New Zealand · Year 9 · Practice Sheet 41

1. 1.

   A car travels 550 km in 5 hours. Find its average speed.

   Formula:Speed

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

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2. 2.

   A current of 7.7 A flows through a 42 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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3. 3.

   A wave has frequency 685 Hz and wavelength 2.28 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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4. 4.

   A train moves at 92 km/h for 3 hours. How far does it travel?

   Formula:Distance from Speed & Time

   $d = v \times t$

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5. 5.

   A bag has 14 equally likely marbles, of which 2 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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6. 6.

   An object has mass 157.7 g and volume 19 cm³. Find its density.

   Formula:Density

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

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7. 7.

   $126 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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8. 8.

   A device runs at 117 V drawing 1.8 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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9. 9.

   A right-angled triangle has legs of 7 cm and 11 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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10. 10.

    Solve for x: 4x + 6 = 26.

    Formula:Solving a Linear Equation

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

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11. 11.

    $2,900 is invested at 8% compound interest per annum for 2 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.

    An object has mass 264 g and volume 30 cm³. Find its density.

    Formula:Density

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

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13. 13.

    A cylinder has radius 10 cm and height 19 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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14. 14.

    A wave has frequency 397 Hz and wavelength 4.96 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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15. 15.

    Find the momentum of a 24 kg object moving at 3 m/s.

    Formula:Momentum

    $p = mv$

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16. 16.

    A bag has 12 equally likely marbles, of which 11 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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17. 17.

    A value changes from 176 to 173. 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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18. 18.

    Find the volume of a sphere of radius 4 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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19. 19.

    A force of 82 N moves an object 14 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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20. 20.

    A cylinder has radius 8 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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