Germany · Klasse 7 · Practice Sheet 17

1. 1.

   Solve for x: 3x + 14 = 23.

   Formula:Solving a Linear Equation

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

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2. 2.

   Find the area of a square with side length 26 cm.

   Formula:Area of a Square

   $A = s^2$

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3. 3.

   A right-angled triangle has legs of 3 cm and 10 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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4. 4.

   A bag has 25 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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5. 5.

   A rectangle is 12 cm long and 30 cm wide. Find its area.

   Formula:Area of a Rectangle

   $A = l \times w$

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6. 6.

   A bag has 22 equally likely marbles, of which 21 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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7. 7.

   €4,300 is invested at 10% simple interest per year for 3 years. Find the interest earned.

   Formula:Simple Interest

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

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8. 8.

   A car travels 378 km in 7 hours. Find its average speed.

   Formula:Speed

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

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9. 9.

   A rectangle is 25 cm long and 10 cm wide. Find its area.

   Formula:Area of a Rectangle

   $A = l \times w$

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10. 10.

    A right-angled triangle has legs of 3 cm and 18 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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11. 11.

    Find the perimeter of a rectangle measuring 7 m by 18 m.

    Formula:Perimeter of a Rectangle

    $P = 2(l + w)$

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12. 12.

    A right-angled triangle has legs of 3 cm and 7 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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13. 13.

    What is 30% of 200?

    Formula:Percentage of a Quantity

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

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14. 14.

    A value changes from 52 to 78. 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.

    One item costs €13.52. Find the total cost of 5 items.

    Formula:Total Cost

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

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16. 16.

    Find the mean (average) of these numbers: 33, 54, 89, 58, 77, 22.

    Formula:Arithmetic Mean

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

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17. 17.

    Find 2/4 of 20.

    Formula:Fraction of a Quantity

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

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18. 18.

    One item costs €12.83. Find the total cost of 10 items.

    Formula:Total Cost

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

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19. 19.

    Find the area of a square with side length 14 cm.

    Formula:Area of a Square

    $A = s^2$

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20. 20.

    Convert 10.67 kilometres into metres.

    Formula:Metric Length Conversion

    $1\,\text{km} = 1000\,\text{m}$

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