Mexico · Grado 8 · Practice Sheet 36

1. 1.

   Solve for x: 7x + 10 = 38.

   Formula:Solving a Linear Equation

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

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2. 2.

   A bag has 15 equally likely marbles, of which 9 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.

   An object has mass 394.8 g and volume 47 cm³. Find its density.

   Formula:Density

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

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4. 4.

   A train moves at 39 km/h for 5.2 hours. How far does it travel?

   Formula:Distance from Speed & Time

   $d = v \times t$

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5. 5.

   $3,400 is invested at 4% simple interest per year for 6 years. Find the interest earned.

   Formula:Simple Interest

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

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6. 6.

   A force of 449 N acts on an area of 1.8 m². Find the pressure.

   Formula:Pressure

   $P = \dfrac{F}{A}$

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7. 7.

   A train moves at 71 km/h for 3.8 hours. How far does it travel?

   Formula:Distance from Speed & Time

   $d = v \times t$

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8. 8.

   A bag has 23 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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9. 9.

   A train moves at 57 km/h for 2.6 hours. How far does it travel?

   Formula:Distance from Speed & Time

   $d = v \times t$

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10. 10.

    $120 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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11. 11.

    Find the circumference of a circle whose radius is 12 m. (Use π ≈ 3.14159)

    Formula:Circumference of a Circle

    $C = 2\pi r$

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12. 12.

    Find the mean (average) of these numbers: 55, 85, 92, 39, 36.

    Formula:Arithmetic Mean

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

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13. 13.

    A right-angled triangle has legs of 15 cm and 4 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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14. 14.

    A triangle has a base of 16 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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15. 15.

    An object has mass 107.3 g and volume 37 cm³. Find its density.

    Formula:Density

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

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16. 16.

    A force of 116 N acts on an area of 2.2 m². Find the pressure.

    Formula:Pressure

    $P = \dfrac{F}{A}$

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17. 17.

    What is 12% of 500?

    Formula:Percentage of a Quantity

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

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18. 18.

    $168 is shared in the ratio 5 : 3. Find each share.

    Formula:Dividing in a Ratio

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

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19. 19.

    A value changes from 122 to 126. 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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20. 20.

    A right-angled triangle has legs of 18 cm and 15 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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