Japan · Grade 7 · Practice Sheet 22

1. 1.

   A right-angled triangle has legs of 19 cm and 7 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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2. 2.

   A bag has 26 equally likely marbles, of which 11 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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3. 3.

   A train moves at 35 km/h for 2.7 hours. How far does it travel?

   Formula:Distance from Speed & Time

   $d = v \times t$

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4. 4.

   Find 1/2 of 38.

   Formula:Fraction of a Quantity

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

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5. 5.

   Solve for x: 7x + 19 = 61.

   Formula:Solving a Linear Equation

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

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6. 6.

   A rectangle is 8 cm long and 6 cm wide. Find its area.

   Formula:Area of a Rectangle

   $A = l \times w$

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7. 7.

   Find the mean (average) of these numbers: 70, 33, 87, 70, 11.

   Formula:Arithmetic Mean

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

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8. 8.

   A triangle has a base of 34 cm and a height of 6 cm. Find its area.

   Formula:Area of a Triangle

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

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9. 9.

   One item costs ¥17.15. Find the total cost of 19 items.

   Formula:Total Cost

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

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10. 10.

    ¥500 is invested at 4% simple interest per year for 4 years. Find the interest earned.

    Formula:Simple Interest

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

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11. 11.

    A value changes from 81 to 100. 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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12. 12.

    A rectangle is 25 cm long and 16 cm wide. Find its area.

    Formula:Area of a Rectangle

    $A = l \times w$

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13. 13.

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

    Formula:Pythagorean Theorem

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

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14. 14.

    Convert 4.73 kilometres into metres.

    Formula:Metric Length Conversion

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

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15. 15.

    ¥5,000 is invested at 6% simple interest per year for 4 years. Find the interest earned.

    Formula:Simple Interest

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

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16. 16.

    Find the mean (average) of these numbers: 62, 34, 82, 62, 48.

    Formula:Arithmetic Mean

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

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17. 17.

    A triangle has a base of 17 cm and a height of 5 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 5 cm. Find its area. (Use π ≈ 3.14159)

    Formula:Area of a Circle

    $A = \pi r^2$

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19. 19.

    A car travels 195 km in 5 hours. Find its average speed.

    Formula:Speed

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

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20. 20.

    A triangle has a base of 12 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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