China · Grade 7 · Practice Sheet 21

1. 1.

   A circle has a radius of 10 cm. Find its area. (Use π ≈ 3.14159)

   Formula:Area of a Circle

   $A = \pi r^2$

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2. 2.

   Find the mean (average) of these numbers: 87, 96, 72, 51, 73, 12.

   Formula:Arithmetic Mean

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

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3. 3.

   ¥100 is shared in the ratio 2 : 3. Find each share.

   Formula:Dividing in a Ratio

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

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4. 4.

   A train moves at 83 km/h for 2 hours. How far does it travel?

   Formula:Distance from Speed & Time

   $d = v \times t$

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5. 5.

   ¥182 is shared in the ratio 4 : 3. Find each share.

   Formula:Dividing in a Ratio

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

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6. 6.

   Find the area of a square with side length 14 cm.

   Formula:Area of a Square

   $A = s^2$

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7. 7.

   A triangle has a base of 30 cm and a height of 24 cm. Find its area.

   Formula:Area of a Triangle

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

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8. 8.

   Solve for x: 2x + 11 = 21.

   Formula:Solving a Linear Equation

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

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9. 9.

   A right-angled triangle has legs of 14 cm and 7 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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10. 10.

    A train moves at 31 km/h for 3.2 hours. How far does it travel?

    Formula:Distance from Speed & Time

    $d = v \times t$

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11. 11.

    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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12. 12.

    Find 2/8 of 32.

    Formula:Fraction of a Quantity

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

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13. 13.

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

    Formula:Pythagorean Theorem

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

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14. 14.

    Convert 9.64 kilometres into metres.

    Formula:Metric Length Conversion

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

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15. 15.

    Find the circumference of a circle whose radius is 6 m. (Use π ≈ 3.14159)

    Formula:Circumference of a Circle

    $C = 2\pi r$

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16. 16.

    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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17. 17.

    One item costs ¥13.6. Find the total cost of 9 items.

    Formula:Total Cost

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

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18. 18.

    A triangle has a base of 7 cm and a height of 21 cm. Find its area.

    Formula:Area of a Triangle

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

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19. 19.

    A circle has a radius of 8 cm. Find its area. (Use π ≈ 3.14159)

    Formula:Area of a Circle

    $A = \pi r^2$

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20. 20.

    Solve for x: 6x + 15 = 69.

    Formula:Solving a Linear Equation

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

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