Japan · Grade 8 · Practice Sheet 12

1. 1.

   A bag has 29 equally likely marbles, of which 9 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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2. 2.

   What is 75% of 510?

   Formula:Percentage of a Quantity

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

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3. 3.

   A triangle has a base of 13 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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4. 4.

   ¥68 is shared in the ratio 3 : 1. Find each share.

   Formula:Dividing in a Ratio

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

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5. 5.

   An object has mass 66.5 g and volume 19 cm³. Find its density.

   Formula:Density

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

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6. 6.

   Find the circumference of a circle whose radius is 28 m. (Use π ≈ 3.14159)

   Formula:Circumference of a Circle

   $C = 2\pi r$

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7. 7.

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

   Formula:Pythagorean Theorem

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

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8. 8.

   ¥3,100 is invested at 8% 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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9. 9.

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

   Formula:Density

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

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10. 10.

    A right-angled triangle has legs of 3 cm and 20 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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11. 11.

    A bag has 8 equally likely marbles, of which 3 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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12. 12.

    A triangle has a base of 6 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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13. 13.

    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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14. 14.

    An object has mass 61.2 g and volume 34 cm³. Find its density.

    Formula:Density

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

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15. 15.

    A car travels 490 km in 7 hours. Find its average speed.

    Formula:Speed

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

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16. 16.

    An object has mass 99.6 g and volume 12 cm³. Find its density.

    Formula:Density

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

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17. 17.

    Find the mean (average) of these numbers: 76, 21, 83, 80.

    Formula:Arithmetic Mean

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

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18. 18.

    Solve for x: 5x + 3 = 63.

    Formula:Solving a Linear Equation

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

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19. 19.

    A force of 109 N acts on an area of 2.3 m². Find the pressure.

    Formula:Pressure

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

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20. 20.

    Find the circumference of a circle whose radius is 7 m. (Use π ≈ 3.14159)

    Formula:Circumference of a Circle

    $C = 2\pi r$

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