Austria · Klasse 7 · Practice Sheet 31

1. 1.

   €60 is shared in the ratio 3 : 2. Find each share.

   Formula:Dividing in a Ratio

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

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2. 2.

   A right-angled triangle has legs of 3 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 perimeter of a rectangle measuring 25 m by 14 m.

   Formula:Perimeter of a Rectangle

   $P = 2(l + w)$

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4. 4.

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

   Formula:Pythagorean Theorem

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

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5. 5.

   Find the mean (average) of these numbers: 32, 95, 10, 79, 17.

   Formula:Arithmetic Mean

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

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6. 6.

   What is 12% of 290?

   Formula:Percentage of a Quantity

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

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7. 7.

   A value changes from 85 to 212. 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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8. 8.

   Convert 2.14 kilometres into metres.

   Formula:Metric Length Conversion

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

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9. 9.

   What is 75% of 310?

   Formula:Percentage of a Quantity

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

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10. 10.

    One item costs €24.71. Find the total cost of 9 items.

    Formula:Total Cost

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

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11. 11.

    Find the perimeter of a rectangle measuring 5 m by 25 m.

    Formula:Perimeter of a Rectangle

    $P = 2(l + w)$

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12. 12.

    A train moves at 33 km/h for 5.6 hours. How far does it travel?

    Formula:Distance from Speed & Time

    $d = v \times t$

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13. 13.

    Find 1/2 of 24.

    Formula:Fraction of a Quantity

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

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14. 14.

    Find the area of a square with side length 23 cm.

    Formula:Area of a Square

    $A = s^2$

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15. 15.

    A right-angled triangle has legs of 13 cm and 16 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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16. 16.

    Find the perimeter of a rectangle measuring 20 m by 17 m.

    Formula:Perimeter of a Rectangle

    $P = 2(l + w)$

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17. 17.

    Find the mean (average) of these numbers: 64, 87, 37, 50, 26, 22.

    Formula:Arithmetic Mean

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

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18. 18.

    Convert 4.27 kilometres into metres.

    Formula:Metric Length Conversion

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

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19. 19.

    €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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20. 20.

    Find the perimeter of a rectangle measuring 32 m by 26 m.

    Formula:Perimeter of a Rectangle

    $P = 2(l + w)$

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