New Zealand · Year 7 · Practice Sheet 42

1. 1.

   Find 1/2 of 16.

   Formula:Fraction of a Quantity

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

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2. 2.

   $160 is shared in the ratio 3 : 5. Find each share.

   Formula:Dividing in a Ratio

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

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3. 3.

   A bag has 28 equally likely marbles, of which 23 are red. Find the probability of drawing a red marble (to 3 d.p.).

   Formula:Simple Probability

   $P(E) = \dfrac{\text{favourable}}{\text{total}}$

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4. 4.

   Convert 2.82 kilometres into metres.

   Formula:Metric Length Conversion

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

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5. 5.

   What is 20% of 190?

   Formula:Percentage of a Quantity

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

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6. 6.

   A circle has a radius of 5 cm. Find its area. (Use π ≈ 3.14159)

   Formula:Area of a Circle

   $A = \pi r^2$

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7. 7.

   A train moves at 33 km/h for 4.4 hours. How far does it travel?

   Formula:Distance from Speed & Time

   $d = v \times t$

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8. 8.

   What is 50% of 400?

   Formula:Percentage of a Quantity

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

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9. 9.

   Convert 9.45 kilometres into metres.

   Formula:Metric Length Conversion

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

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10. 10.

    Solve for x: 9x + 11 = 110.

    Formula:Solving a Linear Equation

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

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11. 11.

    Find the mean (average) of these numbers: 87, 32, 86, 25, 49, 54.

    Formula:Arithmetic Mean

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

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12. 12.

    Find the circumference of a circle whose radius is 4 m. (Use π ≈ 3.14159)

    Formula:Circumference of a Circle

    $C = 2\pi r$

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13. 13.

    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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14. 14.

    A right-angled triangle has legs of 12 cm and 3 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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15. 15.

    Find the mean (average) of these numbers: 79, 76, 12, 66.

    Formula:Arithmetic Mean

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

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16. 16.

    A triangle has a base of 25 cm and a height of 3 cm. Find its area.

    Formula:Area of a Triangle

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

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17. 17.

    A circle has a radius of 5 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 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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19. 19.

    A car travels 168 km in 2 hours. Find its average speed.

    Formula:Speed

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

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20. 20.

    A rectangle is 13 cm long and 27 cm wide. Find its area.

    Formula:Area of a Rectangle

    $A = l \times w$

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