Mexico · Grado 8 · Practice Sheet 25

1. 1.

   $150 is shared in the ratio 1 : 5. Find each share.

   Formula:Dividing in a Ratio

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

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2. 2.

   A value changes from 178 to 67. 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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3. 3.

   A right-angled triangle has legs of 19 cm and 3 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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4. 4.

   What is 20% of 150?

   Formula:Percentage of a Quantity

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

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5. 5.

   Solve for x: 8x + 12 = 28.

   Formula:Solving a Linear Equation

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

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6. 6.

   What is 15% of 260?

   Formula:Percentage of a Quantity

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

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7. 7.

   Find the mean (average) of these numbers: 21, 16, 96, 46, 99.

   Formula:Arithmetic Mean

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

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8. 8.

   A triangle has a base of 22 cm and a height of 30 cm. Find its area.

   Formula:Area of a Triangle

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

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9. 9.

   Solve for x: 3x + 1 = 10.

   Formula:Solving a Linear Equation

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

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10. 10.

    A value changes from 113 to 87. 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.

    A triangle has a base of 36 cm and a height of 22 cm. Find its area.

    Formula:Area of a Triangle

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

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12. 12.

    A circle has a radius of 22 cm. Find its area. (Use π ≈ 3.14159)

    Formula:Area of a Circle

    $A = \pi r^2$

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13. 13.

    A cylinder has radius 9 cm and height 8 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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14. 14.

    A right-angled triangle has legs of 15 cm and 11 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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15. 15.

    $115 is shared in the ratio 4 : 1. Find each share.

    Formula:Dividing in a Ratio

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

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16. 16.

    A current of 7.9 A flows through a 14 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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17. 17.

    A cylinder has radius 4 cm and height 21 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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18. 18.

    $56 is shared in the ratio 2 : 5. 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 circle has a radius of 10 cm. Find its area. (Use π ≈ 3.14159)

    Formula:Area of a Circle

    $A = \pi r^2$

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20. 20.

    What is 15% of 60?

    Formula:Percentage of a Quantity

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

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