Ireland · Year 7 · Practice Sheet 22

1. 1.

   A right-angled triangle has legs of 15 cm and 4 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 27 km/h for 3.9 hours. How far does it travel?

   Formula:Distance from Speed & Time

   $d = v \times t$

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3. 3.

   A rectangle is 5 cm long and 24 cm wide. Find its area.

   Formula:Area of a Rectangle

   $A = l \times w$

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4. 4.

   Find the perimeter of a rectangle measuring 26 m by 19 m.

   Formula:Perimeter of a Rectangle

   $P = 2(l + w)$

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5. 5.

   A right-angled triangle has legs of 9 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.

   Find 2/3 of 51.

   Formula:Fraction of a Quantity

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

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7. 7.

   A car travels 96 km in 2 hours. Find its average speed.

   Formula:Speed

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

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8. 8.

   €2,500 is invested at 3% simple interest per year for 3 years. Find the interest earned.

   Formula:Simple Interest

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

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9. 9.

   What is 25% of 310?

   Formula:Percentage of a Quantity

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

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10. 10.

    Convert 4.62 kilometres into metres.

    Formula:Metric Length Conversion

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

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11. 11.

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

    Formula:Pythagorean Theorem

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

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12. 12.

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

    Formula:Area of a Square

    $A = s^2$

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13. 13.

    €78 is shared in the ratio 1 : 1. Find each share.

    Formula:Dividing in a Ratio

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

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14. 14.

    A triangle has a base of 14 cm and a height of 14 cm. Find its area.

    Formula:Area of a Triangle

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

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15. 15.

    €126 is shared in the ratio 4 : 3. Find each share.

    Formula:Dividing in a Ratio

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

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16. 16.

    Convert 2 kilometres into metres.

    Formula:Metric Length Conversion

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

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17. 17.

    A bag has 14 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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18. 18.

    A circle has a radius of 8 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 circumference of a circle whose radius is 7 m. (Use π ≈ 3.14159)

    Formula:Circumference of a Circle

    $C = 2\pi r$

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20. 20.

    A value changes from 73 to 234. 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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