Australia · Year 7 · Practice Sheet 1

1. 1.

   Find the perimeter of a rectangle measuring 13 m by 19 m.

   Formula:Perimeter of a Rectangle

   $P = 2(l + w)$

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2. 2.

   A bag has 16 equally likely marbles, of which 5 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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3. 3.

   One item costs $13.14. Find the total cost of 20 items.

   Formula:Total Cost

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

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4. 4.

   Convert 7.24 kilometres into metres.

   Formula:Metric Length Conversion

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

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5. 5.

   A right-angled triangle has legs of 7 cm and 16 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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6. 6.

   Find the area of a square with side length 5 cm.

   Formula:Area of a Square

   $A = s^2$

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7. 7.

   A train moves at 45 km/h for 5.2 hours. How far does it travel?

   Formula:Distance from Speed & Time

   $d = v \times t$

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8. 8.

   A value changes from 140 to 132. 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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9. 9.

   Find the area of a square with side length 17 cm.

   Formula:Area of a Square

   $A = s^2$

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10. 10.

    Find the perimeter of a rectangle measuring 14 m by 10 m.

    Formula:Perimeter of a Rectangle

    $P = 2(l + w)$

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11. 11.

    $1,500 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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12. 12.

    A rectangle is 39 cm long and 15 cm wide. Find its area.

    Formula:Area of a Rectangle

    $A = l \times w$

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13. 13.

    Find the mean (average) of these numbers: 17, 15, 88, 56.

    Formula:Arithmetic Mean

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

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14. 14.

    A triangle has a base of 15 cm and a height of 11 cm. Find its area.

    Formula:Area of a Triangle

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

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15. 15.

    Find the mean (average) of these numbers: 15, 85, 77, 32.

    Formula:Arithmetic Mean

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

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16. 16.

    Convert 8.41 kilometres into metres.

    Formula:Metric Length Conversion

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

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17. 17.

    Solve for x: 6x + 10 = 58.

    Formula:Solving a Linear Equation

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

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18. 18.

    Find the circumference of a circle whose radius is 11 m. (Use π ≈ 3.14159)

    Formula:Circumference of a Circle

    $C = 2\pi r$

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19. 19.

    One item costs $4.67. Find the total cost of 14 items.

    Formula:Total Cost

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

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20. 20.

    Find the mean (average) of these numbers: 28, 71, 87, 17, 29, 18.

    Formula:Arithmetic Mean

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

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