United Kingdom · Year 8 · Practice Sheet 12

1. 1.

   Solve for x: 7x + 12 = 40.

   Formula:Solving a Linear Equation

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

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2. 2.

   What is 15% of 400?

   Formula:Percentage of a Quantity

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

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3. 3.

   £147 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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4. 4.

   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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5. 5.

   £2,000 is invested at 8% simple interest per year for 5 years. Find the interest earned.

   Formula:Simple Interest

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

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6. 6.

   Solve for x: 3x + 20 = 47.

   Formula:Solving a Linear Equation

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

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7. 7.

   £66 is shared in the ratio 2 : 1. Find each share.

   Formula:Dividing in a Ratio

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

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8. 8.

   Find the mean (average) of these numbers: 45, 69, 68, 43, 64, 17.

   Formula:Arithmetic Mean

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

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9. 9.

   A car travels 156 km in 3 hours. Find its average speed.

   Formula:Speed

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

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10. 10.

    An object has mass 180 g and volume 24 cm³. Find its density.

    Formula:Density

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

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11. 11.

    A right-angled triangle has legs of 9 cm and 13 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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12. 12.

    A value changes from 162 to 235. 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.

    An object has mass 16 g and volume 5 cm³. Find its density.

    Formula:Density

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

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14. 14.

    £3,700 is invested at 4% 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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15. 15.

    A car travels 432 km in 4 hours. Find its average speed.

    Formula:Speed

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

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16. 16.

    A triangle has a base of 8 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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17. 17.

    A bag has 27 equally likely marbles, of which 24 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.

    What is 10% of 270?

    Formula:Percentage of a Quantity

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

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19. 19.

    £1,500 is invested at 6% 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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20. 20.

    What is 12% of 120?

    Formula:Percentage of a Quantity

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

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