Russia · Grade 7 · Practice Sheet 21

1. 1.

   A right-angled triangle has legs of 13 cm and 12 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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2. 2.

   Find 4/5 of 55.

   Formula:Fraction of a Quantity

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

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3. 3.

   A right-angled triangle has legs of 17 cm and 10 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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4. 4.

   A value changes from 164 to 66. 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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5. 5.

   Convert 4.52 kilometres into metres.

   Formula:Metric Length Conversion

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

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6. 6.

   ₽2,900 is invested at 5% 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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7. 7.

   Solve for x: 7x + 9 = 79.

   Formula:Solving a Linear Equation

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

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8. 8.

   Find 1/2 of 32.

   Formula:Fraction of a Quantity

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

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9. 9.

   Find the mean (average) of these numbers: 68, 87, 12, 50.

   Formula:Arithmetic Mean

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

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10. 10.

    A circle has a radius of 11 cm. Find its area. (Use π ≈ 3.14159)

    Formula:Area of a Circle

    $A = \pi r^2$

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11. 11.

    ₽70 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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12. 12.

    A triangle has a base of 14 cm and a height of 7 cm. Find its area.

    Formula:Area of a Triangle

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

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13. 13.

    A train moves at 86 km/h for 3.9 hours. How far does it travel?

    Formula:Distance from Speed & Time

    $d = v \times t$

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14. 14.

    A triangle has a base of 18 cm and a height of 11 cm. Find its area.

    Formula:Area of a Triangle

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

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15. 15.

    A circle has a radius of 9 cm. Find its area. (Use π ≈ 3.14159)

    Formula:Area of a Circle

    $A = \pi r^2$

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16. 16.

    One item costs ₽8.09. Find the total cost of 3 items.

    Formula:Total Cost

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

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17. 17.

    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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18. 18.

    A value changes from 89 to 248. 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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19. 19.

    Find 3/5 of 60.

    Formula:Fraction of a Quantity

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

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20. 20.

    A rectangle is 7 cm long and 20 cm wide. Find its area.

    Formula:Area of a Rectangle

    $A = l \times w$

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