Russia · Grade 8 · Practice Sheet 38

1. 1.

   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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2. 2.

   A force of 382 N acts on an area of 2.5 m². Find the pressure.

   Formula:Pressure

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

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3. 3.

   ₽180 is shared in the ratio 4 : 1. Find each share.

   Formula:Dividing in a Ratio

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

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4. 4.

   A bag has 12 equally likely marbles, of which 9 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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5. 5.

   A force of 91 N acts on an area of 4.1 m². Find the pressure.

   Formula:Pressure

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

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6. 6.

   A value changes from 176 to 147. 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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7. 7.

   ₽75 is shared in the ratio 1 : 2. Find each share.

   Formula:Dividing in a Ratio

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

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8. 8.

   What is 75% of 350?

   Formula:Percentage of a Quantity

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

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9. 9.

   A value changes from 194 to 156. 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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10. 10.

    A bag has 16 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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11. 11.

    Find the mean (average) of these numbers: 95, 28, 83, 80.

    Formula:Arithmetic Mean

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

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12. 12.

    A cylinder has radius 7 cm and height 21 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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13. 13.

    A right-angled triangle has legs of 20 cm and 4 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 24 cm. Find its area. (Use π ≈ 3.14159)

    Formula:Area of a Circle

    $A = \pi r^2$

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15. 15.

    A train moves at 39 km/h for 3.5 hours. How far does it travel?

    Formula:Distance from Speed & Time

    $d = v \times t$

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16. 16.

    What is 5% of 580?

    Formula:Percentage of a Quantity

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

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17. 17.

    ₽4,500 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.

    A train moves at 46 km/h for 2 hours. How far does it travel?

    Formula:Distance from Speed & Time

    $d = v \times t$

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19. 19.

    Solve for x: 8x + 19 = 99.

    Formula:Solving a Linear Equation

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

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20. 20.

    A current of 5.9 A flows through a 26 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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