Australia · Year 9 · Practice Sheet 40

1. 1.

   A wave has frequency 148 Hz and wavelength 2.53 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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2. 2.

   $189 is shared in the ratio 5 : 4. 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 value changes from 72 to 61. 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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4. 4.

   A current of 7.2 A flows through a 15 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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5. 5.

   A car travels 460 km in 5 hours. Find its average speed.

   Formula:Speed

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

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6. 6.

   A right-angled triangle has legs of 13 cm and 18 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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7. 7.

   Find the momentum of a 8 kg object moving at 25 m/s.

   Formula:Momentum

   $p = mv$

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8. 8.

   Find the volume of a sphere of radius 3 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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9. 9.

   An object has mass 228 g and volume 40 cm³. Find its density.

   Formula:Density

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

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10. 10.

    A device runs at 218 V drawing 4.8 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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11. 11.

    $2,800 is invested at 3% 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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12. 12.

    A cylinder has radius 7 cm and height 17 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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13. 13.

    Solve for x: 4x + 3 = 19.

    Formula:Solving a Linear Equation

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

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14. 14.

    A right-angled triangle has legs of 11 cm and 14 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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15. 15.

    $2,500 is invested at 7.5% 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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16. 16.

    A train moves at 78 km/h for 3.4 hours. How far does it travel?

    Formula:Distance from Speed & Time

    $d = v \times t$

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17. 17.

    A car travels 164 km in 4 hours. Find its average speed.

    Formula:Speed

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

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18. 18.

    Find the momentum of a 21 kg object moving at 28 m/s.

    Formula:Momentum

    $p = mv$

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19. 19.

    A cone has base radius 5 cm and height 12 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.

    A wave has frequency 341 Hz and wavelength 1.77 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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