United States · Grade 7 · Practice Sheet 26

1. 1.

   A right-angled triangle has legs of 3 cm and 8 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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2. 2.

   Find the perimeter of a rectangle measuring 9 m by 6 m.

   Formula:Perimeter of a Rectangle

   $P = 2(l + w)$

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3. 3.

   Find the mean (average) of these numbers: 51, 55, 93, 26, 65.

   Formula:Arithmetic Mean

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

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4. 4.

   A rectangle is 19 cm long and 9 cm wide. Find its area.

   Formula:Area of a Rectangle

   $A = l \times w$

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5. 5.

   Find the circumference of a circle whose radius is 4 m. (Use π ≈ 3.14159)

   Formula:Circumference of a Circle

   $C = 2\pi r$

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6. 6.

   Find the perimeter of a rectangle measuring 24 m by 17 m.

   Formula:Perimeter of a Rectangle

   $P = 2(l + w)$

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7. 7.

   A triangle has a base of 32 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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8. 8.

   One item costs $9.76. Find the total cost of 18 items.

   Formula:Total Cost

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

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9. 9.

   Convert 1.42 kilometres into metres.

   Formula:Metric Length Conversion

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

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10. 10.

    Find 1/2 of 32.

    Formula:Fraction of a Quantity

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

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11. 11.

    Find the mean (average) of these numbers: 48, 51, 85, 46, 99, 33.

    Formula:Arithmetic Mean

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

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12. 12.

    A circle has a radius of 13 cm. Find its area. (Use π ≈ 3.14159)

    Formula:Area of a Circle

    $A = \pi r^2$

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13. 13.

    A car travels 656 km in 8 hours. Find its average speed.

    Formula:Speed

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

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14. 14.

    A bag has 18 equally likely marbles, of which 5 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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15. 15.

    $4,000 is invested at 5% 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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16. 16.

    A value changes from 52 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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17. 17.

    Find the mean (average) of these numbers: 78, 96, 56, 89, 47, 39.

    Formula:Arithmetic Mean

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

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18. 18.

    What is 40% of 590?

    Formula:Percentage of a Quantity

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

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19. 19.

    A right-angled triangle has legs of 11 cm and 3 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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20. 20.

    Solve for x: 6x + 12 = 42.

    Formula:Solving a Linear Equation

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

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