

    Formula:Speed

    $v = \dfrac{d}{t}$

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17. 17.

    A bag has 17 equally likely marbles, of which 10 are red. Find the probability of drawing a red marble (to 3 d.p.).

    Formula:Simple Probability

    $P(E) = \dfrac{\text{favourable}}{\text{total}}$

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18. 18.

    A device runs at 212 V drawing 2.2 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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19. 19.

    Find the momentum of a 44 kg object moving at 3 m/s.

    Formula:Momentum

    $p = mv$

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20. 20.

    A force of 335 N acts on an area of 2.4 m². Find the pressure.

    Formula:Pressure

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

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