Austria · Klasse 7 · Practice Sheet 9

1. 1.

   Solve for x: 3x + 3 = 21.

   Formula:Solving a Linear Equation

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

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2. 2.

   A rectangle is 4 cm long and 26 cm wide. Find its area.

   Formula:Area of a Rectangle

   $A = l \times w$

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3. 3.

   Find the perimeter of a rectangle measuring 12 m by 7 m.

   Formula:Perimeter of a Rectangle

   $P = 2(l + w)$

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4. 4.

   A rectangle is 24 cm long and 8 cm wide. Find its area.

   Formula:Area of a Rectangle

   $A = l \times w$

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5. 5.

   Solve for x: 3x + 12 = 45.

   Formula:Solving a Linear Equation

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

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6. 6.

   A rectangle is 36 cm long and 23 cm wide. Find its area.

   Formula:Area of a Rectangle

   $A = l \times w$

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7. 7.

   Find the area of a square with side length 9 cm.

   Formula:Area of a Square

   $A = s^2$

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8. 8.

   Convert 10.16 kilometres into metres.

   Formula:Metric Length Conversion

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

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9. 9.

   Find the perimeter of a rectangle measuring 5 m by 29 m.

   Formula:Perimeter of a Rectangle

   $P = 2(l + w)$

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10. 10.

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

    Formula:Area of a Square

    $A = s^2$

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11. 11.

    A right-angled triangle has legs of 16 cm and 8 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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12. 12.

    A value changes from 82 to 92. 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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13. 13.

    A triangle has a base of 40 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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14. 14.

    Convert 2.99 kilometres into metres.

    Formula:Metric Length Conversion

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

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15. 15.

    A right-angled triangle has legs of 9 cm and 8 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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16. 16.

    Find the mean (average) of these numbers: 36, 38, 79, 25, 97, 51.

    Formula:Arithmetic Mean

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

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17. 17.

    Solve for x: 6x + 4 = 64.

    Formula:Solving a Linear Equation

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

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18. 18.

    What is 30% of 450?

    Formula:Percentage of a Quantity

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

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19. 19.

    Solve for x: 2x + 11 = 35.

    Formula:Solving a Linear Equation

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

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20. 20.

    A circle has a radius of 20 cm. Find its area. (Use π ≈ 3.14159)

    Formula:Area of a Circle

    $A = \pi r^2$

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