Ukraine · Grade 7 · Practice Sheet 1

1. 1.

   Solve for x: 9x + 10 = 37.

   Formula:Solving a Linear Equation

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

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2. 2.

   A rectangle is 23 cm long and 13 cm wide. Find its area.

   Formula:Area of a Rectangle

   $A = l \times w$

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3. 3.

   A right-angled triangle has legs of 5 cm and 17 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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4. 4.

   Convert 9.8 kilometres into metres.

   Formula:Metric Length Conversion

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

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5. 5.

   Find the perimeter of a rectangle measuring 35 m by 14 m.

   Formula:Perimeter of a Rectangle

   $P = 2(l + w)$

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6. 6.

   What is 20% of 500?

   Formula:Percentage of a Quantity

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

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7. 7.

   A circle has a radius of 13 cm. Find its area. (Use π ≈ 3.14159)

   Formula:Area of a Circle

   $A = \pi r^2$

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8. 8.

   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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9. 9.

   A bag has 13 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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10. 10.

    A rectangle is 8 cm long and 7 cm wide. Find its area.

    Formula:Area of a Rectangle

    $A = l \times w$

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11. 11.

    A circle has a radius of 19 cm. Find its area. (Use π ≈ 3.14159)

    Formula:Area of a Circle

    $A = \pi r^2$

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12. 12.

    What is 30% of 360?

    Formula:Percentage of a Quantity

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

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13. 13.

    One item costs ₴11.9. Find the total cost of 16 items.

    Formula:Total Cost

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

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14. 14.

    Find the area of a square with side length 10 cm.

    Formula:Area of a Square

    $A = s^2$

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15. 15.

    Find the circumference of a circle whose radius is 25 m. (Use π ≈ 3.14159)

    Formula:Circumference of a Circle

    $C = 2\pi r$

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16. 16.

    Find the mean (average) of these numbers: 60, 21, 11, 34, 54.

    Formula:Arithmetic Mean

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

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17. 17.

    A right-angled triangle has legs of 10 cm and 3 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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18. 18.

    Find the area of a square with side length 29 cm.

    Formula:Area of a Square

    $A = s^2$

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19. 19.

    A value changes from 110 to 207. 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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20. 20.

    A car travels 360 km in 5 hours. Find its average speed.

    Formula:Speed

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

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