Germany · Klasse 7 · Practice Sheet 49

1. 1.

   A triangle has a base of 28 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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2. 2.

   A circle has a radius of 18 cm. Find its area. (Use π ≈ 3.14159)

   Formula:Area of a Circle

   $A = \pi r^2$

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3. 3.

   Solve for x: 2x + 5 = 21.

   Formula:Solving a Linear Equation

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

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4. 4.

   Find 1/5 of 45.

   Formula:Fraction of a Quantity

   $\text{result} = \dfrac{a}{b} \times N$

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5. 5.

   A right-angled triangle has legs of 4 cm and 20 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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6. 6.

   One item costs €15.78. Find the total cost of 10 items.

   Formula:Total Cost

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

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7. 7.

   Find the area of a square with side length 7 cm.

   Formula:Area of a Square

   $A = s^2$

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8. 8.

   Convert 5.19 kilometres into metres.

   Formula:Metric Length Conversion

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

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9. 9.

   One item costs €18.08. Find the total cost of 20 items.

   Formula:Total Cost

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

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10. 10.

    Find the perimeter of a rectangle measuring 35 m by 22 m.

    Formula:Perimeter of a Rectangle

    $P = 2(l + w)$

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11. 11.

    €40 is shared in the ratio 1 : 4. Find each share.

    Formula:Dividing in a Ratio

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

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12. 12.

    A car travels 219 km in 3 hours. Find its average speed.

    Formula:Speed

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

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13. 13.

    A train moves at 89 km/h for 1.8 hours. How far does it travel?

    Formula:Distance from Speed & Time

    $d = v \times t$

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14. 14.

    A bag has 18 equally likely marbles, of which 15 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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15. 15.

    A car travels 166 km in 2 hours. Find its average speed.

    Formula:Speed

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

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16. 16.

    €144 is shared in the ratio 4 : 2. Find each share.

    Formula:Dividing in a Ratio

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

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17. 17.

    Find the area of a square with side length 16 cm.

    Formula:Area of a Square

    $A = s^2$

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18. 18.

    Find the circumference of a circle whose radius is 15 m. (Use π ≈ 3.14159)

    Formula:Circumference of a Circle

    $C = 2\pi r$

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19. 19.

    Find the perimeter of a rectangle measuring 31 m by 21 m.

    Formula:Perimeter of a Rectangle

    $P = 2(l + w)$

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20. 20.

    One item costs €8.62. Find the total cost of 8 items.

    Formula:Total Cost

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

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