Austria · Klasse 7 · Practice Sheet 49

1. 1.

   A value changes from 50 to 193. 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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2. 2.

   One item costs €13.77. Find the total cost of 7 items.

   Formula:Total Cost

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

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3. 3.

   Find the area of a square with side length 30 cm.

   Formula:Area of a Square

   $A = s^2$

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4. 4.

   A right-angled triangle has legs of 19 cm and 10 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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5. 5.

   Find the circumference of a circle whose radius is 16 m. (Use π ≈ 3.14159)

   Formula:Circumference of a Circle

   $C = 2\pi r$

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6. 6.

   Find 2/4 of 24.

   Formula:Fraction of a Quantity

   $\text{result} = \dfrac{a}{b} \times N$

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7. 7.

   A car travels 312 km in 8 hours. Find its average speed.

   Formula:Speed

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

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8. 8.

   A train moves at 51 km/h for 3.9 hours. How far does it travel?

   Formula:Distance from Speed & Time

   $d = v \times t$

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9. 9.

   A car travels 246 km in 6 hours. Find its average speed.

   Formula:Speed

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

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10. 10.

    €108 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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11. 11.

    Solve for x: 9x + 1 = 91.

    Formula:Solving a Linear Equation

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

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12. 12.

    Find the circumference of a circle whose radius is 6 m. (Use π ≈ 3.14159)

    Formula:Circumference of a Circle

    $C = 2\pi r$

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13. 13.

    A rectangle is 18 cm long and 16 cm wide. Find its area.

    Formula:Area of a Rectangle

    $A = l \times w$

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14. 14.

    €1,300 is invested at 7.5% 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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15. 15.

    A rectangle is 31 cm long and 4 cm wide. Find its area.

    Formula:Area of a Rectangle

    $A = l \times w$

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16. 16.

    A triangle has a base of 16 cm and a height of 20 cm. Find its area.

    Formula:Area of a Triangle

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

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17. 17.

    Find the mean (average) of these numbers: 65, 37, 58, 58, 72.

    Formula:Arithmetic Mean

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

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18. 18.

    A triangle has a base of 30 cm and a height of 4 cm. Find its area.

    Formula:Area of a Triangle

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

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19. 19.

    A value changes from 153 to 154. 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.

    A right-angled triangle has legs of 6 cm and 11 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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