Ireland · Year 7 · Practice Sheet 34

1. 1.

   A right-angled triangle has legs of 5 cm and 4 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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2. 2.

   A value changes from 168 to 220. 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.

   Convert 3.23 kilometres into metres.

   Formula:Metric Length Conversion

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

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4. 4.

   Find the mean (average) of these numbers: 69, 81, 44, 23, 74.

   Formula:Arithmetic Mean

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

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5. 5.

   A rectangle is 8 cm long and 21 cm wide. Find its area.

   Formula:Area of a Rectangle

   $A = l \times w$

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6. 6.

   Find the circumference of a circle whose radius is 25 m. (Use π ≈ 3.14159)

   Formula:Circumference of a Circle

   $C = 2\pi r$

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7. 7.

   €900 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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8. 8.

   A value changes from 67 to 73. 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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9. 9.

   Solve for x: 9x + 1 = 109.

   Formula:Solving a Linear Equation

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

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10. 10.

    Find the perimeter of a rectangle measuring 43 m by 29 m.

    Formula:Perimeter of a Rectangle

    $P = 2(l + w)$

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11. 11.

    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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12. 12.

    Find the mean (average) of these numbers: 17, 58, 72, 80, 19, 76.

    Formula:Arithmetic Mean

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

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13. 13.

    A train moves at 95 km/h for 2.7 hours. How far does it travel?

    Formula:Distance from Speed & Time

    $d = v \times t$

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14. 14.

    A rectangle is 21 cm long and 25 cm wide. Find its area.

    Formula:Area of a Rectangle

    $A = l \times w$

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15. 15.

    Find the circumference of a circle whose radius is 14 m. (Use π ≈ 3.14159)

    Formula:Circumference of a Circle

    $C = 2\pi r$

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16. 16.

    Solve for x: 8x + 6 = 94.

    Formula:Solving a Linear Equation

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

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17. 17.

    A rectangle is 20 cm long and 25 cm wide. Find its area.

    Formula:Area of a Rectangle

    $A = l \times w$

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18. 18.

    Find the mean (average) of these numbers: 17, 27, 43, 92, 33.

    Formula:Arithmetic Mean

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

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19. 19.

    Find 1/2 of 30.

    Formula:Fraction of a Quantity

    $\text{result} = \dfrac{a}{b} \times N$

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20. 20.

    One item costs €17.19. Find the total cost of 9 items.

    Formula:Total Cost

    $\text{total} = \text{price} \times \text{quantity}$

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