China · Grade 9 · Practice Sheet 15

1. 1.

   A right-angled triangle has legs of 5 cm and 8 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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2. 2.

   Find the force needed to accelerate a 17 kg mass at 4 m/s².

   Formula:Newton's Second Law

   $F = ma$

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3. 3.

   A current of 5.3 A flows through a 57 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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4. 4.

   Find the momentum of a 22 kg object moving at 12 m/s.

   Formula:Momentum

   $p = mv$

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5. 5.

   A force of 66 N moves an object 35 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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6. 6.

   ¥231 is shared in the ratio 4 : 3. Find each share.

   Formula:Dividing in a Ratio

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

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7. 7.

   Find the momentum of a 56 kg object moving at 19 m/s.

   Formula:Momentum

   $p = mv$

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8. 8.

   An object has mass 28 g and volume 7 cm³. Find its density.

   Formula:Density

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

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9. 9.

   A cone has base radius 8 cm and height 4 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.

    Find the force needed to accelerate a 6 kg mass at 1.6 m/s².

    Formula:Newton's Second Law

    $F = ma$

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11. 11.

    Find the momentum of a 49 kg object moving at 21 m/s.

    Formula:Momentum

    $p = mv$

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12. 12.

    A 38 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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13. 13.

    ¥72 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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14. 14.

    Find the circumference of a circle whose radius is 9 m. (Use π ≈ 3.14159)

    Formula:Circumference of a Circle

    $C = 2\pi r$

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15. 15.

    A car travels 462 km in 6 hours. Find its average speed.

    Formula:Speed

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

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16. 16.

    A bag has 20 equally likely marbles, of which 14 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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17. 17.

    Find the gravitational potential energy of a 18 kg object raised 27 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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18. 18.

    A cone has base radius 12 cm and height 19 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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19. 19.

    ¥128 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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20. 20.

    A device runs at 23 V drawing 6.1 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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