Czechia · Grade 8 · Practice Sheet 25

1. 1.

   Find the mean (average) of these numbers: 32, 26, 32, 75, 75, 36.

   Formula:Arithmetic Mean

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

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2. 2.

   Find the circumference of a circle whose radius is 23 m. (Use π ≈ 3.14159)

   Formula:Circumference of a Circle

   $C = 2\pi r$

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3. 3.

   A bag has 13 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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4. 4.

   Kč 900 is invested at 4% 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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5. 5.

   Solve for x: 3x + 8 = 32.

   Formula:Solving a Linear Equation

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

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6. 6.

   A force of 431 N acts on an area of 2.4 m². Find the pressure.

   Formula:Pressure

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

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7. 7.

   A train moves at 100 km/h for 3.5 hours. How far does it travel?

   Formula:Distance from Speed & Time

   $d = v \times t$

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8. 8.

   Find the circumference of a circle whose radius is 22 m. (Use π ≈ 3.14159)

   Formula:Circumference of a Circle

   $C = 2\pi r$

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9. 9.

   A circle has a radius of 16 cm. Find its area. (Use π ≈ 3.14159)

   Formula:Area of a Circle

   $A = \pi r^2$

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10. 10.

    A value changes from 24 to 92. 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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11. 11.

    A force of 343 N acts on an area of 5.9 m². Find the pressure.

    Formula:Pressure

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

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12. 12.

    A car travels 156 km in 4 hours. Find its average speed.

    Formula:Speed

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

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13. 13.

    A train moves at 28 km/h for 2.4 hours. How far does it travel?

    Formula:Distance from Speed & Time

    $d = v \times t$

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14. 14.

    A force of 71 N acts on an area of 1.4 m². Find the pressure.

    Formula:Pressure

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

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15. 15.

    A current of 5 A flows through a 9 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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16. 16.

    An object has mass 67.5 g and volume 25 cm³. Find its density.

    Formula:Density

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

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17. 17.

    A right-angled triangle has legs of 4 cm and 5 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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18. 18.

    Find the mean (average) of these numbers: 54, 39, 29, 58.

    Formula:Arithmetic Mean

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

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19. 19.

    A cylinder has radius 7 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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20. 20.

    A value changes from 113 to 257. 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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