United States · Grade 7 · Practice Sheet 46

1. 1.

   A right-angled triangle has legs of 14 cm and 18 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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2. 2.

   What is 30% of 190?

   Formula:Percentage of a Quantity

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

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3. 3.

   A car travels 308 km in 7 hours. Find its average speed.

   Formula:Speed

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

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4. 4.

   A value changes from 170 to 184. 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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5. 5.

   Convert 2.8 kilometres into metres.

   Formula:Metric Length Conversion

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

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6. 6.

   Find the perimeter of a rectangle measuring 15 m by 13 m.

   Formula:Perimeter of a Rectangle

   $P = 2(l + w)$

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7. 7.

   A circle has a radius of 21 cm. Find its area. (Use π ≈ 3.14159)

   Formula:Area of a Circle

   $A = \pi r^2$

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8. 8.

   Convert 11.75 kilometres into metres.

   Formula:Metric Length Conversion

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

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9. 9.

   Find the perimeter of a rectangle measuring 32 m by 23 m.

   Formula:Perimeter of a Rectangle

   $P = 2(l + w)$

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10. 10.

    $66 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.

    One item costs $13.37. Find the total cost of 16 items.

    Formula:Total Cost

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

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12. 12.

    A car travels 365 km in 5 hours. Find its average speed.

    Formula:Speed

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

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13. 13.

    Convert 5.95 kilometres into metres.

    Formula:Metric Length Conversion

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

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14. 14.

    A right-angled triangle has legs of 4 cm and 19 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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15. 15.

    Find the mean (average) of these numbers: 95, 49, 36, 84.

    Formula:Arithmetic Mean

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

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16. 16.

    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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17. 17.

    A triangle has a base of 6 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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18. 18.

    Find the circumference of a circle whose radius is 20 m. (Use π ≈ 3.14159)

    Formula:Circumference of a Circle

    $C = 2\pi r$

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19. 19.

    Find the area of a square with side length 24 cm.

    Formula:Area of a Square

    $A = s^2$

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20. 20.

    A train moves at 29 km/h for 5.7 hours. How far does it travel?

    Formula:Distance from Speed & Time

    $d = v \times t$

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