Japan · Grade 7 · Practice Sheet 30

1. 1.

   A value changes from 24 to 191. 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 circle has a radius of 21 cm. Find its area. (Use π ≈ 3.14159)

   Formula:Area of a Circle

   $A = \pi r^2$

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3. 3.

   Find the mean (average) of these numbers: 24, 39, 47, 48, 11, 22.

   Formula:Arithmetic Mean

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

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4. 4.

   What is 5% of 540?

   Formula:Percentage of a Quantity

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

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5. 5.

   A triangle has a base of 36 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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6. 6.

   ¥3,000 is invested at 10% 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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7. 7.

   One item costs ¥24.89. Find the total cost of 7 items.

   Formula:Total Cost

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

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8. 8.

   A train moves at 45 km/h for 4.4 hours. How far does it travel?

   Formula:Distance from Speed & Time

   $d = v \times t$

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9. 9.

   A triangle has a base of 20 cm and a height of 12 cm. Find its area.

   Formula:Area of a Triangle

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

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10. 10.

    Find the mean (average) of these numbers: 32, 19, 45, 82, 81.

    Formula:Arithmetic Mean

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

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11. 11.

    A circle has a radius of 21 cm. Find its area. (Use π ≈ 3.14159)

    Formula:Area of a Circle

    $A = \pi r^2$

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12. 12.

    Find the circumference of a circle whose radius is 30 m. (Use π ≈ 3.14159)

    Formula:Circumference of a Circle

    $C = 2\pi r$

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13. 13.

    A train moves at 84 km/h for 3.6 hours. How far does it travel?

    Formula:Distance from Speed & Time

    $d = v \times t$

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14. 14.

    A car travels 480 km in 6 hours. Find its average speed.

    Formula:Speed

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

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15. 15.

    A right-angled triangle has legs of 9 cm and 16 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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16. 16.

    A bag has 22 equally likely marbles, of which 4 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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17. 17.

    A car travels 405 km in 5 hours. Find its average speed.

    Formula:Speed

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

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18. 18.

    Find the perimeter of a rectangle measuring 6 m by 33 m.

    Formula:Perimeter of a Rectangle

    $P = 2(l + w)$

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19. 19.

    A right-angled triangle has legs of 17 cm and 19 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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20. 20.

    Solve for x: 3x + 6 = 12.

    Formula:Solving a Linear Equation

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

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