Germany · Klasse 7 · Practice Sheet 1

1. 1.

   A right-angled triangle has legs of 11 cm and 14 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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2. 2.

   A triangle has a base of 24 cm and a height of 20 cm. Find its area.

   Formula:Area of a Triangle

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

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3. 3.

   One item costs €13.51. Find the total cost of 4 items.

   Formula:Total Cost

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

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4. 4.

   What is 20% of 590?

   Formula:Percentage of a Quantity

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

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5. 5.

   One item costs €1.7. Find the total cost of 3 items.

   Formula:Total Cost

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

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6. 6.

   A car travels 260 km in 5 hours. Find its average speed.

   Formula:Speed

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

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7. 7.

   Solve for x: 6x + 12 = 84.

   Formula:Solving a Linear Equation

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

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8. 8.

   €2,900 is invested at 3% 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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9. 9.

   A rectangle is 17 cm long and 11 cm wide. Find its area.

   Formula:Area of a Rectangle

   $A = l \times w$

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10. 10.

    €216 is shared in the ratio 3 : 5. Find each share.

    Formula:Dividing in a Ratio

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

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11. 11.

    Convert 5.24 kilometres into metres.

    Formula:Metric Length Conversion

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

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12. 12.

    €2,900 is invested at 4% simple interest per year for 5 years. Find the interest earned.

    Formula:Simple Interest

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

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13. 13.

    A right-angled triangle has legs of 9 cm and 12 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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14. 14.

    Find the circumference of a circle whose radius is 16 m. (Use π ≈ 3.14159)

    Formula:Circumference of a Circle

    $C = 2\pi r$

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15. 15.

    What is 20% of 390?

    Formula:Percentage of a Quantity

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

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16. 16.

    Find the circumference of a circle whose radius is 4 m. (Use π ≈ 3.14159)

    Formula:Circumference of a Circle

    $C = 2\pi r$

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17. 17.

    Find the perimeter of a rectangle measuring 28 m by 12 m.

    Formula:Perimeter of a Rectangle

    $P = 2(l + w)$

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18. 18.

    €2,200 is invested at 8% simple interest per year for 4 years. Find the interest earned.

    Formula:Simple Interest

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

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19. 19.

    €228 is shared in the ratio 2 : 4. Find each share.

    Formula:Dividing in a Ratio

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

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20. 20.

    A bag has 23 equally likely marbles, of which 4 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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