Hong Kong · Grade 7 · Practice Sheet 39

1. 1.

   Find the mean (average) of these numbers: 99, 58, 71, 10.

   Formula:Arithmetic Mean

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

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2. 2.

   A bag has 27 equally likely marbles, of which 26 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.

   Find the circumference of a circle whose radius is 17 m. (Use π ≈ 3.14159)

   Formula:Circumference of a Circle

   $C = 2\pi r$

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4. 4.

   Find the mean (average) of these numbers: 24, 37, 92, 99.

   Formula:Arithmetic Mean

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

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5. 5.

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

   Formula:Pythagorean Theorem

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

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6. 6.

   A train moves at 24 km/h for 4.9 hours. How far does it travel?

   Formula:Distance from Speed & Time

   $d = v \times t$

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7. 7.

   A car travels 284 km in 4 hours. Find its average speed.

   Formula:Speed

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

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8. 8.

   A triangle has a base of 15 cm and a height of 3 cm. Find its area.

   Formula:Area of a Triangle

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

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9. 9.

   Solve for x: 6x + 5 = 53.

   Formula:Solving a Linear Equation

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

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10. 10.

    A value changes from 139 to 114. 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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11. 11.

    HK$ 203 is shared in the ratio 4 : 3. Find each share.

    Formula:Dividing in a Ratio

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

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12. 12.

    Find the mean (average) of these numbers: 79, 51, 72, 17, 20, 49.

    Formula:Arithmetic Mean

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

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13. 13.

    A triangle has a base of 36 cm and a height of 11 cm. Find its area.

    Formula:Area of a Triangle

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

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14. 14.

    Find the area of a square with side length 3 cm.

    Formula:Area of a Square

    $A = s^2$

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15. 15.

    A bag has 8 equally likely marbles, of which 2 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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16. 16.

    A rectangle is 9 cm long and 14 cm wide. Find its area.

    Formula:Area of a Rectangle

    $A = l \times w$

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17. 17.

    A value changes from 127 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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18. 18.

    A bag has 18 equally likely marbles, of which 5 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.

    A triangle has a base of 5 cm and a height of 5 cm. Find its area.

    Formula:Area of a Triangle

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

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20. 20.

    Find the circumference of a circle whose radius is 22 m. (Use π ≈ 3.14159)

    Formula:Circumference of a Circle

    $C = 2\pi r$

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