Hong Kong · Grade 9 · Practice Sheet 34

1. 1.

   Find the gravitational potential energy of a 40 kg object raised 10 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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2. 2.

   HK$ 104 is shared in the ratio 2 : 2. Find each share.

   Formula:Dividing in a Ratio

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

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3. 3.

   A car travels 512 km in 8 hours. Find its average speed.

   Formula:Speed

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

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4. 4.

   Solve for x: 2x + 10 = 26.

   Formula:Solving a Linear Equation

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

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5. 5.

   A force of 30 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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6. 6.

   HK$ 48 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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7. 7.

   Find the force needed to accelerate a 16 kg mass at 4.6 m/s².

   Formula:Newton's Second Law

   $F = ma$

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8. 8.

   A car travels 142 km in 2 hours. Find its average speed.

   Formula:Speed

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

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9. 9.

   A wave has frequency 576 Hz and wavelength 0.66 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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10. 10.

    A cone has base radius 5 cm and height 21 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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11. 11.

    A cylinder has radius 9 cm and height 13 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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12. 12.

    A force of 369 N acts on an area of 4.9 m². Find the pressure.

    Formula:Pressure

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

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13. 13.

    A car travels 136 km in 4 hours. Find its average speed.

    Formula:Speed

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

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14. 14.

    A circle has a radius of 9 cm. Find its area. (Use π ≈ 3.14159)

    Formula:Area of a Circle

    $A = \pi r^2$

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15. 15.

    A right-angled triangle has legs of 19 cm and 18 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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16. 16.

    HK$ 78 is shared in the ratio 3 : 3. 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 bag has 26 equally likely marbles, of which 23 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 right-angled triangle has legs of 16 cm and 13 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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19. 19.

    A cone has base radius 10 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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20. 20.

    Find the circumference of a circle whose radius is 16 m. (Use π ≈ 3.14159)

    Formula:Circumference of a Circle

    $C = 2\pi r$

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