Australia · Year 7 · Practice Sheet 17

1. 1.

   A triangle has a base of 29 cm and a height of 9 cm. Find its area.

   Formula:Area of a Triangle

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

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2. 2.

   Find the mean (average) of these numbers: 87, 92, 25, 83.

   Formula:Arithmetic Mean

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

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3. 3.

   $111 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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4. 4.

   One item costs $2.75. Find the total cost of 5 items.

   Formula:Total Cost

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

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5. 5.

   Find 7/8 of 144.

   Formula:Fraction of a Quantity

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

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6. 6.

   Find the perimeter of a rectangle measuring 19 m by 11 m.

   Formula:Perimeter of a Rectangle

   $P = 2(l + w)$

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7. 7.

   $210 is shared in the ratio 2 : 4. Find each share.

   Formula:Dividing in a Ratio

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

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8. 8.

   A value changes from 66 to 54. 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.

   A circle has a radius of 9 cm. Find its area. (Use π ≈ 3.14159)

   Formula:Area of a Circle

   $A = \pi r^2$

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10. 10.

    A train moves at 100 km/h for 2.7 hours. How far does it travel?

    Formula:Distance from Speed & Time

    $d = v \times t$

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11. 11.

    $156 is shared in the ratio 3 : 1. Find each share.

    Formula:Dividing in a Ratio

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

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12. 12.

    A right-angled triangle has legs of 4 cm and 13 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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13. 13.

    A train moves at 66 km/h for 2.6 hours. How far does it travel?

    Formula:Distance from Speed & Time

    $d = v \times t$

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14. 14.

    One item costs $24.03. Find the total cost of 11 items.

    Formula:Total Cost

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

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15. 15.

    Convert 10.44 kilometres into metres.

    Formula:Metric Length Conversion

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

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16. 16.

    $36 is shared in the ratio 1 : 1. Find each share.

    Formula:Dividing in a Ratio

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

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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.

    What is 75% of 180?

    Formula:Percentage of a Quantity

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

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19. 19.

    Solve for x: 5x + 1 = 46.

    Formula:Solving a Linear Equation

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

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20. 20.

    Find the area of a square with side length 19 cm.

    Formula:Area of a Square

    $A = s^2$

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