Germany · Klasse 7 · Practice Sheet 46

1. 1.

   Find the mean (average) of these numbers: 49, 23, 72, 54, 27.

   Formula:Arithmetic Mean

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

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2. 2.

   What is 25% of 310?

   Formula:Percentage of a Quantity

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

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3. 3.

   Solve for x: 7x + 4 = 53.

   Formula:Solving a Linear Equation

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

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4. 4.

   A circle has a radius of 21 cm. Find its area. (Use π ≈ 3.14159)

   Formula:Area of a Circle

   $A = \pi r^2$

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5. 5.

   A train moves at 83 km/h for 4.5 hours. How far does it travel?

   Formula:Distance from Speed & Time

   $d = v \times t$

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6. 6.

   €60 is shared in the ratio 1 : 3. Find each share.

   Formula:Dividing in a Ratio

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

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7. 7.

   Find the area of a square with side length 20 cm.

   Formula:Area of a Square

   $A = s^2$

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8. 8.

   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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9. 9.

   A car travels 165 km in 3 hours. Find its average speed.

   Formula:Speed

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

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10. 10.

    Convert 11.49 kilometres into metres.

    Formula:Metric Length Conversion

    $1\,\text{km} = 1000\,\text{m}$

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11. 11.

    A bag has 17 equally likely marbles, of which 10 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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12. 12.

    A value changes from 198 to 184. 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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13. 13.

    Convert 7.74 kilometres into metres.

    Formula:Metric Length Conversion

    $1\,\text{km} = 1000\,\text{m}$

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14. 14.

    A value changes from 65 to 37. 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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15. 15.

    Solve for x: 6x + 12 = 78.

    Formula:Solving a Linear Equation

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

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16. 16.

    A train moves at 35 km/h for 2.1 hours. How far does it travel?

    Formula:Distance from Speed & Time

    $d = v \times t$

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17. 17.

    A rectangle is 28 cm long and 24 cm wide. Find its area.

    Formula:Area of a Rectangle

    $A = l \times w$

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18. 18.

    Find the perimeter of a rectangle measuring 41 m by 24 m.

    Formula:Perimeter of a Rectangle

    $P = 2(l + w)$

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19. 19.

    A value changes from 95 to 57. 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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20. 20.

    One item costs €19.45. Find the total cost of 11 items.

    Formula:Total Cost

    $\text{total} = \text{price} \times \text{quantity}$

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