New Zealand · Year 7 · Practice Sheet 44

1. 1.

   A circle has a radius of 6 cm. Find its area. (Use π ≈ 3.14159)

   Formula:Area of a Circle

   $A = \pi r^2$

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2. 2.

   $120 is shared in the ratio 3 : 3. Find each share.

   Formula:Dividing in a Ratio

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

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3. 3.

   Convert 2.08 kilometres into metres.

   Formula:Metric Length Conversion

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

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4. 4.

   Find the perimeter of a rectangle measuring 14 m by 32 m.

   Formula:Perimeter of a Rectangle

   $P = 2(l + w)$

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5. 5.

   $200 is shared in the ratio 5 : 3. Find each share.

   Formula:Dividing in a Ratio

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

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6. 6.

   A value changes from 62 to 62. 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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7. 7.

   A train moves at 41 km/h for 3.6 hours. How far does it travel?

   Formula:Distance from Speed & Time

   $d = v \times t$

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8. 8.

   A value changes from 87 to 113. 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.

   Find the circumference of a circle whose radius is 12 m. (Use π ≈ 3.14159)

   Formula:Circumference of a Circle

   $C = 2\pi r$

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10. 10.

    Convert 1.96 kilometres into metres.

    Formula:Metric Length Conversion

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

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11. 11.

    Solve for x: 6x + 7 = 73.

    Formula:Solving a Linear Equation

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

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12. 12.

    Find 3/4 of 20.

    Formula:Fraction of a Quantity

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

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13. 13.

    A value changes from 42 to 205. 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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14. 14.

    A rectangle is 15 cm long and 9 cm wide. Find its area.

    Formula:Area of a Rectangle

    $A = l \times w$

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15. 15.

    A value changes from 119 to 98. 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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16. 16.

    Find the mean (average) of these numbers: 51, 57, 22, 97.

    Formula:Arithmetic Mean

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

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17. 17.

    A circle has a radius of 6 cm. Find its area. (Use π ≈ 3.14159)

    Formula:Area of a Circle

    $A = \pi r^2$

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18. 18.

    Find the perimeter of a rectangle measuring 10 m by 31 m.

    Formula:Perimeter of a Rectangle

    $P = 2(l + w)$

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19. 19.

    A triangle has a base of 10 cm and a height of 18 cm. Find its area.

    Formula:Area of a Triangle

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

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20. 20.

    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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