Taiwan · Grade 8 · Practice Sheet 49

1. 1.

   A bag has 10 equally likely marbles, of which 7 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.

   A force of 472 N acts on an area of 5.5 m². Find the pressure.

   Formula:Pressure

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

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3. 3.

   A circle has a radius of 10 cm. Find its area. (Use π ≈ 3.14159)

   Formula:Area of a Circle

   $A = \pi r^2$

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4. 4.

   Find the mean (average) of these numbers: 79, 42, 33, 89, 18, 54.

   Formula:Arithmetic Mean

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

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5. 5.

   A right-angled triangle has legs of 8 cm and 6 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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6. 6.

   Find the circumference of a circle whose radius is 30 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 8 cm and 20 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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8. 8.

   An object has mass 36 g and volume 24 cm³. Find its density.

   Formula:Density

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

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9. 9.

   A triangle has a base of 18 cm and a height of 17 cm. Find its area.

   Formula:Area of a Triangle

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

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10. 10.

    A force of 485 N acts on an area of 5 m². Find the pressure.

    Formula:Pressure

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

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11. 11.

    An object has mass 38 g and volume 5 cm³. Find its density.

    Formula:Density

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

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12. 12.

    A current of 5.3 A flows through a 24 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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13. 13.

    What is 25% of 410?

    Formula:Percentage of a Quantity

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

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14. 14.

    Find the circumference of a circle whose radius is 8 m. (Use π ≈ 3.14159)

    Formula:Circumference of a Circle

    $C = 2\pi r$

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15. 15.

    Find the mean (average) of these numbers: 77, 62, 69, 91, 31, 51.

    Formula:Arithmetic Mean

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

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16. 16.

    Solve for x: 9x + 11 = 83.

    Formula:Solving a Linear Equation

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

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17. 17.

    A triangle has a base of 24 cm and a height of 17 cm. Find its area.

    Formula:Area of a Triangle

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

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18. 18.

    A right-angled triangle has legs of 4 cm and 17 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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19. 19.

    A train moves at 83 km/h for 4.1 hours. How far does it travel?

    Formula:Distance from Speed & Time

    $d = v \times t$

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20. 20.

    A circle has a radius of 8 cm. Find its area. (Use π ≈ 3.14159)

    Formula:Area of a Circle

    $A = \pi r^2$

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