Japan · Grade 8 · Practice Sheet 16

1. 1.

   ¥156 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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2. 2.

   A right-angled triangle has legs of 5 cm and 8 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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3. 3.

   Find the mean (average) of these numbers: 52, 75, 55, 18.

   Formula:Arithmetic Mean

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

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4. 4.

   A train moves at 36 km/h for 5 hours. How far does it travel?

   Formula:Distance from Speed & Time

   $d = v \times t$

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5. 5.

   Find the mean (average) of these numbers: 94, 47, 10, 21.

   Formula:Arithmetic Mean

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

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6. 6.

   A car travels 93 km in 3 hours. Find its average speed.

   Formula:Speed

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

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7. 7.

   A bag has 11 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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8. 8.

   A current of 5.9 A flows through a 60 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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9. 9.

   A circle has a radius of 12 cm. Find its area. (Use π ≈ 3.14159)

   Formula:Area of a Circle

   $A = \pi r^2$

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10. 10.

    A triangle has a base of 39 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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11. 11.

    A bag has 21 equally likely marbles, of which 17 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.

    What is 75% of 280?

    Formula:Percentage of a Quantity

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

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13. 13.

    Find the mean (average) of these numbers: 99, 95, 87, 10, 30.

    Formula:Arithmetic Mean

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

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14. 14.

    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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15. 15.

    Solve for x: 6x + 13 = 61.

    Formula:Solving a Linear Equation

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

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16. 16.

    A train moves at 97 km/h for 2.8 hours. How far does it travel?

    Formula:Distance from Speed & Time

    $d = v \times t$

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17. 17.

    ¥2,000 is invested at 7.5% 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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18. 18.

    ¥80 is shared in the ratio 3 : 2. Find each share.

    Formula:Dividing in a Ratio

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

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19. 19.

    Find the circumference of a circle whose radius is 13 m. (Use π ≈ 3.14159)

    Formula:Circumference of a Circle

    $C = 2\pi r$

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20. 20.

    A bag has 9 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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