Australia · Year 9 · Practice Sheet 28

1. 1.

   A cylinder has radius 10 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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2. 2.

   Find the momentum of a 13 kg object moving at 8 m/s.

   Formula:Momentum

   $p = mv$

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3. 3.

   A 9 kg object moves at 6 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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4. 4.

   A right-angled triangle has legs of 16 cm and 6 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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5. 5.

   Find the force needed to accelerate a 14 kg mass at 2.2 m/s².

   Formula:Newton's Second Law

   $F = ma$

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6. 6.

   A force of 407 N acts on an area of 1.6 m². Find the pressure.

   Formula:Pressure

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

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7. 7.

   Find the volume of a sphere of radius 2 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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8. 8.

   $3,000 is invested at 3% simple interest per year for 3 years. Find the interest earned.

   Formula:Simple Interest

   $I = \dfrac{P \times r \times t}{100}$

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9. 9.

   A bag has 29 equally likely marbles, of which 19 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.

    $2,600 is invested at 6% simple interest per year for 3 years. Find the interest earned.

    Formula:Simple Interest

    $I = \dfrac{P \times r \times t}{100}$

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11. 11.

    A device runs at 195 V drawing 9.4 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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12. 12.

    A force of 50 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.

    A car travels 400 km in 8 hours. Find its average speed.

    Formula:Speed

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

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14. 14.

    A wave has frequency 572 Hz and wavelength 2.74 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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15. 15.

    $252 is shared in the ratio 5 : 2. Find each share.

    Formula:Dividing in a Ratio

    $\text{share} = \dfrac{\text{part}}{\text{total parts}} \times T$

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16. 16.

    Find the momentum of a 51 kg object moving at 14 m/s.

    Formula:Momentum

    $p = mv$

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17. 17.

    $184 is shared in the ratio 3 : 5. Find each share.

    Formula:Dividing in a Ratio

    $\text{share} = \dfrac{\text{part}}{\text{total parts}} \times T$

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18. 18.

    An object has mass 48 g and volume 8 cm³. Find its density.

    Formula:Density

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

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19. 19.

    A right-angled triangle has legs of 11 cm and 16 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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20. 20.

    A bag has 15 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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