Hong Kong · Grade 9 · Practice Sheet 42

1. 1.

   HK$ 1,900 is invested at 4% compound interest per annum for 3 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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2. 2.

   A wave has frequency 264 Hz and wavelength 0.36 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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3. 3.

   A circle has a radius of 24 cm. Find its area. (Use π ≈ 3.14159)

   Formula:Area of a Circle

   $A = \pi r^2$

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4. 4.

   Find the volume of a sphere of radius 7 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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5. 5.

   HK$ 98 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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6. 6.

   A bag has 25 equally likely marbles, of which 7 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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7. 7.

   A cone has base radius 5 cm and height 20 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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8. 8.

   A force of 399 N acts on an area of 5.8 m². Find the pressure.

   Formula:Pressure

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

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9. 9.

   A cylinder has radius 4 cm and height 30 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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10. 10.

    A 40 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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11. 11.

    Find the gravitational potential energy of a 10 kg object raised 29 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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12. 12.

    Solve for x: 5x + 19 = 29.

    Formula:Solving a Linear Equation

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

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13. 13.

    A car travels 255 km in 3 hours. Find its average speed.

    Formula:Speed

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

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14. 14.

    An object has mass 105 g and volume 30 cm³. Find its density.

    Formula:Density

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

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15. 15.

    HK$ 2,400 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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16. 16.

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

    Formula:Pythagorean Theorem

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

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17. 17.

    A device runs at 87 V drawing 5.7 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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18. 18.

    Find the circumference of a circle whose radius is 5 m. (Use π ≈ 3.14159)

    Formula:Circumference of a Circle

    $C = 2\pi r$

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19. 19.

    A bag has 24 equally likely marbles, of which 6 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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20. 20.

    Find the momentum of a 56 kg object moving at 22 m/s.

    Formula:Momentum

    $p = mv$

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