Russia · Grade 7 · Practice Sheet 34

1. 1.

   A circle has a radius of 4 cm. Find its area. (Use π ≈ 3.14159)

   Formula:Area of a Circle

   $A = \pi r^2$

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2. 2.

   A value changes from 176 to 38. 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.

   Find 3/5 of 50.

   Formula:Fraction of a Quantity

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

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4. 4.

   ₽210 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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5. 5.

   A circle has a radius of 3 cm. Find its area. (Use π ≈ 3.14159)

   Formula:Area of a Circle

   $A = \pi r^2$

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6. 6.

   One item costs ₽2.23. Find the total cost of 13 items.

   Formula:Total Cost

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

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7. 7.

   Find the area of a square with side length 20 cm.

   Formula:Area of a Square

   $A = s^2$

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8. 8.

   ₽39 is shared in the ratio 2 : 1. Find each share.

   Formula:Dividing in a Ratio

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

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9. 9.

   Solve for x: 6x + 6 = 78.

   Formula:Solving a Linear Equation

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

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10. 10.

    A rectangle is 11 cm long and 30 cm wide. Find its area.

    Formula:Area of a Rectangle

    $A = l \times w$

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11. 11.

    A bag has 21 equally likely marbles, of which 2 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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12. 12.

    Find the circumference of a circle whose radius is 8 m. (Use π ≈ 3.14159)

    Formula:Circumference of a Circle

    $C = 2\pi r$

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13. 13.

    One item costs ₽6.48. Find the total cost of 6 items.

    Formula:Total Cost

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

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14. 14.

    Find the mean (average) of these numbers: 32, 23, 97, 54, 72.

    Formula:Arithmetic Mean

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

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15. 15.

    ₽224 is shared in the ratio 4 : 4. Find each share.

    Formula:Dividing in a Ratio

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

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16. 16.

    Find 1/4 of 32.

    Formula:Fraction of a Quantity

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

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17. 17.

    Convert 10.57 kilometres into metres.

    Formula:Metric Length Conversion

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

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18. 18.

    ₽54 is shared in the ratio 2 : 1. Find each share.

    Formula:Dividing in a Ratio

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

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19. 19.

    What is 30% of 40?

    Formula:Percentage of a Quantity

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

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20. 20.

    Find 1/3 of 42.

    Formula:Fraction of a Quantity

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

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