Germany · Klasse 8 · Practice Sheet 12

1. 1.

   Solve for x: 2x + 19 = 27.

   Formula:Solving a Linear Equation

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

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2. 2.

   Find the mean (average) of these numbers: 74, 10, 39, 50.

   Formula:Arithmetic Mean

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

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3. 3.

   A value changes from 179 to 130. 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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4. 4.

   What is 50% of 410?

   Formula:Percentage of a Quantity

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

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5. 5.

   A circle has a radius of 23 cm. Find its area. (Use π ≈ 3.14159)

   Formula:Area of a Circle

   $A = \pi r^2$

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6. 6.

   A train moves at 76 km/h for 1.6 hours. How far does it travel?

   Formula:Distance from Speed & Time

   $d = v \times t$

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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.

   An object has mass 56.7 g and volume 7 cm³. Find its density.

   Formula:Density

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

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9. 9.

   A triangle has a base of 36 cm and a height of 7 cm. Find its area.

   Formula:Area of a Triangle

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

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10. 10.

    A circle has a radius of 13 cm. Find its area. (Use π ≈ 3.14159)

    Formula:Area of a Circle

    $A = \pi r^2$

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11. 11.

    A cylinder has radius 8 cm and height 15 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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12. 12.

    Find the mean (average) of these numbers: 96, 55, 23, 60.

    Formula:Arithmetic Mean

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

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13. 13.

    A triangle has a base of 36 cm and a height of 4 cm. Find its area.

    Formula:Area of a Triangle

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

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14. 14.

    A car travels 236 km in 4 hours. Find its average speed.

    Formula:Speed

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

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15. 15.

    A right-angled triangle has legs of 5 cm and 6 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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16. 16.

    €234 is shared in the ratio 1 : 5. Find each share.

    Formula:Dividing in a Ratio

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

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17. 17.

    A force of 386 N acts on an area of 1.3 m². Find the pressure.

    Formula:Pressure

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

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18. 18.

    Solve for x: 2x + 2 = 6.

    Formula:Solving a Linear Equation

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

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19. 19.

    €900 is invested at 6% 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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20. 20.

    A cylinder has radius 3 cm and height 24 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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