Australia · Year 9 · Practice Sheet 8

1. 1.

   A right-angled triangle has legs of 17 cm and 12 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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2. 2.

   A force of 115 N moves an object 19 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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3. 3.

   Solve for x: 5x + 5 = 65.

   Formula:Solving a Linear Equation

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

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4. 4.

   A train moves at 91 km/h for 5.9 hours. How far does it travel?

   Formula:Distance from Speed & Time

   $d = v \times t$

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5. 5.

   A cylinder has radius 13 cm and height 7 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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6. 6.

   A circle has a radius of 16 cm. Find its area. (Use π ≈ 3.14159)

   Formula:Area of a Circle

   $A = \pi r^2$

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7. 7.

   A device runs at 229 V drawing 9.3 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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8. 8.

   A force of 115 N moves an object 28 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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9. 9.

   $3,600 is invested at 3% simple interest per year for 6 years. Find the interest earned.

   Formula:Simple Interest

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

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10. 10.

    Find the volume of a sphere of radius 5 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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11. 11.

    A circle has a radius of 17 cm. Find its area. (Use π ≈ 3.14159)

    Formula:Area of a Circle

    $A = \pi r^2$

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12. 12.

    Find the momentum of a 10 kg object moving at 27 m/s.

    Formula:Momentum

    $p = mv$

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13. 13.

    $3,300 is invested at 10% simple interest per year for 2 years. Find the interest earned.

    Formula:Simple Interest

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

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14. 14.

    A wave has frequency 269 Hz and wavelength 3.72 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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15. 15.

    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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16. 16.

    Solve for x: 9x + 5 = 68.

    Formula:Solving a Linear Equation

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

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17. 17.

    A current of 7.1 A flows through a 19 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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18. 18.

    $63 is shared in the ratio 3 : 4. Find each share.

    Formula:Dividing in a Ratio

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

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19. 19.

    A force of 26 N acts on an area of 3 m². Find the pressure.

    Formula:Pressure

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

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20. 20.

    $90 is shared in the ratio 5 : 5. Find each share.

    Formula:Dividing in a Ratio

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

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