Ghana · Grade 9 · Practice Sheet 31

1. 1.

   A right-angled triangle has legs of 12 cm and 18 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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2. 2.

   A wave has frequency 108 Hz and wavelength 0.36 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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3. 3.

   Find the momentum of a 18 kg object moving at 4 m/s.

   Formula:Momentum

   $p = mv$

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4. 4.

   Find the circumference of a circle whose radius is 8 m. (Use π ≈ 3.14159)

   Formula:Circumference of a Circle

   $C = 2\pi r$

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5. 5.

   A force of 95 N moves an object 10 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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6. 6.

   Find the circumference of a circle whose radius is 14 m. (Use π ≈ 3.14159)

   Formula:Circumference of a Circle

   $C = 2\pi r$

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7. 7.

   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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8. 8.

   A car travels 224 km in 7 hours. Find its average speed.

   Formula:Speed

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

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9. 9.

   GH₵ 64 is shared in the ratio 1 : 3. Find each share.

   Formula:Dividing in a Ratio

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

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10. 10.

    A right-angled triangle has legs of 3 cm and 15 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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11. 11.

    Find the gravitational potential energy of a 11 kg object raised 38 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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12. 12.

    A cone has base radius 6 cm and height 11 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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13. 13.

    A bag has 20 equally likely marbles, of which 13 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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14. 14.

    A cone has base radius 2 cm and height 14 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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15. 15.

    Find the momentum of a 39 kg object moving at 28 m/s.

    Formula:Momentum

    $p = mv$

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16. 16.

    GH₵ 162 is shared in the ratio 2 : 4. Find each share.

    Formula:Dividing in a Ratio

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

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17. 17.

    A right-angled triangle has legs of 4 cm and 19 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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18. 18.

    A wave has frequency 163 Hz and wavelength 0.88 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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19. 19.

    A train moves at 22 km/h for 1.7 hours. How far does it travel?

    Formula:Distance from Speed & Time

    $d = v \times t$

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20. 20.

    A device runs at 114 V drawing 7.2 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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