Russia · Grade 7 · Practice Sheet 46

1. 1.

   ₽140 is shared in the ratio 2 : 3. Find each share.

   Formula:Dividing in a Ratio

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

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2. 2.

   A value changes from 57 to 120. 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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3. 3.

   Convert 11.03 kilometres into metres.

   Formula:Metric Length Conversion

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

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4. 4.

   A value changes from 149 to 104. 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 circumference of a circle whose radius is 21 m. (Use π ≈ 3.14159)

   Formula:Circumference of a Circle

   $C = 2\pi r$

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6. 6.

   A value changes from 73 to 140. 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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7. 7.

   A triangle has a base of 27 cm and a height of 24 cm. Find its area.

   Formula:Area of a Triangle

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

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8. 8.

   A bag has 17 equally likely marbles, of which 4 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.

   ₽4,000 is invested at 8% simple interest per year for 2 years. Find the interest earned.

   Formula:Simple Interest

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

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10. 10.

    A triangle has a base of 37 cm and a height of 30 cm. Find its area.

    Formula:Area of a Triangle

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

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11. 11.

    Find 1/3 of 15.

    Formula:Fraction of a Quantity

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

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12. 12.

    Find the mean (average) of these numbers: 92, 21, 68, 38.

    Formula:Arithmetic Mean

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

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13. 13.

    A circle has a radius of 25 cm. Find its area. (Use π ≈ 3.14159)

    Formula:Area of a Circle

    $A = \pi r^2$

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14. 14.

    Find 1/5 of 30.

    Formula:Fraction of a Quantity

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

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15. 15.

    Find the circumference of a circle whose radius is 16 m. (Use π ≈ 3.14159)

    Formula:Circumference of a Circle

    $C = 2\pi r$

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16. 16.

    What is 40% of 280?

    Formula:Percentage of a Quantity

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

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17. 17.

    Solve for x: 6x + 19 = 79.

    Formula:Solving a Linear Equation

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

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18. 18.

    A car travels 62 km in 2 hours. Find its average speed.

    Formula:Speed

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

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19. 19.

    A circle has a radius of 12 cm. Find its area. (Use π ≈ 3.14159)

    Formula:Area of a Circle

    $A = \pi r^2$

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20. 20.

    Solve for x: 6x + 9 = 27.

    Formula:Solving a Linear Equation

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

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