New Zealand · Year 7 · Practice Sheet 35

1. 1.

   Find the mean (average) of these numbers: 93, 21, 94, 57, 74, 55.

   Formula:Arithmetic Mean

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

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2. 2.

   A train moves at 76 km/h for 5.4 hours. How far does it travel?

   Formula:Distance from Speed & Time

   $d = v \times t$

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3. 3.

   Find the circumference of a circle whose radius is 16 m. (Use π ≈ 3.14159)

   Formula:Circumference of a Circle

   $C = 2\pi r$

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4. 4.

   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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5. 5.

   One item costs $19.98. Find the total cost of 16 items.

   Formula:Total Cost

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

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6. 6.

   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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7. 7.

   A value changes from 45 to 74. 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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8. 8.

   Find 1/8 of 96.

   Formula:Fraction of a Quantity

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

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9. 9.

   One item costs $1.6. Find the total cost of 17 items.

   Formula:Total Cost

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

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10. 10.

    Convert 3.66 kilometres into metres.

    Formula:Metric Length Conversion

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

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11. 11.

    A value changes from 155 to 157. 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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12. 12.

    Solve for x: 5x + 6 = 61.

    Formula:Solving a Linear Equation

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

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13. 13.

    Find 1/3 of 24.

    Formula:Fraction of a Quantity

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

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14. 14.

    A rectangle is 19 cm long and 22 cm wide. Find its area.

    Formula:Area of a Rectangle

    $A = l \times w$

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15. 15.

    A circle has a radius of 12 cm. Find its area. (Use π ≈ 3.14159)

    Formula:Area of a Circle

    $A = \pi r^2$

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16. 16.

    Find the circumference of a circle whose radius is 9 m. (Use π ≈ 3.14159)

    Formula:Circumference of a Circle

    $C = 2\pi r$

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17. 17.

    Solve for x: 9x + 2 = 110.

    Formula:Solving a Linear Equation

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

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18. 18.

    One item costs $4.4. Find the total cost of 12 items.

    Formula:Total Cost

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

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19. 19.

    A circle has a radius of 15 cm. Find its area. (Use π ≈ 3.14159)

    Formula:Area of a Circle

    $A = \pi r^2$

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20. 20.

    $112 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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