Austria · Klasse 8 · Practice Sheet 1

1. 1.

   A train moves at 58 km/h for 1.7 hours. How far does it travel?

   Formula:Distance from Speed & Time

   $d = v \times t$

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2. 2.

   €90 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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3. 3.

   Solve for x: 2x + 14 = 24.

   Formula:Solving a Linear Equation

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

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4. 4.

   Find the circumference of a circle whose radius is 25 m. (Use π ≈ 3.14159)

   Formula:Circumference of a Circle

   $C = 2\pi r$

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5. 5.

   Find the mean (average) of these numbers: 29, 55, 63, 85.

   Formula:Arithmetic Mean

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

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6. 6.

   A triangle has a base of 38 cm and a height of 29 cm. Find its area.

   Formula:Area of a Triangle

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

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7. 7.

   A bag has 22 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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8. 8.

   A right-angled triangle has legs of 4 cm and 12 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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9. 9.

   A car travels 165 km in 3 hours. Find its average speed.

   Formula:Speed

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

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10. 10.

    Find the mean (average) of these numbers: 48, 99, 43, 61, 96.

    Formula:Arithmetic Mean

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

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11. 11.

    A triangle has a base of 29 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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12. 12.

    What is 12% of 280?

    Formula:Percentage of a Quantity

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

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13. 13.

    An object has mass 193.6 g and volume 44 cm³. Find its density.

    Formula:Density

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

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14. 14.

    A right-angled triangle has legs of 9 cm and 16 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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15. 15.

    A force of 194 N acts on an area of 2.2 m². Find the pressure.

    Formula:Pressure

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

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16. 16.

    A value changes from 43 to 176. 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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17. 17.

    Solve for x: 3x + 1 = 34.

    Formula:Solving a Linear Equation

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

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18. 18.

    Find the circumference of a circle whose radius is 29 m. (Use π ≈ 3.14159)

    Formula:Circumference of a Circle

    $C = 2\pi r$

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19. 19.

    A current of 5.8 A flows through a 52 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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20. 20.

    An object has mass 53.2 g and volume 7 cm³. Find its density.

    Formula:Density

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

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