Ukraine · Grade 7 · Practice Sheet 33

1. 1.

   A bag has 10 equally likely marbles, of which 3 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.

   A right-angled triangle has legs of 6 cm and 4 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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3. 3.

   A bag has 18 equally likely marbles, of which 1 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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4. 4.

   Solve for x: 7x + 9 = 30.

   Formula:Solving a Linear Equation

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

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5. 5.

   A car travels 328 km in 4 hours. Find its average speed.

   Formula:Speed

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

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6. 6.

   Find the mean (average) of these numbers: 58, 61, 59, 24.

   Formula:Arithmetic Mean

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

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7. 7.

   Find 1/2 of 24.

   Formula:Fraction of a Quantity

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

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8. 8.

   Convert 8.76 kilometres into metres.

   Formula:Metric Length Conversion

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

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9. 9.

   A train moves at 20 km/h for 4.4 hours. How far does it travel?

   Formula:Distance from Speed & Time

   $d = v \times t$

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10. 10.

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

    Formula:Area of a Square

    $A = s^2$

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11. 11.

    Find the mean (average) of these numbers: 31, 44, 76, 16.

    Formula:Arithmetic Mean

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

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12. 12.

    ₴72 is shared in the ratio 5 : 3. Find each share.

    Formula:Dividing in a Ratio

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

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13. 13.

    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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14. 14.

    Find the mean (average) of these numbers: 12, 85, 70, 32.

    Formula:Arithmetic Mean

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

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15. 15.

    What is 15% of 260?

    Formula:Percentage of a Quantity

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

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16. 16.

    One item costs ₴23.51. Find the total cost of 14 items.

    Formula:Total Cost

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

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17. 17.

    A bag has 25 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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18. 18.

    Find 4/5 of 65.

    Formula:Fraction of a Quantity

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

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19. 19.

    A rectangle is 7 cm long and 7 cm wide. Find its area.

    Formula:Area of a Rectangle

    $A = l \times w$

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20. 20.

    A car travels 410 km in 5 hours. Find its average speed.

    Formula:Speed

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

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