Japan · Grade 7 · Practice Sheet 24

1. 1.

   A triangle has a base of 10 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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2. 2.

   A value changes from 175 to 86. 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 right-angled triangle has legs of 6 cm and 16 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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4. 4.

   ¥3,300 is invested at 7.5% 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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5. 5.

   Convert 5.73 kilometres into metres.

   Formula:Metric Length Conversion

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

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6. 6.

   Find the area of a square with side length 23 cm.

   Formula:Area of a Square

   $A = s^2$

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7. 7.

   A car travels 520 km in 5 hours. Find its average speed.

   Formula:Speed

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

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8. 8.

   ¥1,000 is invested at 5% 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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9. 9.

   One item costs ¥6.86. Find the total cost of 4 items.

   Formula:Total Cost

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

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10. 10.

    A train moves at 65 km/h for 4.7 hours. How far does it travel?

    Formula:Distance from Speed & Time

    $d = v \times t$

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11. 11.

    Find the perimeter of a rectangle measuring 16 m by 22 m.

    Formula:Perimeter of a Rectangle

    $P = 2(l + w)$

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12. 12.

    What is 40% of 390?

    Formula:Percentage of a Quantity

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

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13. 13.

    Find the area of a square with side length 22 cm.

    Formula:Area of a Square

    $A = s^2$

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14. 14.

    What is 10% of 330?

    Formula:Percentage of a Quantity

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

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15. 15.

    A car travels 414 km in 6 hours. Find its average speed.

    Formula:Speed

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

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16. 16.

    Solve for x: 7x + 18 = 53.

    Formula:Solving a Linear Equation

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

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17. 17.

    Find the mean (average) of these numbers: 49, 64, 28, 84, 27, 77.

    Formula:Arithmetic Mean

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

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18. 18.

    Find the circumference of a circle whose radius is 29 m. (Use π ≈ 3.14159)

    Formula:Circumference of a Circle

    $C = 2\pi r$

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19. 19.

    Find the mean (average) of these numbers: 20, 99, 79, 50, 40, 17.

    Formula:Arithmetic Mean

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

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20. 20.

    Find the circumference of a circle whose radius is 10 m. (Use π ≈ 3.14159)

    Formula:Circumference of a Circle

    $C = 2\pi r$

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