South Korea · Grade 8 · Practice Sheet 13

1. 1.

   A right-angled triangle has legs of 9 cm and 14 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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2. 2.

   Find the circumference of a circle whose radius is 9 m. (Use π ≈ 3.14159)

   Formula:Circumference of a Circle

   $C = 2\pi r$

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3. 3.

   An object has mass 169.2 g and volume 36 cm³. Find its density.

   Formula:Density

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

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4. 4.

   A train moves at 23 km/h for 3.1 hours. How far does it travel?

   Formula:Distance from Speed & Time

   $d = v \times t$

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5. 5.

   A car travels 256 km in 8 hours. Find its average speed.

   Formula:Speed

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

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6. 6.

   Find the mean (average) of these numbers: 83, 55, 25, 13, 82, 62.

   Formula:Arithmetic Mean

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

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7. 7.

   ₩3,000 is invested at 7.5% simple interest per year for 6 years. Find the interest earned.

   Formula:Simple Interest

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

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8. 8.

   A cylinder has radius 6 cm and height 17 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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9. 9.

   A circle has a radius of 16 cm. Find its area. (Use π ≈ 3.14159)

   Formula:Area of a Circle

   $A = \pi r^2$

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10. 10.

    A force of 238 N acts on an area of 5.4 m². Find the pressure.

    Formula:Pressure

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

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11. 11.

    A triangle has a base of 10 cm and a height of 3 cm. Find its area.

    Formula:Area of a Triangle

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

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12. 12.

    A force of 239 N acts on an area of 9.4 m². Find the pressure.

    Formula:Pressure

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

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13. 13.

    A bag has 25 equally likely marbles, of which 22 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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14. 14.

    What is 20% of 240?

    Formula:Percentage of a Quantity

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

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15. 15.

    ₩1,300 is invested at 6% simple interest per year for 5 years. Find the interest earned.

    Formula:Simple Interest

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

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16. 16.

    ₩126 is shared in the ratio 3 : 4. Find each share.

    Formula:Dividing in a Ratio

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

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17. 17.

    A right-angled triangle has legs of 19 cm and 11 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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18. 18.

    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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19. 19.

    A train moves at 88 km/h for 3.9 hours. How far does it travel?

    Formula:Distance from Speed & Time

    $d = v \times t$

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20. 20.

    Find the mean (average) of these numbers: 80, 75, 45, 83, 66, 53.

    Formula:Arithmetic Mean

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

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