Japan · Grade 7 · Practice Sheet 4

1. 1.

   Find 1/4 of 56.

   Formula:Fraction of a Quantity

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

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2. 2.

   A right-angled triangle has legs of 14 cm and 14 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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3. 3.

   Find the mean (average) of these numbers: 51, 34, 50, 20, 77.

   Formula:Arithmetic Mean

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

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4. 4.

   A rectangle is 38 cm long and 6 cm wide. Find its area.

   Formula:Area of a Rectangle

   $A = l \times w$

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5. 5.

   Find the perimeter of a rectangle measuring 38 m by 34 m.

   Formula:Perimeter of a Rectangle

   $P = 2(l + w)$

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6. 6.

   ¥92 is shared in the ratio 1 : 3. Find each share.

   Formula:Dividing in a Ratio

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

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7. 7.

   A car travels 232 km in 4 hours. Find its average speed.

   Formula:Speed

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

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8. 8.

   A value changes from 198 to 57. 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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9. 9.

   A bag has 23 equally likely marbles, of which 14 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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10. 10.

    Convert 9.99 kilometres into metres.

    Formula:Metric Length Conversion

    $1\,\text{km} = 1000\,\text{m}$

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11. 11.

    Find 3/4 of 80.

    Formula:Fraction of a Quantity

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

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12. 12.

    Convert 7.29 kilometres into metres.

    Formula:Metric Length Conversion

    $1\,\text{km} = 1000\,\text{m}$

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13. 13.

    Find 1/3 of 27.

    Formula:Fraction of a Quantity

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

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14. 14.

    A triangle has a base of 35 cm and a height of 27 cm. Find its area.

    Formula:Area of a Triangle

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

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15. 15.

    Find 3/5 of 90.

    Formula:Fraction of a Quantity

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

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16. 16.

    A right-angled triangle has legs of 12 cm and 16 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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17. 17.

    What is 12% of 140?

    Formula:Percentage of a Quantity

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

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18. 18.

    A circle has a radius of 22 cm. Find its area. (Use π ≈ 3.14159)

    Formula:Area of a Circle

    $A = \pi r^2$

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19. 19.

    A triangle has a base of 37 cm and a height of 28 cm. Find its area.

    Formula:Area of a Triangle

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

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20. 20.

    Find the mean (average) of these numbers: 20, 75, 11, 98, 18, 47.

    Formula:Arithmetic Mean

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

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