Hong Kong · Grade 8 · Practice Sheet 38

1. 1.

   Solve for x: 5x + 16 = 46.

   Formula:Solving a Linear Equation

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

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2. 2.

   HK$ 104 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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3. 3.

   An object has mass 43.2 g and volume 16 cm³. Find its density.

   Formula:Density

   $\rho = \dfrac{m}{V}$

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4. 4.

   A right-angled triangle has legs of 15 cm and 17 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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5. 5.

   Find the mean (average) of these numbers: 38, 72, 20, 64, 23, 89.

   Formula:Arithmetic Mean

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

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6. 6.

   A bag has 27 equally likely marbles, of which 20 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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7. 7.

   A triangle has a base of 35 cm and a height of 13 cm. Find its area.

   Formula:Area of a Triangle

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

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8. 8.

   A value changes from 175 to 227. 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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9. 9.

   Find the mean (average) of these numbers: 63, 61, 88, 88, 83.

   Formula:Arithmetic Mean

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

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10. 10.

    A car travels 679 km in 7 hours. Find its average speed.

    Formula:Speed

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

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11. 11.

    An object has mass 110.4 g and volume 24 cm³. Find its density.

    Formula:Density

    $\rho = \dfrac{m}{V}$

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12. 12.

    A current of 2.1 A flows through a 60 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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13. 13.

    A car travels 618 km in 6 hours. Find its average speed.

    Formula:Speed

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

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14. 14.

    HK$ 138 is shared in the ratio 4 : 2. Find each share.

    Formula:Dividing in a Ratio

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

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15. 15.

    HK$ 3,000 is invested at 3% simple interest per year for 2 years. Find the interest earned.

    Formula:Simple Interest

    $I = \dfrac{P \times r \times t}{100}$

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16. 16.

    A cylinder has radius 9 cm and height 17 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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17. 17.

    A bag has 10 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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18. 18.

    Find the mean (average) of these numbers: 42, 42, 23, 45.

    Formula:Arithmetic Mean

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

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19. 19.

    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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20. 20.

    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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