United Kingdom · Year 8 · Practice Sheet 27

1. 1.

   A right-angled triangle has legs of 12 cm and 9 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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2. 2.

   A car travels 660 km in 6 hours. Find its average speed.

   Formula:Speed

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

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3. 3.

   An object has mass 40.5 g and volume 45 cm³. Find its density.

   Formula:Density

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

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4. 4.

   A train moves at 25 km/h for 5.7 hours. How far does it travel?

   Formula:Distance from Speed & Time

   $d = v \times t$

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5. 5.

   A triangle has a base of 4 cm and a height of 8 cm. Find its area.

   Formula:Area of a Triangle

   $A = \tfrac{1}{2} b h$

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6. 6.

   £1,300 is invested at 7.5% 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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7. 7.

   A car travels 525 km in 5 hours. Find its average speed.

   Formula:Speed

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

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8. 8.

   A bag has 21 equally likely marbles, of which 9 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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9. 9.

   £56 is shared in the ratio 4 : 3. Find each share.

   Formula:Dividing in a Ratio

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

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10. 10.

    A right-angled triangle has legs of 19 cm and 7 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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11. 11.

    A car travels 288 km in 3 hours. Find its average speed.

    Formula:Speed

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

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12. 12.

    Solve for x: 9x + 9 = 45.

    Formula:Solving a Linear Equation

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

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13. 13.

    A value changes from 25 to 78. 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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14. 14.

    £20 is shared in the ratio 1 : 1. Find each share.

    Formula:Dividing in a Ratio

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

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15. 15.

    Find the mean (average) of these numbers: 59, 98, 57, 42, 43.

    Formula:Arithmetic Mean

    $\bar{x} = \dfrac{\sum x}{n}$

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16. 16.

    A circle has a radius of 24 cm. Find its area. (Use π ≈ 3.14159)

    Formula:Area of a Circle

    $A = \pi r^2$

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17. 17.

    A right-angled triangle has legs of 9 cm and 10 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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18. 18.

    A train moves at 79 km/h for 2.5 hours. How far does it travel?

    Formula:Distance from Speed & Time

    $d = v \times t$

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19. 19.

    A value changes from 69 to 77. 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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20. 20.

    What is 40% of 490?

    Formula:Percentage of a Quantity

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

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