New Zealand · Year 8 · Practice Sheet 42

1. 1.

   A car travels 528 km in 6 hours. Find its average speed.

   Formula:Speed

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

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2. 2.

   $57 is shared in the ratio 1 : 2. 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 force of 42 N acts on an area of 9.9 m². Find the pressure.

   Formula:Pressure

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

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4. 4.

   A value changes from 133 to 216. 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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5. 5.

   A cylinder has radius 14 cm and height 11 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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6. 6.

   $128 is shared in the ratio 2 : 2. Find each share.

   Formula:Dividing in a Ratio

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

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7. 7.

   $900 is invested at 4% simple interest per year for 4 years. Find the interest earned.

   Formula:Simple Interest

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

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8. 8.

   A right-angled triangle has legs of 18 cm and 17 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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9. 9.

   $1,000 is invested at 8% simple interest per year for 5 years. Find the interest earned.

   Formula:Simple Interest

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

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10. 10.

    A force of 269 N acts on an area of 5.8 m². Find the pressure.

    Formula:Pressure

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

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11. 11.

    An object has mass 105.6 g and volume 12 cm³. Find its density.

    Formula:Density

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

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12. 12.

    A current of 4.2 A flows through a 49 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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13. 13.

    Solve for x: 6x + 6 = 36.

    Formula:Solving a Linear Equation

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

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14. 14.

    A cylinder has radius 11 cm and height 18 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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15. 15.

    What is 5% of 410?

    Formula:Percentage of a Quantity

    $\text{result} = \dfrac{p}{100} \times N$

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16. 16.

    A circle has a radius of 6 cm. Find its area. (Use π ≈ 3.14159)

    Formula:Area of a Circle

    $A = \pi r^2$

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17. 17.

    A force of 113 N acts on an area of 3.1 m². Find the pressure.

    Formula:Pressure

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

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18. 18.

    A cylinder has radius 3 cm and height 11 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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19. 19.

    A train moves at 30 km/h for 3.7 hours. How far does it travel?

    Formula:Distance from Speed & Time

    $d = v \times t$

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20. 20.

    An object has mass 11.4 g and volume 6 cm³. Find its density.

    Formula:Density

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

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