Germany · Klasse 7 · Practice Sheet 5

1. 1.

   A right-angled triangle has legs of 7 cm and 8 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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2. 2.

   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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3. 3.

   Find 1/3 of 21.

   Formula:Fraction of a Quantity

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

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4. 4.

   A rectangle is 12 cm long and 11 cm wide. Find its area.

   Formula:Area of a Rectangle

   $A = l \times w$

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5. 5.

   Find 2/4 of 20.

   Formula:Fraction of a Quantity

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

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6. 6.

   A car travels 427 km in 7 hours. Find its average speed.

   Formula:Speed

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

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7. 7.

   A right-angled triangle has legs of 15 cm and 12 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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8. 8.

   A value changes from 147 to 131. 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 circle has a radius of 23 cm. Find its area. (Use π ≈ 3.14159)

   Formula:Area of a Circle

   $A = \pi r^2$

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10. 10.

    What is 20% of 390?

    Formula:Percentage of a Quantity

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

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11. 11.

    Find the perimeter of a rectangle measuring 18 m by 24 m.

    Formula:Perimeter of a Rectangle

    $P = 2(l + w)$

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12. 12.

    A train moves at 67 km/h for 1.7 hours. How far does it travel?

    Formula:Distance from Speed & Time

    $d = v \times t$

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13. 13.

    Convert 2.12 kilometres into metres.

    Formula:Metric Length Conversion

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

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14. 14.

    What is 10% of 170?

    Formula:Percentage of a Quantity

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

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15. 15.

    One item costs €18.27. Find the total cost of 9 items.

    Formula:Total Cost

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

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16. 16.

    Find 7/8 of 136.

    Formula:Fraction of a Quantity

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

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17. 17.

    €2,500 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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18. 18.

    €180 is shared in the ratio 5 : 4. Find each share.

    Formula:Dividing in a Ratio

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

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19. 19.

    A car travels 291 km in 3 hours. Find its average speed.

    Formula:Speed

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

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20. 20.

    Find the circumference of a circle whose radius is 5 m. (Use π ≈ 3.14159)

    Formula:Circumference of a Circle

    $C = 2\pi r$

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