Italy · Classe 8 · Practice Sheet 45

1. 1.

   A right-angled triangle has legs of 12 cm and 15 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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2. 2.

   A value changes from 137 to 68. 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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3. 3.

   A circle has a radius of 3 cm. Find its area. (Use π ≈ 3.14159)

   Formula:Area of a Circle

   $A = \pi r^2$

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4. 4.

   An object has mass 125 g and volume 50 cm³. Find its density.

   Formula:Density

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

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5. 5.

   Find the circumference of a circle whose radius is 17 m. (Use π ≈ 3.14159)

   Formula:Circumference of a Circle

   $C = 2\pi r$

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6. 6.

   Find the mean (average) of these numbers: 54, 50, 72, 49, 32, 21.

   Formula:Arithmetic Mean

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

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7. 7.

   A circle has a radius of 14 cm. Find its area. (Use π ≈ 3.14159)

   Formula:Area of a Circle

   $A = \pi r^2$

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8. 8.

   A current of 7.2 A flows through a 51 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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9. 9.

   €2,800 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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10. 10.

    Find the mean (average) of these numbers: 88, 21, 95, 83, 18, 85.

    Formula:Arithmetic Mean

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

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11. 11.

    A value changes from 54 to 35. 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.

    Solve for x: 5x + 15 = 55.

    Formula:Solving a Linear Equation

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

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13. 13.

    A train moves at 83 km/h for 1.7 hours. How far does it travel?

    Formula:Distance from Speed & Time

    $d = v \times t$

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14. 14.

    What is 5% of 170?

    Formula:Percentage of a Quantity

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

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15. 15.

    Find the mean (average) of these numbers: 69, 74, 46, 33, 47.

    Formula:Arithmetic Mean

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

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16. 16.

    What is 15% of 170?

    Formula:Percentage of a Quantity

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

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17. 17.

    A car travels 201 km in 3 hours. Find its average speed.

    Formula:Speed

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

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18. 18.

    A train moves at 91 km/h for 4.7 hours. How far does it travel?

    Formula:Distance from Speed & Time

    $d = v \times t$

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19. 19.

    A right-angled triangle has legs of 10 cm and 13 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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20. 20.

    A current of 7.4 A flows through a 56 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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