Switzerland · Grade 7 · Practice Sheet 6

1. 1.

   A right-angled triangle has legs of 12 cm and 18 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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2. 2.

   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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3. 3.

   Find the mean (average) of these numbers: 59, 77, 45, 35, 69, 37.

   Formula:Arithmetic Mean

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

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4. 4.

   Find 2/8 of 80.

   Formula:Fraction of a Quantity

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

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5. 5.

   Find the mean (average) of these numbers: 66, 90, 25, 41.

   Formula:Arithmetic Mean

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

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6. 6.

   A triangle has a base of 37 cm and a height of 9 cm. Find its area.

   Formula:Area of a Triangle

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

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7. 7.

   One item costs CHF 7.03. Find the total cost of 19 items.

   Formula:Total Cost

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

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8. 8.

   A bag has 25 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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9. 9.

   A car travels 297 km in 3 hours. Find its average speed.

   Formula:Speed

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

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10. 10.

    Find the circumference of a circle whose radius is 28 m. (Use π ≈ 3.14159)

    Formula:Circumference of a Circle

    $C = 2\pi r$

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11. 11.

    Find the area of a square with side length 28 cm.

    Formula:Area of a Square

    $A = s^2$

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12. 12.

    A car travels 322 km in 7 hours. Find its average speed.

    Formula:Speed

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

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13. 13.

    Convert 5.78 kilometres into metres.

    Formula:Metric Length Conversion

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

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14. 14.

    Find the area of a square with side length 28 cm.

    Formula:Area of a Square

    $A = s^2$

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15. 15.

    A value changes from 99 to 116. 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.

    CHF 200 is shared in the ratio 3 : 5. Find each share.

    Formula:Dividing in a Ratio

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

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17. 17.

    A triangle has a base of 24 cm and a height of 23 cm. Find its area.

    Formula:Area of a Triangle

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

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18. 18.

    Convert 6.86 kilometres into metres.

    Formula:Metric Length Conversion

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

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19. 19.

    Find 2/5 of 100.

    Formula:Fraction of a Quantity

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

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20. 20.

    A car travels 237 km in 3 hours. Find its average speed.

    Formula:Speed

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

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