Russia · Grade 8 · Practice Sheet 37

1. 1.

   A circle has a radius of 17 cm. Find its area. (Use π ≈ 3.14159)

   Formula:Area of a Circle

   $A = \pi r^2$

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2. 2.

   ₽4,500 is invested at 6% 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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3. 3.

   A cylinder has radius 12 cm and height 30 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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4. 4.

   A train moves at 99 km/h for 3.8 hours. How far does it travel?

   Formula:Distance from Speed & Time

   $d = v \times t$

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5. 5.

   Solve for x: 9x + 19 = 109.

   Formula:Solving a Linear Equation

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

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6. 6.

   A force of 377 N acts on an area of 6.5 m². Find the pressure.

   Formula:Pressure

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

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7. 7.

   Find the mean (average) of these numbers: 69, 76, 81, 93, 36, 90.

   Formula:Arithmetic Mean

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

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8. 8.

   ₽266 is shared in the ratio 2 : 5. Find each share.

   Formula:Dividing in a Ratio

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

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9. 9.

   Solve for x: 2x + 1 = 17.

   Formula:Solving a Linear Equation

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

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10. 10.

    A triangle has a base of 33 cm and a height of 20 cm. Find its area.

    Formula:Area of a Triangle

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

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11. 11.

    A value changes from 59 to 160. 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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12. 12.

    ₽3,100 is invested at 6% 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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13. 13.

    Find the mean (average) of these numbers: 55, 83, 50, 33.

    Formula:Arithmetic Mean

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

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14. 14.

    A current of 5.3 A flows through a 33 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 11 m. (Use π ≈ 3.14159)

    Formula:Circumference of a Circle

    $C = 2\pi r$

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16. 16.

    A force of 492 N acts on an area of 3.8 m². Find the pressure.

    Formula:Pressure

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

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17. 17.

    A cylinder has radius 3 cm and height 19 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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18. 18.

    A train moves at 72 km/h for 2.7 hours. How far does it travel?

    Formula:Distance from Speed & Time

    $d = v \times t$

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19. 19.

    ₽45 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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20. 20.

    Find the mean (average) of these numbers: 83, 45, 72, 69, 55.

    Formula:Arithmetic Mean

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

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