China · Grade 7 · Practice Sheet 4

1. 1.

   Find the mean (average) of these numbers: 71, 61, 24, 18.

   Formula:Arithmetic Mean

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

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2. 2.

   Find 2/3 of 15.

   Formula:Fraction of a Quantity

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

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3. 3.

   ¥85 is shared in the ratio 4 : 1. Find each share.

   Formula:Dividing in a Ratio

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

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4. 4.

   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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5. 5.

   Find the area of a square with side length 9 cm.

   Formula:Area of a Square

   $A = s^2$

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6. 6.

   A circle has a radius of 9 cm. Find its area. (Use π ≈ 3.14159)

   Formula:Area of a Circle

   $A = \pi r^2$

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7. 7.

   Find the circumference of a circle whose radius is 10 m. (Use π ≈ 3.14159)

   Formula:Circumference of a Circle

   $C = 2\pi r$

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8. 8.

   ¥78 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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9. 9.

   Find the circumference of a circle whose radius is 10 m. (Use π ≈ 3.14159)

   Formula:Circumference of a Circle

   $C = 2\pi r$

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10. 10.

    Find the mean (average) of these numbers: 34, 64, 44, 48.

    Formula:Arithmetic Mean

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

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11. 11.

    A triangle has a base of 39 cm and a height of 14 cm. Find its area.

    Formula:Area of a Triangle

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

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12. 12.

    A circle has a radius of 4 cm. Find its area. (Use π ≈ 3.14159)

    Formula:Area of a Circle

    $A = \pi r^2$

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13. 13.

    Find the circumference of a circle whose radius is 18 m. (Use π ≈ 3.14159)

    Formula:Circumference of a Circle

    $C = 2\pi r$

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14. 14.

    Solve for x: 4x + 1 = 33.

    Formula:Solving a Linear Equation

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

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15. 15.

    A bag has 20 equally likely marbles, of which 18 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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16. 16.

    What is 15% of 300?

    Formula:Percentage of a Quantity

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

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17. 17.

    A right-angled triangle has legs of 3 cm and 7 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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18. 18.

    What is 30% of 510?

    Formula:Percentage of a Quantity

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

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19. 19.

    A car travels 704 km in 8 hours. Find its average speed.

    Formula:Speed

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

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20. 20.

    What is 10% of 240?

    Formula:Percentage of a Quantity

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

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