Ecuador · Grado 7 · Practice Sheet 27

1. 1.

   A value changes from 33 to 69. 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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2. 2.

   A right-angled triangle has legs of 6 cm and 5 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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3. 3.

   Find the area of a square with side length 27 cm.

   Formula:Area of a Square

   $A = s^2$

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4. 4.

   A right-angled triangle has legs of 19 cm and 20 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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5. 5.

   A rectangle is 34 cm long and 14 cm wide. Find its area.

   Formula:Area of a Rectangle

   $A = l \times w$

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6. 6.

   Find the mean (average) of these numbers: 95, 93, 23, 95, 15.

   Formula:Arithmetic Mean

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

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7. 7.

   A train moves at 45 km/h for 4.7 hours. How far does it travel?

   Formula:Distance from Speed & Time

   $d = v \times t$

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8. 8.

   A circle has a radius of 17 cm. Find its area. (Use π ≈ 3.14159)

   Formula:Area of a Circle

   $A = \pi r^2$

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9. 9.

   A rectangle is 40 cm long and 23 cm wide. Find its area.

   Formula:Area of a Rectangle

   $A = l \times w$

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10. 10.

    Find the area of a square with side length 27 cm.

    Formula:Area of a Square

    $A = s^2$

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11. 11.

    Find the perimeter of a rectangle measuring 15 m by 20 m.

    Formula:Perimeter of a Rectangle

    $P = 2(l + w)$

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12. 12.

    A value changes from 72 to 37. 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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13. 13.

    Find the mean (average) of these numbers: 31, 46, 37, 77, 78.

    Formula:Arithmetic Mean

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

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14. 14.

    Find the area of a square with side length 6 cm.

    Formula:Area of a Square

    $A = s^2$

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15. 15.

    Find the perimeter of a rectangle measuring 18 m by 32 m.

    Formula:Perimeter of a Rectangle

    $P = 2(l + w)$

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16. 16.

    Solve for x: 9x + 20 = 38.

    Formula:Solving a Linear Equation

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

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17. 17.

    A circle has a radius of 7 cm. Find its area. (Use π ≈ 3.14159)

    Formula:Area of a Circle

    $A = \pi r^2$

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18. 18.

    A right-angled triangle has legs of 9 cm and 19 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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19. 19.

    Solve for x: 7x + 3 = 31.

    Formula:Solving a Linear Equation

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

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20. 20.

    Convert 8.59 kilometres into metres.

    Formula:Metric Length Conversion

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

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