United States · Grade 7 · Practice Sheet 29

1. 1.

   $270 is shared in the ratio 5 : 4. Find each share.

   Formula:Dividing in a Ratio

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

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2. 2.

   Find the mean (average) of these numbers: 73, 61, 54, 57.

   Formula:Arithmetic Mean

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

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3. 3.

   A rectangle is 14 cm long and 23 cm wide. Find its area.

   Formula:Area of a Rectangle

   $A = l \times w$

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4. 4.

   Find the perimeter of a rectangle measuring 42 m by 15 m.

   Formula:Perimeter of a Rectangle

   $P = 2(l + w)$

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5. 5.

   Find the circumference of a circle whose radius is 14 m. (Use π ≈ 3.14159)

   Formula:Circumference of a Circle

   $C = 2\pi r$

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6. 6.

   Find the mean (average) of these numbers: 44, 17, 21, 83, 72, 35.

   Formula:Arithmetic Mean

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

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7. 7.

   A car travels 240 km in 5 hours. Find its average speed.

   Formula:Speed

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

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8. 8.

   A bag has 29 equally likely marbles, of which 22 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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9. 9.

   Find the perimeter of a rectangle measuring 11 m by 10 m.

   Formula:Perimeter of a Rectangle

   $P = 2(l + w)$

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10. 10.

    Find 1/5 of 25.

    Formula:Fraction of a Quantity

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

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11. 11.

    Solve for x: 2x + 6 = 14.

    Formula:Solving a Linear Equation

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

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12. 12.

    A value changes from 187 to 58. 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.

    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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14. 14.

    A bag has 27 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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15. 15.

    Find the circumference of a circle whose radius is 29 m. (Use π ≈ 3.14159)

    Formula:Circumference of a Circle

    $C = 2\pi r$

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16. 16.

    Find 1/4 of 24.

    Formula:Fraction of a Quantity

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

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17. 17.

    Find the mean (average) of these numbers: 21, 50, 88, 79.

    Formula:Arithmetic Mean

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

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18. 18.

    Find the perimeter of a rectangle measuring 38 m by 11 m.

    Formula:Perimeter of a Rectangle

    $P = 2(l + w)$

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19. 19.

    Convert 10.6 kilometres into metres.

    Formula:Metric Length Conversion

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

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20. 20.

    $168 is shared in the ratio 3 : 3. Find each share.

    Formula:Dividing in a Ratio

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

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