Japan · Grade 8 · Practice Sheet 36

1. 1.

   ¥300 is shared in the ratio 5 : 5. Find each share.

   Formula:Dividing in a Ratio

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

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2. 2.

   A car travels 567 km in 7 hours. Find its average speed.

   Formula:Speed

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

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3. 3.

   Solve for x: 3x + 10 = 40.

   Formula:Solving a Linear Equation

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

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4. 4.

   ¥140 is shared in the ratio 5 : 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.

   A circle has a radius of 23 cm. Find its area. (Use π ≈ 3.14159)

   Formula:Area of a Circle

   $A = \pi r^2$

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6. 6.

   ¥4,400 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.

   A force of 333 N acts on an area of 4.8 m². Find the pressure.

   Formula:Pressure

   $P = \dfrac{F}{A}$

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8. 8.

   A circle has a radius of 18 cm. Find its area. (Use π ≈ 3.14159)

   Formula:Area of a Circle

   $A = \pi r^2$

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9. 9.

   A bag has 14 equally likely marbles, of which 6 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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10. 10.

    A triangle has a base of 32 cm and a height of 9 cm. Find its area.

    Formula:Area of a Triangle

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

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11. 11.

    Solve for x: 9x + 18 = 63.

    Formula:Solving a Linear Equation

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

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12. 12.

    An object has mass 142.6 g and volume 46 cm³. Find its density.

    Formula:Density

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

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13. 13.

    A triangle has a base of 16 cm and a height of 19 cm. Find its area.

    Formula:Area of a Triangle

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

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14. 14.

    Solve for x: 9x + 16 = 34.

    Formula:Solving a Linear Equation

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

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15. 15.

    A circle has a radius of 20 cm. Find its area. (Use π ≈ 3.14159)

    Formula:Area of a Circle

    $A = \pi r^2$

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16. 16.

    A force of 205 N acts on an area of 6.4 m². Find the pressure.

    Formula:Pressure

    $P = \dfrac{F}{A}$

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17. 17.

    A right-angled triangle has legs of 4 cm and 7 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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18. 18.

    Find the mean (average) of these numbers: 84, 23, 55, 50, 76.

    Formula:Arithmetic Mean

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

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19. 19.

    What is 40% of 200?

    Formula:Percentage of a Quantity

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

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20. 20.

    A train moves at 44 km/h for 2.6 hours. How far does it travel?

    Formula:Distance from Speed & Time

    $d = v \times t$

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