Japan · Grade 7 · Practice Sheet 37

1. 1.

   A right-angled triangle has legs of 5 cm and 12 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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2. 2.

   Find the perimeter of a rectangle measuring 38 m by 30 m.

   Formula:Perimeter of a Rectangle

   $P = 2(l + w)$

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3. 3.

   A triangle has a base of 36 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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4. 4.

   A car travels 201 km in 3 hours. Find its average speed.

   Formula:Speed

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

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5. 5.

   A bag has 21 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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6. 6.

   ¥4,200 is invested at 4% simple interest per year for 6 years. Find the interest earned.

   Formula:Simple Interest

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

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7. 7.

   Convert 3.49 kilometres into metres.

   Formula:Metric Length Conversion

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

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8. 8.

   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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9. 9.

   A circle has a radius of 3 cm. Find its area. (Use π ≈ 3.14159)

   Formula:Area of a Circle

   $A = \pi r^2$

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10. 10.

    ¥1,400 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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11. 11.

    A right-angled triangle has legs of 5 cm and 10 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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12. 12.

    What is 30% of 100?

    Formula:Percentage of a Quantity

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

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13. 13.

    A triangle has a base of 29 cm and a height of 25 cm. Find its area.

    Formula:Area of a Triangle

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

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14. 14.

    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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15. 15.

    A triangle has a base of 18 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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16. 16.

    ¥39 is shared in the ratio 2 : 1. Find each share.

    Formula:Dividing in a Ratio

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

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17. 17.

    A car travels 240 km in 4 hours. Find its average speed.

    Formula:Speed

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

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18. 18.

    A circle has a radius of 19 cm. Find its area. (Use π ≈ 3.14159)

    Formula:Area of a Circle

    $A = \pi r^2$

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19. 19.

    One item costs ¥1.79. Find the total cost of 19 items.

    Formula:Total Cost

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

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20. 20.

    A value changes from 67 to 125. 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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