Germany · Klasse 7 · Practice Sheet 35

1. 1.

   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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2. 2.

   A right-angled triangle has legs of 3 cm and 7 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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3. 3.

   Convert 10.33 kilometres into metres.

   Formula:Metric Length Conversion

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

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4. 4.

   €2,000 is invested at 4% 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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5. 5.

   Find the area of a square with side length 24 cm.

   Formula:Area of a Square

   $A = s^2$

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6. 6.

   Find the mean (average) of these numbers: 22, 88, 55, 19, 61.

   Formula:Arithmetic Mean

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

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7. 7.

   One item costs €15.83. Find the total cost of 11 items.

   Formula:Total Cost

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

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8. 8.

   A value changes from 136 to 139. 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.

   €2,900 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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10. 10.

    One item costs €22.28. Find the total cost of 5 items.

    Formula:Total Cost

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

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11. 11.

    A bag has 30 equally likely marbles, of which 13 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.

    Find the area of a square with side length 10 cm.

    Formula:Area of a Square

    $A = s^2$

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13. 13.

    A bag has 17 equally likely marbles, of which 3 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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14. 14.

    A rectangle is 9 cm long and 24 cm wide. Find its area.

    Formula:Area of a Rectangle

    $A = l \times w$

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15. 15.

    Find the perimeter of a rectangle measuring 8 m by 17 m.

    Formula:Perimeter of a Rectangle

    $P = 2(l + w)$

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16. 16.

    Find 3/8 of 160.

    Formula:Fraction of a Quantity

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

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17. 17.

    €3,600 is invested at 7.5% 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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18. 18.

    One item costs €21.28. Find the total cost of 4 items.

    Formula:Total Cost

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

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19. 19.

    A bag has 17 equally likely marbles, of which 5 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.

    €126 is shared in the ratio 3 : 3. Find each share.

    Formula:Dividing in a Ratio

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

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