Austria · Klasse 8 · Practice Sheet 23

1. 1.

   A force of 378 N acts on an area of 3.7 m². Find the pressure.

   Formula:Pressure

   $P = \dfrac{F}{A}$

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2. 2.

   A right-angled triangle has legs of 17 cm and 8 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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3. 3.

   A triangle has a base of 27 cm and a height of 3 cm. Find its area.

   Formula:Area of a Triangle

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

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4. 4.

   A train moves at 87 km/h for 3.8 hours. How far does it travel?

   Formula:Distance from Speed & Time

   $d = v \times t$

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5. 5.

   A bag has 17 equally likely marbles, of which 6 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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6. 6.

   What is 25% of 550?

   Formula:Percentage of a Quantity

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

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7. 7.

   A circle has a radius of 21 cm. Find its area. (Use π ≈ 3.14159)

   Formula:Area of a Circle

   $A = \pi r^2$

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8. 8.

   Find the mean (average) of these numbers: 22, 93, 91, 81.

   Formula:Arithmetic Mean

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

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9. 9.

   A triangle has a base of 11 cm and a height of 20 cm. Find its area.

   Formula:Area of a Triangle

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

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10. 10.

    A right-angled triangle has legs of 5 cm and 19 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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11. 11.

    What is 15% of 560?

    Formula:Percentage of a Quantity

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

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12. 12.

    A force of 67 N acts on an area of 2.3 m². Find the pressure.

    Formula:Pressure

    $P = \dfrac{F}{A}$

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13. 13.

    €231 is shared in the ratio 2 : 5. 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 right-angled triangle has legs of 3 cm and 18 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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15. 15.

    Solve for x: 2x + 11 = 19.

    Formula:Solving a Linear Equation

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

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16. 16.

    What is 12% of 570?

    Formula:Percentage of a Quantity

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

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17. 17.

    A bag has 24 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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18. 18.

    A cylinder has radius 11 cm and height 7 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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19. 19.

    A right-angled triangle has legs of 16 cm and 6 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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20. 20.

    €105 is shared in the ratio 2 : 5. Find each share.

    Formula:Dividing in a Ratio

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

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