South Korea · Grade 7 · Practice Sheet 29

1. 1.

   A right-angled triangle has legs of 9 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.

   A bag has 22 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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3. 3.

   One item costs ₩23.56. Find the total cost of 3 items.

   Formula:Total Cost

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

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4. 4.

   Solve for x: 8x + 17 = 49.

   Formula:Solving a Linear Equation

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

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5. 5.

   A triangle has a base of 19 cm and a height of 27 cm. Find its area.

   Formula:Area of a Triangle

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

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6. 6.

   A right-angled triangle has legs of 6 cm and 11 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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7. 7.

   Solve for x: 4x + 4 = 24.

   Formula:Solving a Linear Equation

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

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8. 8.

   One item costs ₩23.36. Find the total cost of 13 items.

   Formula:Total Cost

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

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9. 9.

   Find the mean (average) of these numbers: 16, 38, 88, 27.

   Formula:Arithmetic Mean

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

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10. 10.

    A triangle has a base of 35 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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11. 11.

    Find the perimeter of a rectangle measuring 15 m by 21 m.

    Formula:Perimeter of a Rectangle

    $P = 2(l + w)$

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12. 12.

    A value changes from 147 to 243. 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.

    A circle has a radius of 16 cm. Find its area. (Use π ≈ 3.14159)

    Formula:Area of a Circle

    $A = \pi r^2$

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14. 14.

    Find the circumference of a circle whose radius is 7 m. (Use π ≈ 3.14159)

    Formula:Circumference of a Circle

    $C = 2\pi r$

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15. 15.

    Find the perimeter of a rectangle measuring 20 m by 17 m.

    Formula:Perimeter of a Rectangle

    $P = 2(l + w)$

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16. 16.

    A triangle has a base of 13 cm and a height of 8 cm. Find its area.

    Formula:Area of a Triangle

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

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17. 17.

    Convert 9 kilometres into metres.

    Formula:Metric Length Conversion

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

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18. 18.

    One item costs ₩4.01. Find the total cost of 11 items.

    Formula:Total Cost

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

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19. 19.

    A right-angled triangle has legs of 7 cm and 12 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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20. 20.

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

    Formula:Area of a Square

    $A = s^2$

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