Austria · Klasse 8 · Practice Sheet 36

1. 1.

   Find the circumference of a circle whose radius is 13 m. (Use π ≈ 3.14159)

   Formula:Circumference of a Circle

   $C = 2\pi r$

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2. 2.

   Solve for x: 9x + 4 = 94.

   Formula:Solving a Linear Equation

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

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3. 3.

   A force of 490 N acts on an area of 1.7 m². Find the pressure.

   Formula:Pressure

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

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4. 4.

   A train moves at 27 km/h for 5.5 hours. How far does it travel?

   Formula:Distance from Speed & Time

   $d = v \times t$

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5. 5.

   €2,800 is invested at 8% simple interest per year for 3 years. Find the interest earned.

   Formula:Simple Interest

   $I = \dfrac{P \times r \times t}{100}$

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6. 6.

   A current of 6.4 A flows through a 43 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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7. 7.

   A train moves at 77 km/h for 4.2 hours. How far does it travel?

   Formula:Distance from Speed & Time

   $d = v \times t$

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8. 8.

   A force of 291 N acts on an area of 6.3 m². Find the pressure.

   Formula:Pressure

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

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9. 9.

   €70 is shared in the ratio 1 : 1. Find each share.

   Formula:Dividing in a Ratio

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

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10. 10.

    A circle has a radius of 18 cm. Find its area. (Use π ≈ 3.14159)

    Formula:Area of a Circle

    $A = \pi r^2$

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11. 11.

    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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12. 12.

    Solve for x: 3x + 3 = 24.

    Formula:Solving a Linear Equation

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

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13. 13.

    A value changes from 108 to 229. 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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14. 14.

    What is 50% of 390?

    Formula:Percentage of a Quantity

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

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15. 15.

    A bag has 11 equally likely marbles, of which 1 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 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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17. 17.

    Solve for x: 6x + 17 = 77.

    Formula:Solving a Linear Equation

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

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18. 18.

    A value changes from 107 to 94. 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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19. 19.

    Solve for x: 4x + 13 = 57.

    Formula:Solving a Linear Equation

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

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20. 20.

    A car travels 462 km in 6 hours. Find its average speed.

    Formula:Speed

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

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