Belgium · Year 8 · Practice Sheet 5

1. 1.

   Find the mean (average) of these numbers: 99, 73, 56, 23.

   Formula:Arithmetic Mean

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

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2. 2.

   €210 is shared in the ratio 1 : 5. Find each share.

   Formula:Dividing in a Ratio

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

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3. 3.

   Find the mean (average) of these numbers: 20, 76, 24, 65, 69, 76.

   Formula:Arithmetic Mean

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

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4. 4.

   Find the circumference of a circle whose radius is 17 m. (Use π ≈ 3.14159)

   Formula:Circumference of a Circle

   $C = 2\pi r$

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5. 5.

   Solve for x: 3x + 13 = 37.

   Formula:Solving a Linear Equation

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

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6. 6.

   An object has mass 134.4 g and volume 32 cm³. Find its density.

   Formula:Density

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

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7. 7.

   What is 30% of 360?

   Formula:Percentage of a Quantity

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

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8. 8.

   A force of 441 N acts on an area of 3.1 m². Find the pressure.

   Formula:Pressure

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

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9. 9.

   A bag has 17 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.

    An object has mass 192.7 g and volume 41 cm³. Find its density.

    Formula:Density

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

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11. 11.

    A current of 5.7 A flows through a 18 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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12. 12.

    Solve for x: 2x + 3 = 27.

    Formula:Solving a Linear Equation

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

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13. 13.

    A right-angled triangle has legs of 16 cm and 6 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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14. 14.

    A circle has a radius of 15 cm. Find its area. (Use π ≈ 3.14159)

    Formula:Area of a Circle

    $A = \pi r^2$

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15. 15.

    What is 25% of 130?

    Formula:Percentage of a Quantity

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

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16. 16.

    A triangle has a base of 7 cm and a height of 10 cm. Find its area.

    Formula:Area of a Triangle

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

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17. 17.

    A force of 296 N acts on an area of 3.3 m². Find the pressure.

    Formula:Pressure

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

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18. 18.

    A right-angled triangle has legs of 16 cm and 19 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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19. 19.

    A value changes from 195 to 238. Find the percentage change (to 2 d.p.).

    Formula:Percentage Change

    $\%\,\text{change} = \dfrac{\text{new} - \text{old}}{\text{old}} \times 100$

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20. 20.

    A cylinder has radius 9 cm and height 6 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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