New Zealand · Year 7 · Practice Sheet 6

1. 1.

   A triangle has a base of 9 cm and a height of 24 cm. Find its area.

   Formula:Area of a Triangle

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

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2. 2.

   Find 1/8 of 112.

   Formula:Fraction of a Quantity

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

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3. 3.

   $3,200 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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4. 4.

   Find the circumference of a circle whose radius is 10 m. (Use π ≈ 3.14159)

   Formula:Circumference of a Circle

   $C = 2\pi r$

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5. 5.

   $4,300 is invested at 7.5% 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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6. 6.

   Find the perimeter of a rectangle measuring 35 m by 23 m.

   Formula:Perimeter of a Rectangle

   $P = 2(l + w)$

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7. 7.

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

   Formula:Area of a Rectangle

   $A = l \times w$

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8. 8.

   Convert 3.46 kilometres into metres.

   Formula:Metric Length Conversion

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

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9. 9.

   A triangle has a base of 33 cm and a height of 9 cm. Find its area.

   Formula:Area of a Triangle

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

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10. 10.

    $105 is shared in the ratio 1 : 2. Find each share.

    Formula:Dividing in a Ratio

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

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11. 11.

    A car travels 117 km in 3 hours. Find its average speed.

    Formula:Speed

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

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12. 12.

    Solve for x: 2x + 14 = 26.

    Formula:Solving a Linear Equation

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

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13. 13.

    A bag has 27 equally likely marbles, of which 15 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.

    Convert 11.38 kilometres into metres.

    Formula:Metric Length Conversion

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

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15. 15.

    A right-angled triangle has legs of 11 cm and 10 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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16. 16.

    A train moves at 22 km/h for 1.7 hours. How far does it travel?

    Formula:Distance from Speed & Time

    $d = v \times t$

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17. 17.

    Find the mean (average) of these numbers: 42, 89, 33, 67, 78, 63.

    Formula:Arithmetic Mean

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

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18. 18.

    A value changes from 113 to 138. 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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19. 19.

    What is 25% of 170?

    Formula:Percentage of a Quantity

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

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20. 20.

    $1,900 is invested at 4% 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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