South Korea · Grade 7 · Practice Sheet 22

1. 1.

   A right-angled triangle has legs of 4 cm and 6 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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2. 2.

   Find the mean (average) of these numbers: 74, 56, 70, 28, 26.

   Formula:Arithmetic Mean

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

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3. 3.

   What is 50% of 410?

   Formula:Percentage of a Quantity

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

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4. 4.

   A rectangle is 24 cm long and 11 cm wide. Find its area.

   Formula:Area of a Rectangle

   $A = l \times w$

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5. 5.

   A triangle has a base of 8 cm and a height of 23 cm. Find its area.

   Formula:Area of a Triangle

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

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6. 6.

   What is 30% of 290?

   Formula:Percentage of a Quantity

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

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7. 7.

   A train moves at 77 km/h for 2.4 hours. How far does it travel?

   Formula:Distance from Speed & Time

   $d = v \times t$

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8. 8.

   Find the circumference of a circle whose radius is 10 m. (Use π ≈ 3.14159)

   Formula:Circumference of a Circle

   $C = 2\pi r$

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9. 9.

   A rectangle is 7 cm long and 4 cm wide. Find its area.

   Formula:Area of a Rectangle

   $A = l \times w$

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10. 10.

    A circle has a radius of 25 cm. Find its area. (Use π ≈ 3.14159)

    Formula:Area of a Circle

    $A = \pi r^2$

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11. 11.

    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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12. 12.

    A rectangle is 33 cm long and 26 cm wide. Find its area.

    Formula:Area of a Rectangle

    $A = l \times w$

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13. 13.

    Convert 4.17 kilometres into metres.

    Formula:Metric Length Conversion

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

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14. 14.

    Solve for x: 9x + 10 = 100.

    Formula:Solving a Linear Equation

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

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15. 15.

    ₩85 is shared in the ratio 1 : 4. Find each share.

    Formula:Dividing in a Ratio

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

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16. 16.

    Find the mean (average) of these numbers: 19, 11, 18, 11, 79, 45.

    Formula:Arithmetic Mean

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

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17. 17.

    Find the perimeter of a rectangle measuring 25 m by 27 m.

    Formula:Perimeter of a Rectangle

    $P = 2(l + w)$

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18. 18.

    A bag has 9 equally likely marbles, of which 3 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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19. 19.

    Solve for x: 3x + 12 = 45.

    Formula:Solving a Linear Equation

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

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20. 20.

    Find the area of a square with side length 20 cm.

    Formula:Area of a Square

    $A = s^2$

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