New Zealand · Year 7 · Practice Sheet 13

1. 1.

   A value changes from 165 to 118. 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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2. 2.

   A right-angled triangle has legs of 20 cm and 19 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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3. 3.

   $175 is shared in the ratio 2 : 3. Find each share.

   Formula:Dividing in a Ratio

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

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4. 4.

   Convert 7.91 kilometres into metres.

   Formula:Metric Length Conversion

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

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5. 5.

   $75 is shared in the ratio 2 : 1. Find each share.

   Formula:Dividing in a Ratio

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

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6. 6.

   Find the circumference of a circle whose radius is 29 m. (Use π ≈ 3.14159)

   Formula:Circumference of a Circle

   $C = 2\pi r$

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7. 7.

   Find the mean (average) of these numbers: 68, 10, 30, 99, 82.

   Formula:Arithmetic Mean

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

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8. 8.

   $240 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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9. 9.

   $2,900 is invested at 8% simple interest per year for 2 years. Find the interest earned.

   Formula:Simple Interest

   $I = \dfrac{P \times r \times t}{100}$

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10. 10.

    One item costs $1.8. Find the total cost of 7 items.

    Formula:Total Cost

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

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11. 11.

    A rectangle is 14 cm long and 23 cm wide. Find its area.

    Formula:Area of a Rectangle

    $A = l \times w$

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12. 12.

    A bag has 8 equally likely marbles, of which 2 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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13. 13.

    One item costs $15.86. Find the total cost of 8 items.

    Formula:Total Cost

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

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14. 14.

    A train moves at 23 km/h for 3.3 hours. How far does it travel?

    Formula:Distance from Speed & Time

    $d = v \times t$

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15. 15.

    What is 50% of 200?

    Formula:Percentage of a Quantity

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

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16. 16.

    A train moves at 38 km/h for 5.6 hours. How far does it travel?

    Formula:Distance from Speed & Time

    $d = v \times t$

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17. 17.

    Find the area of a square with side length 12 cm.

    Formula:Area of a Square

    $A = s^2$

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18. 18.

    Convert 6.24 kilometres into metres.

    Formula:Metric Length Conversion

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

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19. 19.

    $1,500 is invested at 10% simple interest per year for 5 years. Find the interest earned.

    Formula:Simple Interest

    $I = \dfrac{P \times r \times t}{100}$

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20. 20.

    A rectangle is 39 cm long and 3 cm wide. Find its area.

    Formula:Area of a Rectangle

    $A = l \times w$

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