Russia · Grade 8 · Practice Sheet 11

1. 1.

   Find the mean (average) of these numbers: 32, 31, 19, 90, 48.

   Formula:Arithmetic Mean

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

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2. 2.

   A triangle has a base of 35 cm and a height of 8 cm. Find its area.

   Formula:Area of a Triangle

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

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3. 3.

   A circle has a radius of 9 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 circumference of a circle whose radius is 12 m. (Use π ≈ 3.14159)

   Formula:Circumference of a Circle

   $C = 2\pi r$

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5. 5.

   Find the mean (average) of these numbers: 68, 20, 51, 90, 78, 17.

   Formula:Arithmetic Mean

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

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6. 6.

   ₽3,800 is invested at 3% 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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7. 7.

   A current of 2.3 A flows through a 10 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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8. 8.

   ₽3,200 is invested at 7.5% 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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9. 9.

   A cylinder has radius 13 cm and height 12 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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10. 10.

    A force of 353 N acts on an area of 8.9 m². Find the pressure.

    Formula:Pressure

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

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11. 11.

    A cylinder has radius 6 cm and height 23 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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12. 12.

    A car travels 70 km in 2 hours. Find its average speed.

    Formula:Speed

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

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13. 13.

    What is 40% of 450?

    Formula:Percentage of a Quantity

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

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14. 14.

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

    Formula:Pythagorean Theorem

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

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15. 15.

    ₽150 is shared in the ratio 3 : 2. Find each share.

    Formula:Dividing in a Ratio

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

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16. 16.

    What is 75% of 250?

    Formula:Percentage of a Quantity

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

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17. 17.

    Solve for x: 3x + 20 = 29.

    Formula:Solving a Linear Equation

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

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18. 18.

    Find the mean (average) of these numbers: 93, 46, 60, 53.

    Formula:Arithmetic Mean

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

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19. 19.

    A force of 133 N acts on an area of 9.6 m². Find the pressure.

    Formula:Pressure

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

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20. 20.

    A bag has 20 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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