Russia · Grade 7 · Practice Sheet 44

1. 1.

   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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2. 2.

   ₽126 is shared in the ratio 2 : 5. Find each share.

   Formula:Dividing in a Ratio

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

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3. 3.

   A car travels 648 km in 8 hours. Find its average speed.

   Formula:Speed

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

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4. 4.

   Find the perimeter of a rectangle measuring 38 m by 19 m.

   Formula:Perimeter of a Rectangle

   $P = 2(l + w)$

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5. 5.

   A circle has a radius of 10 cm. Find its area. (Use π ≈ 3.14159)

   Formula:Area of a Circle

   $A = \pi r^2$

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6. 6.

   A right-angled triangle has legs of 9 cm and 5 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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7. 7.

   Solve for x: 7x + 5 = 47.

   Formula:Solving a Linear Equation

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

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8. 8.

   A triangle has a base of 37 cm and a height of 5 cm. Find its area.

   Formula:Area of a Triangle

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

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9. 9.

   Convert 5.38 kilometres into metres.

   Formula:Metric Length Conversion

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

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10. 10.

    One item costs ₽17.58. Find the total cost of 8 items.

    Formula:Total Cost

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

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11. 11.

    ₽144 is shared in the ratio 1 : 5. Find each share.

    Formula:Dividing in a Ratio

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

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12. 12.

    A train moves at 81 km/h for 3.7 hours. How far does it travel?

    Formula:Distance from Speed & Time

    $d = v \times t$

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13. 13.

    A circle has a radius of 21 cm. Find its area. (Use π ≈ 3.14159)

    Formula:Area of a Circle

    $A = \pi r^2$

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14. 14.

    A bag has 22 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.

    Find the mean (average) of these numbers: 10, 98, 14, 85, 67.

    Formula:Arithmetic Mean

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

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16. 16.

    A right-angled triangle has legs of 4 cm and 20 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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17. 17.

    A triangle has a base of 10 cm and a height of 19 cm. Find its area.

    Formula:Area of a Triangle

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

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18. 18.

    A circle has a radius of 5 cm. Find its area. (Use π ≈ 3.14159)

    Formula:Area of a Circle

    $A = \pi r^2$

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19. 19.

    Find the mean (average) of these numbers: 84, 87, 53, 13, 82.

    Formula:Arithmetic Mean

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

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20. 20.

    A train moves at 43 km/h for 1.9 hours. How far does it travel?

    Formula:Distance from Speed & Time

    $d = v \times t$

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