Switzerland · Grade 7 · Practice Sheet 21

1. 1.

   A right-angled triangle has legs of 12 cm and 18 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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2. 2.

   A rectangle is 34 cm long and 30 cm wide. Find its area.

   Formula:Area of a Rectangle

   $A = l \times w$

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3. 3.

   Find the circumference of a circle whose radius is 25 m. (Use π ≈ 3.14159)

   Formula:Circumference of a Circle

   $C = 2\pi r$

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4. 4.

   A value changes from 75 to 148. 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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5. 5.

   Find the mean (average) of these numbers: 39, 78, 39, 79, 77, 69.

   Formula:Arithmetic Mean

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

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6. 6.

   A circle has a radius of 5 cm. Find its area. (Use π ≈ 3.14159)

   Formula:Area of a Circle

   $A = \pi r^2$

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7. 7.

   A bag has 23 equally likely marbles, of which 16 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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8. 8.

   CHF 4,600 is invested at 5% 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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9. 9.

   Solve for x: 6x + 15 = 69.

   Formula:Solving a Linear Equation

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

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10. 10.

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

    Formula:Area of a Triangle

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

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11. 11.

    A value changes from 146 to 90. 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.

    One item costs CHF 22.53. Find the total cost of 8 items.

    Formula:Total Cost

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

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13. 13.

    A value changes from 105 to 103. 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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14. 14.

    CHF 40 is shared in the ratio 2 : 2. Find each share.

    Formula:Dividing in a Ratio

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

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15. 15.

    A bag has 16 equally likely marbles, of which 14 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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16. 16.

    Solve for x: 4x + 11 = 19.

    Formula:Solving a Linear Equation

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

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17. 17.

    Find the perimeter of a rectangle measuring 39 m by 17 m.

    Formula:Perimeter of a Rectangle

    $P = 2(l + w)$

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18. 18.

    What is 20% of 290?

    Formula:Percentage of a Quantity

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

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19. 19.

    A car travels 186 km in 2 hours. Find its average speed.

    Formula:Speed

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

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20. 20.

    A value changes from 170 to 152. 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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