Germany · Klasse 8 · Practice Sheet 15

1. 1.

   An object has mass 40.8 g and volume 6 cm³. Find its density.

   Formula:Density

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

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2. 2.

   Solve for x: 4x + 2 = 42.

   Formula:Solving a Linear Equation

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

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3. 3.

   €304 is shared in the ratio 3 : 5. Find each share.

   Formula:Dividing in a Ratio

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

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4. 4.

   Find the mean (average) of these numbers: 45, 25, 72, 11, 18.

   Formula:Arithmetic Mean

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

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5. 5.

   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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6. 6.

   A right-angled triangle has legs of 19 cm and 16 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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7. 7.

   Find the circumference of a circle whose radius is 6 m. (Use π ≈ 3.14159)

   Formula:Circumference of a Circle

   $C = 2\pi r$

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8. 8.

   A bag has 19 equally likely marbles, of which 4 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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9. 9.

   A value changes from 196 to 211. 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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10. 10.

    Find the circumference of a circle whose radius is 20 m. (Use π ≈ 3.14159)

    Formula:Circumference of a Circle

    $C = 2\pi r$

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11. 11.

    A train moves at 55 km/h for 4 hours. How far does it travel?

    Formula:Distance from Speed & Time

    $d = v \times t$

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12. 12.

    A current of 5 A flows through a 53 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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13. 13.

    A force of 377 N acts on an area of 4.6 m². Find the pressure.

    Formula:Pressure

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

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14. 14.

    €261 is shared in the ratio 5 : 4. 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 13 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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16. 16.

    What is 30% of 390?

    Formula:Percentage of a Quantity

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

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17. 17.

    Find the circumference of a circle whose radius is 14 m. (Use π ≈ 3.14159)

    Formula:Circumference of a Circle

    $C = 2\pi r$

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18. 18.

    A current of 1.5 A flows through a 23 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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19. 19.

    An object has mass 67.6 g and volume 13 cm³. Find its density.

    Formula:Density

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

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20. 20.

    Solve for x: 2x + 4 = 10.

    Formula:Solving a Linear Equation

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

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