Austria · Klasse 8 · Practice Sheet 37

1. 1.

   What is 25% of 120?

   Formula:Percentage of a Quantity

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

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2. 2.

   A cylinder has radius 9 cm and height 20 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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3. 3.

   €4,800 is invested at 6% 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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4. 4.

   A car travels 162 km in 2 hours. Find its average speed.

   Formula:Speed

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

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5. 5.

   Solve for x: 4x + 15 = 23.

   Formula:Solving a Linear Equation

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

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6. 6.

   A value changes from 145 to 230. 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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7. 7.

   Find the circumference of a circle whose radius is 7 m. (Use π ≈ 3.14159)

   Formula:Circumference of a Circle

   $C = 2\pi r$

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8. 8.

   A right-angled triangle has legs of 19 cm and 8 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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9. 9.

   €1,200 is invested at 5% simple interest per year for 2 years. Find the interest earned.

   Formula:Simple Interest

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

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10. 10.

    A bag has 15 equally likely marbles, of which 14 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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11. 11.

    A value changes from 66 to 74. 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 train moves at 24 km/h for 1.6 hours. How far does it travel?

    Formula:Distance from Speed & Time

    $d = v \times t$

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13. 13.

    Find the mean (average) of these numbers: 62, 62, 88, 16, 77, 30.

    Formula:Arithmetic Mean

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

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14. 14.

    €27 is shared in the ratio 1 : 2. Find each share.

    Formula:Dividing in a Ratio

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

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15. 15.

    A bag has 26 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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16. 16.

    An object has mass 176.3 g and volume 43 cm³. Find its density.

    Formula:Density

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

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17. 17.

    A current of 4.6 A flows through a 5 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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18. 18.

    A car travels 138 km in 2 hours. Find its average speed.

    Formula:Speed

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

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19. 19.

    A circle has a radius of 11 cm. Find its area. (Use π ≈ 3.14159)

    Formula:Area of a Circle

    $A = \pi r^2$

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20. 20.

    Find the mean (average) of these numbers: 45, 64, 23, 64.

    Formula:Arithmetic Mean

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

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