South Korea · Grade 7 · Practice Sheet 30

1. 1.

   A value changes from 114 to 29. 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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2. 2.

   A right-angled triangle has legs of 14 cm and 12 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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3. 3.

   A bag has 23 equally likely marbles, of which 21 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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4. 4.

   Find the mean (average) of these numbers: 67, 46, 94, 13, 92.

   Formula:Arithmetic Mean

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

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5. 5.

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

   Formula:Area of a Triangle

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

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6. 6.

   Convert 5.31 kilometres into metres.

   Formula:Metric Length Conversion

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

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7. 7.

   Find 1/5 of 45.

   Formula:Fraction of a Quantity

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

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8. 8.

   A car travels 768 km in 8 hours. Find its average speed.

   Formula:Speed

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

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9. 9.

   A right-angled triangle has legs of 15 cm and 9 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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10. 10.

    What is 25% of 500?

    Formula:Percentage of a Quantity

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

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11. 11.

    A car travels 186 km in 3 hours. Find its average speed.

    Formula:Speed

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

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12. 12.

    A circle has a radius of 20 cm. Find its area. (Use π ≈ 3.14159)

    Formula:Area of a Circle

    $A = \pi r^2$

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13. 13.

    Convert 1.73 kilometres into metres.

    Formula:Metric Length Conversion

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

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14. 14.

    A rectangle is 35 cm long and 30 cm wide. Find its area.

    Formula:Area of a Rectangle

    $A = l \times w$

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15. 15.

    Find 1/2 of 14.

    Formula:Fraction of a Quantity

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

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16. 16.

    A right-angled triangle has legs of 15 cm and 9 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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17. 17.

    Convert 5.6 kilometres into metres.

    Formula:Metric Length Conversion

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

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18. 18.

    Find 1/2 of 18.

    Formula:Fraction of a Quantity

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

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19. 19.

    A train moves at 90 km/h for 3.4 hours. How far does it travel?

    Formula:Distance from Speed & Time

    $d = v \times t$

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20. 20.

    A bag has 11 equally likely marbles, of which 7 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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