Hong Kong · Grade 9 · Practice Sheet 4

1. 1.

   HK$ 68 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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2. 2.

   A force of 134 N acts on an area of 4.6 m². Find the pressure.

   Formula:Pressure

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

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3. 3.

   A circle has a radius of 6 cm. Find its area. (Use π ≈ 3.14159)

   Formula:Area of a Circle

   $A = \pi r^2$

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4. 4.

   A bag has 25 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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5. 5.

   A car travels 198 km in 3 hours. Find its average speed.

   Formula:Speed

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

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6. 6.

   Find the force needed to accelerate a 54 kg mass at 2.6 m/s².

   Formula:Newton's Second Law

   $F = ma$

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7. 7.

   HK$ 3,000 is invested at 4% compound interest per annum for 5 years. Find the final amount (to 2 d.p.).

   Formula:Compound Interest

   $A = P\left(1 + \dfrac{r}{100}\right)^{t}$

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8. 8.

   Solve for x: 3x + 6 = 12.

   Formula:Solving a Linear Equation

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

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9. 9.

   A current of 4.2 A flows through a 24 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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10. 10.

    A 4 kg object moves at 23 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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11. 11.

    A force of 472 N acts on an area of 1.5 m². Find the pressure.

    Formula:Pressure

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

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12. 12.

    A circle has a radius of 6 cm. Find its area. (Use π ≈ 3.14159)

    Formula:Area of a Circle

    $A = \pi r^2$

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13. 13.

    A value changes from 152 to 210. Find the percentage change (to 2 d.p.).

    Formula:Percentage Change

    $\%\,\text{change} = \dfrac{\text{new} - \text{old}}{\text{old}} \times 100$

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14. 14.

    A car travels 532 km in 7 hours. Find its average speed.

    Formula:Speed

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

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15. 15.

    A cylinder has radius 14 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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16. 16.

    A right-angled triangle has legs of 12 cm and 15 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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17. 17.

    A force of 486 N acts on an area of 4.8 m². Find the pressure.

    Formula:Pressure

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

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18. 18.

    A 3 kg object moves at 19 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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19. 19.

    A wave has frequency 305 Hz and wavelength 4.54 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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20. 20.

    A value changes from 91 to 125. Find the percentage change (to 2 d.p.).

    Formula:Percentage Change

    $\%\,\text{change} = \dfrac{\text{new} - \text{old}}{\text{old}} \times 100$

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