Ukraine · Grade 8 · Practice Sheet 1

1. 1.

   Find the mean (average) of these numbers: 10, 74, 25, 28, 12.

   Formula:Arithmetic Mean

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

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2. 2.

   What is 15% of 150?

   Formula:Percentage of a Quantity

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

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3. 3.

   Solve for x: 4x + 13 = 41.

   Formula:Solving a Linear Equation

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

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4. 4.

   ₴4,100 is invested at 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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5. 5.

   ₴102 is shared in the ratio 4 : 2. Find each share.

   Formula:Dividing in a Ratio

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

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6. 6.

   A bag has 30 equally likely marbles, of which 5 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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7. 7.

   A current of 5.1 A flows through a 32 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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8. 8.

   Find the mean (average) of these numbers: 63, 80, 53, 40, 47.

   Formula:Arithmetic Mean

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

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9. 9.

   A train moves at 25 km/h for 3.6 hours. How far does it travel?

   Formula:Distance from Speed & Time

   $d = v \times t$

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10. 10.

    A car travels 435 km in 5 hours. Find its average speed.

    Formula:Speed

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

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11. 11.

    A circle has a radius of 5 cm. Find its area. (Use π ≈ 3.14159)

    Formula:Area of a Circle

    $A = \pi r^2$

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12. 12.

    An object has mass 34.2 g and volume 19 cm³. Find its density.

    Formula:Density

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

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13. 13.

    A value changes from 27 to 45. 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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14. 14.

    A current of 8 A flows through a 16 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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15. 15.

    Find the circumference of a circle whose radius is 16 m. (Use π ≈ 3.14159)

    Formula:Circumference of a Circle

    $C = 2\pi r$

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16. 16.

    A value changes from 152 to 120. 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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17. 17.

    A train moves at 71 km/h for 4.9 hours. How far does it travel?

    Formula:Distance from Speed & Time

    $d = v \times t$

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18. 18.

    A bag has 20 equally likely marbles, of which 12 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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19. 19.

    A force of 150 N acts on an area of 3.7 m². Find the pressure.

    Formula:Pressure

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

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20. 20.

    Find the mean (average) of these numbers: 29, 77, 44, 60, 28, 35.

    Formula:Arithmetic Mean

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

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