United Kingdom · Year 7 · Practice Sheet 3

1. 1.

   A right-angled triangle has legs of 20 cm and 17 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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2. 2.

   Convert 3.15 kilometres into metres.

   Formula:Metric Length Conversion

   $1\,\text{km} = 1000\,\text{m}$

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3. 3.

   £80 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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4. 4.

   A value changes from 20 to 117. 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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5. 5.

   A car travels 354 km in 6 hours. Find its average speed.

   Formula:Speed

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

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6. 6.

   A circle has a radius of 24 cm. Find its area. (Use π ≈ 3.14159)

   Formula:Area of a Circle

   $A = \pi r^2$

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7. 7.

   A bag has 16 equally likely marbles, of which 11 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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8. 8.

   £3,000 is invested at 5% simple interest per year for 4 years. Find the interest earned.

   Formula:Simple Interest

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

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9. 9.

   A car travels 612 km in 6 hours. Find its average speed.

   Formula:Speed

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

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10. 10.

    What is 40% of 520?

    Formula:Percentage of a Quantity

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

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11. 11.

    A rectangle is 10 cm long and 9 cm wide. Find its area.

    Formula:Area of a Rectangle

    $A = l \times w$

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12. 12.

    Find the circumference of a circle whose radius is 15 m. (Use π ≈ 3.14159)

    Formula:Circumference of a Circle

    $C = 2\pi r$

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13. 13.

    £51 is shared in the ratio 1 : 2. Find each share.

    Formula:Dividing in a Ratio

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

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14. 14.

    Solve for x: 8x + 13 = 101.

    Formula:Solving a Linear Equation

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

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15. 15.

    A rectangle is 14 cm long and 26 cm wide. Find its area.

    Formula:Area of a Rectangle

    $A = l \times w$

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16. 16.

    A circle has a radius of 8 cm. Find its area. (Use π ≈ 3.14159)

    Formula:Area of a Circle

    $A = \pi r^2$

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17. 17.

    A train moves at 63 km/h for 4.5 hours. How far does it travel?

    Formula:Distance from Speed & Time

    $d = v \times t$

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18. 18.

    Solve for x: 7x + 20 = 104.

    Formula:Solving a Linear Equation

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

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19. 19.

    Find the mean (average) of these numbers: 78, 57, 88, 23.

    Formula:Arithmetic Mean

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

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20. 20.

    Find the area of a square with side length 15 cm.

    Formula:Area of a Square

    $A = s^2$

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