Germany · Klasse 8 · Practice Sheet 7

1. 1.

   Solve for x: 6x + 11 = 71.

   Formula:Solving a Linear Equation

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

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2. 2.

   A bag has 20 equally likely marbles, of which 5 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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3. 3.

   A train moves at 85 km/h for 4.4 hours. How far does it travel?

   Formula:Distance from Speed & Time

   $d = v \times t$

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4. 4.

   A triangle has a base of 34 cm and a height of 22 cm. Find its area.

   Formula:Area of a Triangle

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

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5. 5.

   A bag has 9 equally likely marbles, of which 8 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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6. 6.

   A force of 490 N acts on an area of 1.3 m². Find the pressure.

   Formula:Pressure

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

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7. 7.

   A triangle has a base of 16 cm and a height of 6 cm. Find its area.

   Formula:Area of a Triangle

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

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8. 8.

   A current of 4.9 A flows through a 60 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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9. 9.

   A value changes from 124 to 123. 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.

    A car travels 220 km in 2 hours. Find its average speed.

    Formula:Speed

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

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11. 11.

    A train moves at 46 km/h for 5.8 hours. How far does it travel?

    Formula:Distance from Speed & Time

    $d = v \times t$

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12. 12.

    An object has mass 48.6 g and volume 18 cm³. Find its density.

    Formula:Density

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

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13. 13.

    Find the mean (average) of these numbers: 94, 92, 21, 72, 84, 18.

    Formula:Arithmetic Mean

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

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14. 14.

    A right-angled triangle has legs of 11 cm and 13 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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15. 15.

    What is 5% of 460?

    Formula:Percentage of a Quantity

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

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16. 16.

    A circle has a radius of 12 cm. Find its area. (Use π ≈ 3.14159)

    Formula:Area of a Circle

    $A = \pi r^2$

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17. 17.

    A current of 5.4 A flows through a 59 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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18. 18.

    Find the mean (average) of these numbers: 13, 75, 45, 59, 79, 81.

    Formula:Arithmetic Mean

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

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19. 19.

    A current of 5.4 A flows through a 59 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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20. 20.

    A train moves at 71 km/h for 2.4 hours. How far does it travel?

    Formula:Distance from Speed & Time

    $d = v \times t$

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