Japan · Grade 8 · Practice Sheet 23

1. 1.

   Find the mean (average) of these numbers: 64, 14, 84, 45, 24.

   Formula:Arithmetic Mean

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

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2. 2.

   A value changes from 130 to 89. 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.

   An object has mass 235.2 g and volume 48 cm³. Find its density.

   Formula:Density

   $\rho = \dfrac{m}{V}$

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4. 4.

   ¥135 is shared in the ratio 1 : 4. Find each share.

   Formula:Dividing in a Ratio

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

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5. 5.

   A bag has 29 equally likely marbles, of which 28 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.

   A value changes from 129 to 246. 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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7. 7.

   Solve for x: 8x + 19 = 43.

   Formula:Solving a Linear Equation

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

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8. 8.

   A train moves at 26 km/h for 5 hours. How far does it travel?

   Formula:Distance from Speed & Time

   $d = v \times t$

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9. 9.

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

   Formula:Speed

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

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10. 10.

    ¥1,700 is invested at 8% 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 train moves at 42 km/h for 5.7 hours. How far does it travel?

    Formula:Distance from Speed & Time

    $d = v \times t$

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12. 12.

    A right-angled triangle has legs of 6 cm and 12 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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13. 13.

    Solve for x: 4x + 3 = 27.

    Formula:Solving a Linear Equation

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

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14. 14.

    A triangle has a base of 26 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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15. 15.

    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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16. 16.

    ¥1,400 is invested at 4% simple interest per year for 3 years. Find the interest earned.

    Formula:Simple Interest

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

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17. 17.

    A train moves at 87 km/h for 5.8 hours. How far does it travel?

    Formula:Distance from Speed & Time

    $d = v \times t$

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18. 18.

    A triangle has a base of 9 cm and a height of 22 cm. Find its area.

    Formula:Area of a Triangle

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

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19. 19.

    Find the mean (average) of these numbers: 58, 96, 37, 43.

    Formula:Arithmetic Mean

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

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20. 20.

    Find the circumference of a circle whose radius is 24 m. (Use π ≈ 3.14159)

    Formula:Circumference of a Circle

    $C = 2\pi r$

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