Portugal · Ano 7 · Practice Sheet 6

1. 1.

   Find the mean (average) of these numbers: 36, 63, 79, 54, 63.

   Formula:Arithmetic Mean

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

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2. 2.

   What is 20% of 510?

   Formula:Percentage of a Quantity

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

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3. 3.

   A right-angled triangle has legs of 6 cm and 16 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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4. 4.

   €333 is shared in the ratio 4 : 5. Find each share.

   Formula:Dividing in a Ratio

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

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5. 5.

   Find the area of a square with side length 29 cm.

   Formula:Area of a Square

   $A = s^2$

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6. 6.

   A triangle has a base of 8 cm and a height of 10 cm. Find its area.

   Formula:Area of a Triangle

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

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7. 7.

   Find the circumference of a circle whose radius is 15 m. (Use π ≈ 3.14159)

   Formula:Circumference of a Circle

   $C = 2\pi r$

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8. 8.

   Find the perimeter of a rectangle measuring 18 m by 17 m.

   Formula:Perimeter of a Rectangle

   $P = 2(l + w)$

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9. 9.

   €1,700 is invested at 8% simple interest per year for 6 years. Find the interest earned.

   Formula:Simple Interest

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

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10. 10.

    What is 30% of 110?

    Formula:Percentage of a Quantity

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

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11. 11.

    Solve for x: 8x + 16 = 112.

    Formula:Solving a Linear Equation

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

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12. 12.

    One item costs €1.99. Find the total cost of 6 items.

    Formula:Total Cost

    $\text{total} = \text{price} \times \text{quantity}$

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13. 13.

    A car travels 260 km in 5 hours. Find its average speed.

    Formula:Speed

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

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14. 14.

    A value changes from 63 to 206. 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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15. 15.

    €135 is shared in the ratio 4 : 5. Find each share.

    Formula:Dividing in a Ratio

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

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16. 16.

    Find the mean (average) of these numbers: 46, 43, 36, 83.

    Formula:Arithmetic Mean

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

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17. 17.

    One item costs €22.24. Find the total cost of 10 items.

    Formula:Total Cost

    $\text{total} = \text{price} \times \text{quantity}$

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18. 18.

    Solve for x: 2x + 7 = 23.

    Formula:Solving a Linear Equation

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

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19. 19.

    A value changes from 167 to 136. 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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20. 20.

    €190 is shared in the ratio 2 : 3. Find each share.

    Formula:Dividing in a Ratio

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

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