Belgium · Year 7 · Practice Sheet 3

1. 1.

   A right-angled triangle has legs of 16 cm and 8 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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2. 2.

   A value changes from 42 to 59. 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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3. 3.

   What is 30% of 550?

   Formula:Percentage of a Quantity

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

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4. 4.

   Find the mean (average) of these numbers: 22, 35, 65, 40, 62, 99.

   Formula:Arithmetic Mean

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

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5. 5.

   €2,500 is invested at 4% 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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6. 6.

   A right-angled triangle has legs of 14 cm and 10 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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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 mean (average) of these numbers: 58, 32, 63, 49, 28.

   Formula:Arithmetic Mean

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

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9. 9.

   A right-angled triangle has legs of 12 cm and 6 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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10. 10.

    A circle has a radius of 17 cm. Find its area. (Use π ≈ 3.14159)

    Formula:Area of a Circle

    $A = \pi r^2$

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11. 11.

    A bag has 23 equally likely marbles, of which 17 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 car travels 64 km in 2 hours. Find its average speed.

    Formula:Speed

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

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13. 13.

    A right-angled triangle has legs of 5 cm and 16 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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14. 14.

    What is 25% of 470?

    Formula:Percentage of a Quantity

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

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15. 15.

    A bag has 9 equally likely marbles, of which 8 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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16. 16.

    Find 2/5 of 20.

    Formula:Fraction of a Quantity

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

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17. 17.

    A value changes from 121 to 179. 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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18. 18.

    A rectangle is 28 cm long and 27 cm wide. Find its area.

    Formula:Area of a Rectangle

    $A = l \times w$

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19. 19.

    Find the mean (average) of these numbers: 33, 72, 69, 56, 45.

    Formula:Arithmetic Mean

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

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20. 20.

    Find the area of a square with side length 14 cm.

    Formula:Area of a Square

    $A = s^2$

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