Austria · Klasse 7 · Practice Sheet 14

1. 1.

   A triangle has a base of 25 cm and a height of 15 cm. Find its area.

   Formula:Area of a Triangle

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

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2. 2.

   €140 is shared in the ratio 4 : 3. Find each share.

   Formula:Dividing in a Ratio

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

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3. 3.

   Find the mean (average) of these numbers: 41, 49, 97, 84, 72, 24.

   Formula:Arithmetic Mean

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

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4. 4.

   Find 1/3 of 48.

   Formula:Fraction of a Quantity

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

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5. 5.

   A rectangle is 7 cm long and 23 cm wide. Find its area.

   Formula:Area of a Rectangle

   $A = l \times w$

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6. 6.

   A train moves at 49 km/h for 3 hours. How far does it travel?

   Formula:Distance from Speed & Time

   $d = v \times t$

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7. 7.

   A rectangle is 20 cm long and 27 cm wide. Find its area.

   Formula:Area of a Rectangle

   $A = l \times w$

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8. 8.

   A right-angled triangle has legs of 14 cm and 9 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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9. 9.

   A circle has a radius of 3 cm. Find its area. (Use π ≈ 3.14159)

   Formula:Area of a Circle

   $A = \pi r^2$

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10. 10.

    Find the perimeter of a rectangle measuring 9 m by 24 m.

    Formula:Perimeter of a Rectangle

    $P = 2(l + w)$

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11. 11.

    One item costs €1.85. Find the total cost of 12 items.

    Formula:Total Cost

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

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12. 12.

    Find the mean (average) of these numbers: 58, 74, 86, 44.

    Formula:Arithmetic Mean

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

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13. 13.

    €160 is shared in the ratio 2 : 3. Find each share.

    Formula:Dividing in a Ratio

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

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14. 14.

    A train moves at 24 km/h for 3.1 hours. How far does it travel?

    Formula:Distance from Speed & Time

    $d = v \times t$

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15. 15.

    Solve for x: 3x + 7 = 43.

    Formula:Solving a Linear Equation

    $x = \dfrac{c - b}{a}$

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16. 16.

    A bag has 21 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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17. 17.

    Find the circumference of a circle whose radius is 19 m. (Use π ≈ 3.14159)

    Formula:Circumference of a Circle

    $C = 2\pi r$

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18. 18.

    A train moves at 55 km/h for 5.8 hours. How far does it travel?

    Formula:Distance from Speed & Time

    $d = v \times t$

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19. 19.

    €180 is shared in the ratio 1 : 5. Find each share.

    Formula:Dividing in a Ratio

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

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20. 20.

    Convert 8.13 kilometres into metres.

    Formula:Metric Length Conversion

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

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