New Zealand · Year 7 · Practice Sheet 3

1. 1.

   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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2. 2.

   $54 is shared in the ratio 3 : 3. 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 12 equally likely marbles, of which 7 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.

   Solve for x: 7x + 10 = 38.

   Formula:Solving a Linear Equation

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

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5. 5.

   Find the perimeter of a rectangle measuring 43 m by 13 m.

   Formula:Perimeter of a Rectangle

   $P = 2(l + w)$

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6. 6.

   A rectangle is 37 cm long and 23 cm wide. Find its area.

   Formula:Area of a Rectangle

   $A = l \times w$

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7. 7.

   Find the perimeter of a rectangle measuring 26 m by 8 m.

   Formula:Perimeter of a Rectangle

   $P = 2(l + w)$

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8. 8.

   A triangle has a base of 24 cm and a height of 18 cm. Find its area.

   Formula:Area of a Triangle

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

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9. 9.

   A car travels 240 km in 5 hours. Find its average speed.

   Formula:Speed

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

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10. 10.

    One item costs $20.83. Find the total cost of 8 items.

    Formula:Total Cost

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

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11. 11.

    Convert 6.11 kilometres into metres.

    Formula:Metric Length Conversion

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

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12. 12.

    A value changes from 31 to 101. 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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13. 13.

    A triangle has a base of 10 cm and a height of 12 cm. Find its area.

    Formula:Area of a Triangle

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

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14. 14.

    Find the mean (average) of these numbers: 66, 58, 61, 98, 82.

    Formula:Arithmetic Mean

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

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15. 15.

    Find 1/2 of 20.

    Formula:Fraction of a Quantity

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

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16. 16.

    $2,600 is invested at 6% simple interest per year for 3 years. Find the interest earned.

    Formula:Simple Interest

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

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17. 17.

    Find 2/8 of 160.

    Formula:Fraction of a Quantity

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

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18. 18.

    Find the perimeter of a rectangle measuring 38 m by 9 m.

    Formula:Perimeter of a Rectangle

    $P = 2(l + w)$

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19. 19.

    What is 75% of 410?

    Formula:Percentage of a Quantity

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

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20. 20.

    $1,300 is invested at 3% 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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