Colombia · Grado 8 · Practice Sheet 9

1. 1.

   A bag has 8 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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2. 2.

   A right-angled triangle has legs of 6 cm and 6 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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3. 3.

   Find the mean (average) of these numbers: 91, 45, 83, 57.

   Formula:Arithmetic Mean

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

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4. 4.

   Solve for x: 7x + 9 = 58.

   Formula:Solving a Linear Equation

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

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5. 5.

   A value changes from 43 to 209. 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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6. 6.

   What is 75% of 110?

   Formula:Percentage of a Quantity

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

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7. 7.

   A right-angled triangle has legs of 19 cm and 9 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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8. 8.

   Find the mean (average) of these numbers: 38, 93, 49, 91, 37, 62.

   Formula:Arithmetic Mean

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

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9. 9.

   What is 30% of 290?

   Formula:Percentage of a Quantity

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

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10. 10.

    A triangle has a base of 10 cm and a height of 29 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 145 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.

    A current of 4.3 A flows through a 4 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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13. 13.

    A car travels 536 km in 8 hours. Find its average speed.

    Formula:Speed

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

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14. 14.

    A right-angled triangle has legs of 5 cm and 7 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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15. 15.

    A triangle has a base of 6 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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16. 16.

    A circle has a radius of 25 cm. Find its area. (Use π ≈ 3.14159)

    Formula:Area of a Circle

    $A = \pi r^2$

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17. 17.

    Solve for x: 9x + 5 = 59.

    Formula:Solving a Linear Equation

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

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18. 18.

    $1,000 is invested at 8% simple interest per year for 2 years. Find the interest earned.

    Formula:Simple Interest

    $I = \dfrac{P \times r \times t}{100}$

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19. 19.

    A force of 241 N acts on an area of 9.1 m². Find the pressure.

    Formula:Pressure

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

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20. 20.

    A triangle has a base of 38 cm and a height of 16 cm. Find its area.

    Formula:Area of a Triangle

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

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