China · Grade 9 · Practice Sheet 27

1. 1.

   A right-angled triangle has legs of 15 cm and 5 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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2. 2.

   A circle has a radius of 14 cm. Find its area. (Use π ≈ 3.14159)

   Formula:Area of a Circle

   $A = \pi r^2$

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3. 3.

   A 4 kg object moves at 10 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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4. 4.

   ¥4,100 is invested at 8% simple interest per year for 3 years. Find the interest earned.

   Formula:Simple Interest

   $I = \dfrac{P \times r \times t}{100}$

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5. 5.

   Find the momentum of a 24 kg object moving at 20 m/s.

   Formula:Momentum

   $p = mv$

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6. 6.

   A device runs at 31 V drawing 6.6 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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7. 7.

   A right-angled triangle has legs of 4 cm and 7 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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8. 8.

   ¥75 is shared in the ratio 2 : 3. Find each share.

   Formula:Dividing in a Ratio

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

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9. 9.

   An object has mass 144 g and volume 18 cm³. Find its density.

   Formula:Density

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

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10. 10.

    ¥160 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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11. 11.

    A wave has frequency 500 Hz and wavelength 1.84 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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12. 12.

    A value changes from 23 to 197. 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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13. 13.

    A circle has a radius of 12 cm. Find its area. (Use π ≈ 3.14159)

    Formula:Area of a Circle

    $A = \pi r^2$

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14. 14.

    A train moves at 68 km/h for 4.7 hours. How far does it travel?

    Formula:Distance from Speed & Time

    $d = v \times t$

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15. 15.

    A force of 99 N moves an object 39 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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16. 16.

    Find the circumference of a circle whose radius is 4 m. (Use π ≈ 3.14159)

    Formula:Circumference of a Circle

    $C = 2\pi r$

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17. 17.

    A force of 42 N moves an object 27 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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18. 18.

    A device runs at 129 V drawing 8.1 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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19. 19.

    A force of 403 N acts on an area of 7.1 m². Find the pressure.

    Formula:Pressure

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

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20. 20.

    A force of 78 N moves an object 11 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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