Germany · Klasse 7 · Practice Sheet 23

1. 1.

   A right-angled triangle has legs of 9 cm and 19 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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2. 2.

   A train moves at 23 km/h for 3.3 hours. How far does it travel?

   Formula:Distance from Speed & Time

   $d = v \times t$

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3. 3.

   Find 1/8 of 160.

   Formula:Fraction of a Quantity

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

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4. 4.

   A bag has 18 equally likely marbles, of which 13 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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5. 5.

   One item costs €8.59. Find the total cost of 15 items.

   Formula:Total Cost

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

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6. 6.

   A bag has 9 equally likely marbles, of which 2 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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7. 7.

   A value changes from 114 to 175. 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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8. 8.

   A triangle has a base of 35 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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9. 9.

   €600 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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10. 10.

    A value changes from 185 to 216. 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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11. 11.

    Solve for x: 5x + 13 = 68.

    Formula:Solving a Linear Equation

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

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12. 12.

    A train moves at 93 km/h for 4.7 hours. How far does it travel?

    Formula:Distance from Speed & Time

    $d = v \times t$

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13. 13.

    What is 50% of 370?

    Formula:Percentage of a Quantity

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

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14. 14.

    Solve for x: 6x + 9 = 69.

    Formula:Solving a Linear Equation

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

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15. 15.

    A right-angled triangle has legs of 16 cm and 18 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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16. 16.

    Find the circumference of a circle whose radius is 27 m. (Use π ≈ 3.14159)

    Formula:Circumference of a Circle

    $C = 2\pi r$

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17. 17.

    A triangle has a base of 5 cm and a height of 21 cm. Find its area.

    Formula:Area of a Triangle

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

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18. 18.

    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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19. 19.

    Find the area of a square with side length 3 cm.

    Formula:Area of a Square

    $A = s^2$

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20. 20.

    One item costs €12.26. Find the total cost of 13 items.

    Formula:Total Cost

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

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