United Kingdom · Year 7 · Practice Sheet 35

1. 1.

   £63 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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2. 2.

   A triangle has a base of 21 cm and a height of 30 cm. Find its area.

   Formula:Area of a Triangle

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

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3. 3.

   A bag has 13 equally likely marbles, of which 12 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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4. 4.

   A value changes from 77 to 68. 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.

   Find the mean (average) of these numbers: 19, 36, 42, 28, 58.

   Formula:Arithmetic Mean

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

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6. 6.

   Find the perimeter of a rectangle measuring 5 m by 10 m.

   Formula:Perimeter of a Rectangle

   $P = 2(l + w)$

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7. 7.

   A right-angled triangle has legs of 18 cm and 5 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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8. 8.

   Find the perimeter of a rectangle measuring 14 m by 34 m.

   Formula:Perimeter of a Rectangle

   $P = 2(l + w)$

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9. 9.

   A circle has a radius of 15 cm. Find its area. (Use π ≈ 3.14159)

   Formula:Area of a Circle

   $A = \pi r^2$

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10. 10.

    A triangle has a base of 11 cm and a height of 18 cm. Find its area.

    Formula:Area of a Triangle

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

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11. 11.

    A rectangle is 18 cm long and 30 cm wide. Find its area.

    Formula:Area of a Rectangle

    $A = l \times w$

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12. 12.

    £234 is shared in the ratio 4 : 5. Find each share.

    Formula:Dividing in a Ratio

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

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13. 13.

    £5,000 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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14. 14.

    Find the mean (average) of these numbers: 42, 46, 34, 84.

    Formula:Arithmetic Mean

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

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15. 15.

    A triangle has a base of 31 cm and a height of 21 cm. Find its area.

    Formula:Area of a Triangle

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

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16. 16.

    A value changes from 107 to 134. 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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17. 17.

    £1,400 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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18. 18.

    A train moves at 75 km/h for 2.3 hours. How far does it travel?

    Formula:Distance from Speed & Time

    $d = v \times t$

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19. 19.

    What is 40% of 380?

    Formula:Percentage of a Quantity

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

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20. 20.

    £700 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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