Portugal · Ano 7 · Practice Sheet 5

1. 1.

   A right-angled triangle has legs of 14 cm and 15 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 20 cm and a height of 15 cm. Find its area.

   Formula:Area of a Triangle

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

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3. 3.

   Find the area of a square with side length 29 cm.

   Formula:Area of a Square

   $A = s^2$

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4. 4.

   A rectangle is 31 cm long and 12 cm wide. Find its area.

   Formula:Area of a Rectangle

   $A = l \times w$

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5. 5.

   Find the mean (average) of these numbers: 16, 94, 66, 61, 48, 71.

   Formula:Arithmetic Mean

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

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6. 6.

   A right-angled triangle has legs of 7 cm and 7 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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7. 7.

   €180 is shared in the ratio 3 : 3. Find each share.

   Formula:Dividing in a Ratio

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

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8. 8.

   Find the mean (average) of these numbers: 25, 69, 19, 38, 73.

   Formula:Arithmetic Mean

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

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9. 9.

   What is 40% of 510?

   Formula:Percentage of a Quantity

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

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10. 10.

    A value changes from 147 to 55. 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.

    Find the mean (average) of these numbers: 19, 14, 70, 23, 40, 25.

    Formula:Arithmetic Mean

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

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12. 12.

    A bag has 19 equally likely marbles, of which 5 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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13. 13.

    One item costs €2.4. Find the total cost of 7 items.

    Formula:Total Cost

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

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14. 14.

    €65 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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15. 15.

    A train moves at 40 km/h for 5.8 hours. How far does it travel?

    Formula:Distance from Speed & Time

    $d = v \times t$

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16. 16.

    A rectangle is 31 cm long and 23 cm wide. Find its area.

    Formula:Area of a Rectangle

    $A = l \times w$

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17. 17.

    Find the circumference of a circle whose radius is 30 m. (Use π ≈ 3.14159)

    Formula:Circumference of a Circle

    $C = 2\pi r$

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18. 18.

    A bag has 13 equally likely marbles, of which 12 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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19. 19.

    A value changes from 181 to 79. 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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20. 20.

    Solve for x: 8x + 20 = 108.

    Formula:Solving a Linear Equation

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

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