Austria · Klasse 7 · Practice Sheet 32

1. 1.

   A circle has a radius of 15 cm. Find its area. (Use π ≈ 3.14159)

   Formula:Area of a Circle

   $A = \pi r^2$

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2. 2.

   One item costs €19.15. Find the total cost of 5 items.

   Formula:Total Cost

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

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3. 3.

   Find the mean (average) of these numbers: 50, 66, 57, 28, 69.

   Formula:Arithmetic Mean

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

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4. 4.

   A rectangle is 39 cm long and 12 cm wide. Find its area.

   Formula:Area of a Rectangle

   $A = l \times w$

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5. 5.

   Convert 11.22 kilometres into metres.

   Formula:Metric Length Conversion

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

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6. 6.

   A right-angled triangle has legs of 10 cm and 5 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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7. 7.

   Convert 9.06 kilometres into metres.

   Formula:Metric Length Conversion

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

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8. 8.

   Find the perimeter of a rectangle measuring 45 m by 19 m.

   Formula:Perimeter of a Rectangle

   $P = 2(l + w)$

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9. 9.

   A bag has 25 equally likely marbles, of which 20 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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10. 10.

    Find the perimeter of a rectangle measuring 23 m by 18 m.

    Formula:Perimeter of a Rectangle

    $P = 2(l + w)$

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11. 11.

    Solve for x: 6x + 1 = 25.

    Formula:Solving a Linear Equation

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

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12. 12.

    A car travels 570 km in 6 hours. Find its average speed.

    Formula:Speed

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

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13. 13.

    Find the mean (average) of these numbers: 94, 72, 11, 21, 69, 26.

    Formula:Arithmetic Mean

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

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14. 14.

    A train moves at 42 km/h for 2.2 hours. How far does it travel?

    Formula:Distance from Speed & Time

    $d = v \times t$

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15. 15.

    Solve for x: 8x + 11 = 59.

    Formula:Solving a Linear Equation

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

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16. 16.

    A bag has 13 equally likely marbles, of which 1 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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17. 17.

    €600 is invested at 6% simple interest per year for 6 years. Find the interest earned.

    Formula:Simple Interest

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

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18. 18.

    A train moves at 30 km/h for 1.7 hours. How far does it travel?

    Formula:Distance from Speed & Time

    $d = v \times t$

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19. 19.

    €54 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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20. 20.

    Find the perimeter of a rectangle measuring 6 m by 32 m.

    Formula:Perimeter of a Rectangle

    $P = 2(l + w)$

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