Japan · Grade 7 · Practice Sheet 13

1. 1.

   Find the circumference of a circle whose radius is 25 m. (Use π ≈ 3.14159)

   Formula:Circumference of a Circle

   $C = 2\pi r$

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2. 2.

   A value changes from 123 to 93. 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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3. 3.

   A triangle has a base of 10 cm and a height of 3 cm. Find its area.

   Formula:Area of a Triangle

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

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4. 4.

   ¥228 is shared in the ratio 4 : 2. Find each share.

   Formula:Dividing in a Ratio

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

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5. 5.

   ¥4,500 is invested at 10% 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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6. 6.

   Convert 11.63 kilometres into metres.

   Formula:Metric Length Conversion

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

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7. 7.

   A car travels 196 km in 2 hours. Find its average speed.

   Formula:Speed

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

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8. 8.

   A circle has a radius of 7 cm. Find its area. (Use π ≈ 3.14159)

   Formula:Area of a Circle

   $A = \pi r^2$

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9. 9.

   Find the circumference of a circle whose radius is 19 m. (Use π ≈ 3.14159)

   Formula:Circumference of a Circle

   $C = 2\pi r$

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10. 10.

    A value changes from 145 to 186. 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.

    A triangle has a base of 10 cm and a height of 4 cm. Find its area.

    Formula:Area of a Triangle

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

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12. 12.

    Find the mean (average) of these numbers: 45, 19, 78, 38, 78, 18.

    Formula:Arithmetic Mean

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

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13. 13.

    What is 75% of 570?

    Formula:Percentage of a Quantity

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

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14. 14.

    One item costs ¥9.06. Find the total cost of 5 items.

    Formula:Total Cost

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

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15. 15.

    Find the area of a square with side length 3 cm.

    Formula:Area of a Square

    $A = s^2$

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16. 16.

    Find the perimeter of a rectangle measuring 27 m by 35 m.

    Formula:Perimeter of a Rectangle

    $P = 2(l + w)$

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17. 17.

    A rectangle is 8 cm long and 22 cm wide. Find its area.

    Formula:Area of a Rectangle

    $A = l \times w$

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18. 18.

    A value changes from 165 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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19. 19.

    Find the mean (average) of these numbers: 31, 20, 46, 72, 99.

    Formula:Arithmetic Mean

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

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20. 20.

    A car travels 416 km in 8 hours. Find its average speed.

    Formula:Speed

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

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