United Kingdom · Year 8 · Practice Sheet 43

1. 1.

   A right-angled triangle has legs of 12 cm and 6 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 442 N acts on an area of 8.7 m². Find the pressure.

   Formula:Pressure

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

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3. 3.

   A triangle has a base of 16 cm and a height of 24 cm. Find its area.

   Formula:Area of a Triangle

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

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4. 4.

   Solve for x: 2x + 2 = 20.

   Formula:Solving a Linear Equation

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

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5. 5.

   A right-angled triangle has legs of 7 cm and 16 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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6. 6.

   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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7. 7.

   A value changes from 156 to 236. 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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8. 8.

   £231 is shared in the ratio 2 : 5. Find each share.

   Formula:Dividing in a Ratio

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

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9. 9.

   A cylinder has radius 3 cm and height 26 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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10. 10.

    £30 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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11. 11.

    A force of 125 N acts on an area of 8.3 m². Find the pressure.

    Formula:Pressure

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

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12. 12.

    A triangle has a base of 32 cm and a height of 19 cm. Find its area.

    Formula:Area of a Triangle

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

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13. 13.

    Find the mean (average) of these numbers: 72, 69, 48, 53, 31.

    Formula:Arithmetic Mean

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

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14. 14.

    An object has mass 139.4 g and volume 17 cm³. Find its density.

    Formula:Density

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

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15. 15.

    A value changes from 163 to 166. 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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16. 16.

    £4,000 is invested at 7.5% 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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17. 17.

    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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18. 18.

    £900 is invested at 3% 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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19. 19.

    A triangle has a base of 33 cm and a height of 7 cm. Find its area.

    Formula:Area of a Triangle

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

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20. 20.

    What is 50% of 560?

    Formula:Percentage of a Quantity

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

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