United Kingdom · Year 7 · Practice Sheet 36

1. 1.

   Find the mean (average) of these numbers: 65, 33, 67, 18.

   Formula:Arithmetic Mean

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

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2. 2.

   Find the perimeter of a rectangle measuring 14 m by 18 m.

   Formula:Perimeter of a Rectangle

   $P = 2(l + w)$

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3. 3.

   £105 is shared in the ratio 1 : 4. Find each share.

   Formula:Dividing in a Ratio

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

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4. 4.

   £4,300 is invested at 10% 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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5. 5.

   A value changes from 59 to 98. 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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6. 6.

   One item costs £13.25. Find the total cost of 18 items.

   Formula:Total Cost

   $\text{total} = \text{price} \times \text{quantity}$

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7. 7.

   A circle has a radius of 25 cm. Find its area. (Use π ≈ 3.14159)

   Formula:Area of a Circle

   $A = \pi r^2$

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8. 8.

   What is 75% of 200?

   Formula:Percentage of a Quantity

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

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9. 9.

   A circle has a radius of 18 cm. Find its area. (Use π ≈ 3.14159)

   Formula:Area of a Circle

   $A = \pi r^2$

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10. 10.

    Find the circumference of a circle whose radius is 16 m. (Use π ≈ 3.14159)

    Formula:Circumference of a Circle

    $C = 2\pi r$

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11. 11.

    A bag has 27 equally likely marbles, of which 24 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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12. 12.

    A rectangle is 29 cm long and 29 cm wide. Find its area.

    Formula:Area of a Rectangle

    $A = l \times w$

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13. 13.

    A value changes from 112 to 28. 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.

    A bag has 20 equally likely marbles, of which 4 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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15. 15.

    Find 1/3 of 42.

    Formula:Fraction of a Quantity

    $\text{result} = \dfrac{a}{b} \times N$

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16. 16.

    A car travels 235 km in 5 hours. Find its average speed.

    Formula:Speed

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

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17. 17.

    One item costs £6.57. Find the total cost of 9 items.

    Formula:Total Cost

    $\text{total} = \text{price} \times \text{quantity}$

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18. 18.

    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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19. 19.

    £84 is shared in the ratio 3 : 1. Find each share.

    Formula:Dividing in a Ratio

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

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20. 20.

    A value changes from 139 to 99. 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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