Russia · Grade 7 · Practice Sheet 27

1. 1.

   A right-angled triangle has legs of 4 cm and 9 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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2. 2.

   A value changes from 108 to 202. 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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3. 3.

   ₽261 is shared in the ratio 4 : 5. Find each share.

   Formula:Dividing in a Ratio

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

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4. 4.

   Solve for x: 8x + 20 = 108.

   Formula:Solving a Linear Equation

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

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5. 5.

   A train moves at 83 km/h for 4.5 hours. How far does it travel?

   Formula:Distance from Speed & Time

   $d = v \times t$

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6. 6.

   One item costs ₽22.76. Find the total cost of 19 items.

   Formula:Total Cost

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

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7. 7.

   Find the circumference of a circle whose radius is 18 m. (Use π ≈ 3.14159)

   Formula:Circumference of a Circle

   $C = 2\pi r$

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8. 8.

   Find the perimeter of a rectangle measuring 44 m by 4 m.

   Formula:Perimeter of a Rectangle

   $P = 2(l + w)$

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9. 9.

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

   Formula:Area of a Square

   $A = s^2$

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10. 10.

    One item costs ₽5.41. Find the total cost of 4 items.

    Formula:Total Cost

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

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11. 11.

    A triangle has a base of 34 cm and a height of 4 cm. Find its area.

    Formula:Area of a Triangle

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

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12. 12.

    A right-angled triangle has legs of 9 cm and 17 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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13. 13.

    Convert 5.96 kilometres into metres.

    Formula:Metric Length Conversion

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

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14. 14.

    A bag has 22 equally likely marbles, of which 7 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 perimeter of a rectangle measuring 10 m by 10 m.

    Formula:Perimeter of a Rectangle

    $P = 2(l + w)$

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16. 16.

    A triangle has a base of 18 cm and a height of 26 cm. Find its area.

    Formula:Area of a Triangle

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

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17. 17.

    ₽228 is shared in the ratio 5 : 1. Find each share.

    Formula:Dividing in a Ratio

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

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18. 18.

    Find the circumference of a circle whose radius is 9 m. (Use π ≈ 3.14159)

    Formula:Circumference of a Circle

    $C = 2\pi r$

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19. 19.

    One item costs ₽7.57. Find the total cost of 14 items.

    Formula:Total Cost

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

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20. 20.

    Find the perimeter of a rectangle measuring 9 m by 32 m.

    Formula:Perimeter of a Rectangle

    $P = 2(l + w)$

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