Russia · Grade 7 · Practice Sheet 8

1. 1.

   One item costs ₽17.19. Find the total cost of 14 items.

   Formula:Total Cost

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

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2. 2.

   A bag has 22 equally likely marbles, of which 20 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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3. 3.

   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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4. 4.

   Find the area of a square with side length 4 cm.

   Formula:Area of a Square

   $A = s^2$

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5. 5.

   Find the perimeter of a rectangle measuring 18 m by 6 m.

   Formula:Perimeter of a Rectangle

   $P = 2(l + w)$

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6. 6.

   ₽60 is shared in the ratio 3 : 2. Find each share.

   Formula:Dividing in a Ratio

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

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7. 7.

   ₽2,000 is invested at 10% simple interest per year for 4 years. Find the interest earned.

   Formula:Simple Interest

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

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8. 8.

   Find the area of a square with side length 19 cm.

   Formula:Area of a Square

   $A = s^2$

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9. 9.

   Find the mean (average) of these numbers: 72, 98, 26, 60, 91.

   Formula:Arithmetic Mean

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

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10. 10.

    Find the circumference of a circle whose radius is 13 m. (Use π ≈ 3.14159)

    Formula:Circumference of a Circle

    $C = 2\pi r$

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11. 11.

    A value changes from 113 to 70. 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.

    A bag has 15 equally likely marbles, of which 9 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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13. 13.

    Solve for x: 9x + 18 = 108.

    Formula:Solving a Linear Equation

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

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14. 14.

    A right-angled triangle has legs of 15 cm and 20 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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15. 15.

    One item costs ₽5.18. Find the total cost of 18 items.

    Formula:Total Cost

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

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16. 16.

    Find the mean (average) of these numbers: 40, 18, 10, 39, 76, 83.

    Formula:Arithmetic Mean

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

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17. 17.

    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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18. 18.

    Solve for x: 9x + 13 = 49.

    Formula:Solving a Linear Equation

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

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19. 19.

    Convert 6.42 kilometres into metres.

    Formula:Metric Length Conversion

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

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20. 20.

    Find the area of a square with side length 8 cm.

    Formula:Area of a Square

    $A = s^2$

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