Czechia · Grade 8 · Practice Sheet 36

1. 1.

   A train moves at 92 km/h for 2 hours. How far does it travel?

   Formula:Distance from Speed & Time

   $d = v \times t$

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2. 2.

   Find the mean (average) of these numbers: 32, 32, 12, 93.

   Formula:Arithmetic Mean

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

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3. 3.

   A value changes from 93 to 151. 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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4. 4.

   A right-angled triangle has legs of 4 cm and 9 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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5. 5.

   An object has mass 204.4 g and volume 28 cm³. Find its density.

   Formula:Density

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

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6. 6.

   A triangle has a base of 13 cm and a height of 7 cm. Find its area.

   Formula:Area of a Triangle

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

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7. 7.

   What is 10% of 510?

   Formula:Percentage of a Quantity

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

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8. 8.

   A cylinder has radius 13 cm and height 28 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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9. 9.

   A value changes from 95 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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10. 10.

    Solve for x: 6x + 11 = 23.

    Formula:Solving a Linear Equation

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

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11. 11.

    A right-angled triangle has legs of 7 cm and 9 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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12. 12.

    A circle has a radius of 12 cm. Find its area. (Use π ≈ 3.14159)

    Formula:Area of a Circle

    $A = \pi r^2$

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13. 13.

    A train moves at 90 km/h for 3.1 hours. How far does it travel?

    Formula:Distance from Speed & Time

    $d = v \times t$

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14. 14.

    Find the mean (average) of these numbers: 37, 17, 36, 20, 84, 62.

    Formula:Arithmetic Mean

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

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15. 15.

    A bag has 10 equally likely marbles, of which 6 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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16. 16.

    A train moves at 69 km/h for 4.3 hours. How far does it travel?

    Formula:Distance from Speed & Time

    $d = v \times t$

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17. 17.

    A car travels 469 km in 7 hours. Find its average speed.

    Formula:Speed

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

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18. 18.

    A bag has 19 equally likely marbles, of which 1 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.

    An object has mass 224.4 g and volume 44 cm³. Find its density.

    Formula:Density

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

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20. 20.

    A force of 426 N acts on an area of 5.9 m². Find the pressure.

    Formula:Pressure

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

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