United Kingdom · Year 7 · Practice Sheet 47

1. 1.

   A circle has a radius of 18 cm. Find its area. (Use π ≈ 3.14159)

   Formula:Area of a Circle

   $A = \pi r^2$

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2. 2.

   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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3. 3.

   Solve for x: 5x + 2 = 42.

   Formula:Solving a Linear Equation

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

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4. 4.

   A right-angled triangle has legs of 19 cm and 6 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: 95, 63, 19, 98, 37.

   Formula:Arithmetic Mean

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

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6. 6.

   A circle has a radius of 20 cm. Find its area. (Use π ≈ 3.14159)

   Formula:Area of a Circle

   $A = \pi r^2$

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7. 7.

   What is 15% of 110?

   Formula:Percentage of a Quantity

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

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8. 8.

   £900 is invested at 7.5% 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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9. 9.

   A triangle has a base of 31 cm and a height of 19 cm. Find its area.

   Formula:Area of a Triangle

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

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10. 10.

    Convert 4.58 kilometres into metres.

    Formula:Metric Length Conversion

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

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11. 11.

    Solve for x: 9x + 6 = 96.

    Formula:Solving a Linear Equation

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

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12. 12.

    Find the mean (average) of these numbers: 58, 14, 64, 95, 67.

    Formula:Arithmetic Mean

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

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13. 13.

    What is 10% of 50?

    Formula:Percentage of a Quantity

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

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14. 14.

    Convert 5.45 kilometres into metres.

    Formula:Metric Length Conversion

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

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15. 15.

    Solve for x: 3x + 7 = 22.

    Formula:Solving a Linear Equation

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

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16. 16.

    A rectangle is 31 cm long and 28 cm wide. Find its area.

    Formula:Area of a Rectangle

    $A = l \times w$

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17. 17.

    A right-angled triangle has legs of 10 cm and 16 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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18. 18.

    Find the perimeter of a rectangle measuring 31 m by 14 m.

    Formula:Perimeter of a Rectangle

    $P = 2(l + w)$

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19. 19.

    What is 75% of 130?

    Formula:Percentage of a Quantity

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

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20. 20.

    A car travels 225 km in 3 hours. Find its average speed.

    Formula:Speed

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

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