Austria · Klasse 8 · Practice Sheet 12

1. 1.

   A bag has 19 equally likely marbles, of which 10 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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2. 2.

   €185 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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3. 3.

   A cylinder has radius 9 cm and height 6 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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4. 4.

   €93 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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5. 5.

   A right-angled triangle has legs of 11 cm and 18 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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6. 6.

   Find the mean (average) of these numbers: 45, 74, 95, 35.

   Formula:Arithmetic Mean

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

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7. 7.

   A cylinder has radius 14 cm and height 26 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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8. 8.

   A right-angled triangle has legs of 13 cm and 4 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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9. 9.

   Find the mean (average) of these numbers: 39, 86, 24, 98, 39.

   Formula:Arithmetic Mean

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

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10. 10.

    What is 40% of 430?

    Formula:Percentage of a Quantity

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

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11. 11.

    A car travels 350 km in 7 hours. Find its average speed.

    Formula:Speed

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

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12. 12.

    What is 25% of 60?

    Formula:Percentage of a Quantity

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

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13. 13.

    A right-angled triangle has legs of 11 cm and 7 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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14. 14.

    A car travels 498 km in 6 hours. Find its average speed.

    Formula:Speed

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

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15. 15.

    A bag has 25 equally likely marbles, of which 18 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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16. 16.

    A triangle has a base of 25 cm and a height of 18 cm. Find its area.

    Formula:Area of a Triangle

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

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17. 17.

    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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18. 18.

    An object has mass 23.8 g and volume 14 cm³. Find its density.

    Formula:Density

    $\rho = \dfrac{m}{V}$

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19. 19.

    A train moves at 33 km/h for 4.7 hours. How far does it travel?

    Formula:Distance from Speed & Time

    $d = v \times t$

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20. 20.

    A bag has 30 equally likely marbles, of which 8 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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