Czechia · Grade 7 · Practice Sheet 26

1. 1.

   A right-angled triangle has legs of 4 cm and 8 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 45 to 161. 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.

   Convert 4.9 kilometres into metres.

   Formula:Metric Length Conversion

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

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4. 4.

   What is 20% of 480?

   Formula:Percentage of a Quantity

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

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5. 5.

   A rectangle is 20 cm long and 23 cm wide. Find its area.

   Formula:Area of a Rectangle

   $A = l \times w$

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6. 6.

   Convert 9.99 kilometres into metres.

   Formula:Metric Length Conversion

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

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7. 7.

   Find the perimeter of a rectangle measuring 37 m by 29 m.

   Formula:Perimeter of a Rectangle

   $P = 2(l + w)$

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8. 8.

   A car travels 206 km in 2 hours. Find its average speed.

   Formula:Speed

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

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9. 9.

   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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10. 10.

    A car travels 238 km in 7 hours. Find its average speed.

    Formula:Speed

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

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11. 11.

    Solve for x: 5x + 17 = 57.

    Formula:Solving a Linear Equation

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

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12. 12.

    A train moves at 20 km/h for 5.8 hours. How far does it travel?

    Formula:Distance from Speed & Time

    $d = v \times t$

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13. 13.

    Find the perimeter of a rectangle measuring 43 m by 15 m.

    Formula:Perimeter of a Rectangle

    $P = 2(l + w)$

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14. 14.

    Kč 4,600 is invested at 4% 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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15. 15.

    Find 1/8 of 136.

    Formula:Fraction of a Quantity

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

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16. 16.

    Solve for x: 8x + 5 = 101.

    Formula:Solving a Linear Equation

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

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17. 17.

    Kč 304 is shared in the ratio 3 : 5. 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 1/2 of 36.

    Formula:Fraction of a Quantity

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

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19. 19.

    Find the area of a square with side length 28 cm.

    Formula:Area of a Square

    $A = s^2$

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20. 20.

    Solve for x: 2x + 8 = 12.

    Formula:Solving a Linear Equation

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

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