Australia · Year 7 · Practice Sheet 30

1. 1.

   $50 is shared in the ratio 1 : 4. Find each share.

   Formula:Dividing in a Ratio

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

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2. 2.

   A circle has a radius of 12 cm. Find its area. (Use π ≈ 3.14159)

   Formula:Area of a Circle

   $A = \pi r^2$

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3. 3.

   $3,100 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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4. 4.

   A train moves at 86 km/h for 3.2 hours. How far does it travel?

   Formula:Distance from Speed & Time

   $d = v \times t$

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5. 5.

   Find the circumference of a circle whose radius is 24 m. (Use π ≈ 3.14159)

   Formula:Circumference of a Circle

   $C = 2\pi r$

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6. 6.

   A car travels 412 km in 4 hours. Find its average speed.

   Formula:Speed

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

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7. 7.

   A triangle has a base of 10 cm and a height of 26 cm. Find its area.

   Formula:Area of a Triangle

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

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8. 8.

   One item costs $13.25. Find the total cost of 14 items.

   Formula:Total Cost

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

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9. 9.

   A triangle has a base of 17 cm and a height of 29 cm. Find its area.

   Formula:Area of a Triangle

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

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10. 10.

    A train moves at 63 km/h for 6 hours. How far does it travel?

    Formula:Distance from Speed & Time

    $d = v \times t$

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11. 11.

    Find the circumference of a circle whose radius is 7 m. (Use π ≈ 3.14159)

    Formula:Circumference of a Circle

    $C = 2\pi r$

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12. 12.

    A train moves at 44 km/h for 4.9 hours. How far does it travel?

    Formula:Distance from Speed & Time

    $d = v \times t$

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13. 13.

    Solve for x: 7x + 12 = 96.

    Formula:Solving a Linear Equation

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

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14. 14.

    A value changes from 134 to 181. 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.

    One item costs $19.45. Find the total cost of 17 items.

    Formula:Total Cost

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

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16. 16.

    A value changes from 57 to 241. 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.

    A triangle has a base of 14 cm and a height of 22 cm. Find its area.

    Formula:Area of a Triangle

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

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18. 18.

    A rectangle is 5 cm long and 5 cm wide. Find its area.

    Formula:Area of a Rectangle

    $A = l \times w$

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19. 19.

    Find the mean (average) of these numbers: 56, 23, 88, 18, 48.

    Formula:Arithmetic Mean

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

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20. 20.

    A right-angled triangle has legs of 7 cm and 18 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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