New Zealand · Year 7 · Practice Sheet 11

1. 1.

   Find the mean (average) of these numbers: 90, 14, 50, 77, 82, 15.

   Formula:Arithmetic Mean

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

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2. 2.

   A right-angled triangle has legs of 19 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.

   A train moves at 55 km/h for 2 hours. How far does it travel?

   Formula:Distance from Speed & Time

   $d = v \times t$

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4. 4.

   $3,600 is invested at 4% simple interest per year for 4 years. Find the interest earned.

   Formula:Simple Interest

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

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5. 5.

   A value changes from 145 to 207. 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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6. 6.

   $700 is invested at 10% 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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7. 7.

   One item costs $14.78. Find the total cost of 9 items.

   Formula:Total Cost

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

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8. 8.

   A right-angled triangle has legs of 13 cm and 10 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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9. 9.

   A value changes from 89 to 76. 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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10. 10.

    Find 4/5 of 100.

    Formula:Fraction of a Quantity

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

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11. 11.

    A triangle has a base of 28 cm and a height of 10 cm. Find its area.

    Formula:Area of a Triangle

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

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12. 12.

    Find the mean (average) of these numbers: 23, 87, 94, 84, 26, 92.

    Formula:Arithmetic Mean

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

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13. 13.

    A bag has 27 equally likely marbles, of which 25 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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14. 14.

    A value changes from 31 to 66. 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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15. 15.

    A bag has 15 equally likely marbles, of which 9 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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16. 16.

    One item costs $8.47. Find the total cost of 11 items.

    Formula:Total Cost

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

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17. 17.

    A car travels 495 km in 5 hours. Find its average speed.

    Formula:Speed

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

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18. 18.

    A train moves at 74 km/h for 1.7 hours. How far does it travel?

    Formula:Distance from Speed & Time

    $d = v \times t$

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19. 19.

    A car travels 62 km in 2 hours. Find its average speed.

    Formula:Speed

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

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20. 20.

    Find 5/8 of 32.

    Formula:Fraction of a Quantity

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

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