Germany · Klasse 7 · Practice Sheet 15

1. 1.

   A rectangle is 9 cm long and 27 cm wide. Find its area.

   Formula:Area of a Rectangle

   $A = l \times w$

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2. 2.

   Find the mean (average) of these numbers: 46, 45, 25, 52, 37.

   Formula:Arithmetic Mean

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

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3. 3.

   Convert 1.89 kilometres into metres.

   Formula:Metric Length Conversion

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

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4. 4.

   A circle has a radius of 24 cm. Find its area. (Use π ≈ 3.14159)

   Formula:Area of a Circle

   $A = \pi r^2$

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5. 5.

   Find the mean (average) of these numbers: 95, 65, 58, 71, 44, 75.

   Formula:Arithmetic Mean

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

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6. 6.

   What is 10% of 500?

   Formula:Percentage of a Quantity

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

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7. 7.

   €2,400 is invested at 8% simple interest per year for 2 years. Find the interest earned.

   Formula:Simple Interest

   $I = \dfrac{P \times r \times t}{100}$

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8. 8.

   A bag has 27 equally likely marbles, of which 1 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.

   Find the mean (average) of these numbers: 53, 46, 13, 83, 27, 42.

   Formula:Arithmetic Mean

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

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10. 10.

    What is 15% of 140?

    Formula:Percentage of a Quantity

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

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11. 11.

    Find the circumference of a circle whose radius is 22 m. (Use π ≈ 3.14159)

    Formula:Circumference of a Circle

    $C = 2\pi r$

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12. 12.

    €111 is shared in the ratio 2 : 1. Find each share.

    Formula:Dividing in a Ratio

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

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13. 13.

    Find the perimeter of a rectangle measuring 41 m by 4 m.

    Formula:Perimeter of a Rectangle

    $P = 2(l + w)$

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14. 14.

    A value changes from 80 to 142. 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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15. 15.

    Find the mean (average) of these numbers: 13, 74, 41, 13, 27, 42.

    Formula:Arithmetic Mean

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

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16. 16.

    A value changes from 163 to 77. 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.

    A right-angled triangle has legs of 5 cm and 6 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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18. 18.

    A triangle has a base of 32 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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19. 19.

    A bag has 16 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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20. 20.

    €2,900 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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