Australia · Year 7 · Practice Sheet 47

1. 1.

   Solve for x: 6x + 11 = 53.

   Formula:Solving a Linear Equation

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

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2. 2.

   One item costs $2.02. Find the total cost of 19 items.

   Formula:Total Cost

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

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3. 3.

   A circle has a radius of 11 cm. Find its area. (Use π ≈ 3.14159)

   Formula:Area of a Circle

   $A = \pi r^2$

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4. 4.

   A triangle has a base of 11 cm and a height of 17 cm. Find its area.

   Formula:Area of a Triangle

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

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5. 5.

   Solve for x: 5x + 3 = 13.

   Formula:Solving a Linear Equation

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

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6. 6.

   $36 is shared in the ratio 1 : 1. Find each share.

   Formula:Dividing in a Ratio

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

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7. 7.

   Find the circumference of a circle whose radius is 13 m. (Use π ≈ 3.14159)

   Formula:Circumference of a Circle

   $C = 2\pi r$

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8. 8.

   A value changes from 120 to 236. 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 perimeter of a rectangle measuring 9 m by 5 m.

   Formula:Perimeter of a Rectangle

   $P = 2(l + w)$

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10. 10.

    A train moves at 59 km/h for 3.4 hours. How far does it travel?

    Formula:Distance from Speed & Time

    $d = v \times t$

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11. 11.

    One item costs $16.02. Find the total cost of 17 items.

    Formula:Total Cost

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

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12. 12.

    $180 is shared in the ratio 5 : 1. Find each share.

    Formula:Dividing in a Ratio

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

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13. 13.

    A value changes from 81 to 48. 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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14. 14.

    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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15. 15.

    $4,600 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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16. 16.

    A value changes from 26 to 130. 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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17. 17.

    Find the mean (average) of these numbers: 98, 29, 84, 65, 28.

    Formula:Arithmetic Mean

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

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18. 18.

    A car travels 372 km in 4 hours. Find its average speed.

    Formula:Speed

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

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19. 19.

    A train moves at 55 km/h for 4.1 hours. How far does it travel?

    Formula:Distance from Speed & Time

    $d = v \times t$

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20. 20.

    Find the circumference of a circle whose radius is 21 m. (Use π ≈ 3.14159)

    Formula:Circumference of a Circle

    $C = 2\pi r$

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