Germany · Klasse 8 · Practice Sheet 49

1. 1.

   A right-angled triangle has legs of 18 cm and 4 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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2. 2.

   A car travels 90 km in 2 hours. Find its average speed.

   Formula:Speed

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

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3. 3.

   A triangle has a base of 6 cm and a height of 17 cm. Find its area.

   Formula:Area of a Triangle

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

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4. 4.

   A force of 262 N acts on an area of 6.1 m². Find the pressure.

   Formula:Pressure

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

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5. 5.

   What is 75% of 270?

   Formula:Percentage of a Quantity

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

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6. 6.

   €124 is shared in the ratio 1 : 3. Find each share.

   Formula:Dividing in a Ratio

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

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7. 7.

   A force of 251 N acts on an area of 6.1 m². Find the pressure.

   Formula:Pressure

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

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8. 8.

   What is 75% of 120?

   Formula:Percentage of a Quantity

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

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9. 9.

   A circle has a radius of 22 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 circumference of a circle whose radius is 24 m. (Use π ≈ 3.14159)

    Formula:Circumference of a Circle

    $C = 2\pi r$

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11. 11.

    A value changes from 107 to 168. 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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12. 12.

    A right-angled triangle has legs of 13 cm and 17 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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13. 13.

    A bag has 9 equally likely marbles, of which 2 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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14. 14.

    A current of 1.4 A flows through a 31 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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15. 15.

    A train moves at 86 km/h for 4.7 hours. How far does it travel?

    Formula:Distance from Speed & Time

    $d = v \times t$

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16. 16.

    Solve for x: 5x + 20 = 45.

    Formula:Solving a Linear Equation

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

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17. 17.

    A train moves at 54 km/h for 4.9 hours. How far does it travel?

    Formula:Distance from Speed & Time

    $d = v \times t$

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18. 18.

    A right-angled triangle has legs of 19 cm and 6 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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19. 19.

    A triangle has a base of 26 cm and a height of 12 cm. Find its area.

    Formula:Area of a Triangle

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

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20. 20.

    A current of 3 A flows through a 36 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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