Japan · Grade 7 · Practice Sheet 47

1. 1.

   A bag has 29 equally likely marbles, of which 2 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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2. 2.

   Solve for x: 3x + 7 = 43.

   Formula:Solving a Linear Equation

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

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3. 3.

   Find the circumference of a circle whose radius is 14 m. (Use π ≈ 3.14159)

   Formula:Circumference of a Circle

   $C = 2\pi r$

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4. 4.

   Find the area of a square with side length 12 cm.

   Formula:Area of a Square

   $A = s^2$

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5. 5.

   Find the circumference of a circle whose radius is 30 m. (Use π ≈ 3.14159)

   Formula:Circumference of a Circle

   $C = 2\pi r$

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6. 6.

   Solve for x: 3x + 1 = 37.

   Formula:Solving a Linear Equation

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

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7. 7.

   A circle has a radius of 17 cm. Find its area. (Use π ≈ 3.14159)

   Formula:Area of a Circle

   $A = \pi r^2$

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8. 8.

   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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9. 9.

   ¥231 is shared in the ratio 3 : 4. Find each share.

   Formula:Dividing in a Ratio

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

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10. 10.

    One item costs ¥1.81. Find the total cost of 3 items.

    Formula:Total Cost

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

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11. 11.

    A right-angled triangle has legs of 19 cm and 17 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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12. 12.

    Solve for x: 3x + 10 = 16.

    Formula:Solving a Linear Equation

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

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13. 13.

    Find the perimeter of a rectangle measuring 21 m by 28 m.

    Formula:Perimeter of a Rectangle

    $P = 2(l + w)$

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14. 14.

    Find the circumference of a circle whose radius is 17 m. (Use π ≈ 3.14159)

    Formula:Circumference of a Circle

    $C = 2\pi r$

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15. 15.

    Convert 4.19 kilometres into metres.

    Formula:Metric Length Conversion

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

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16. 16.

    Find the mean (average) of these numbers: 74, 41, 11, 13, 71, 60.

    Formula:Arithmetic Mean

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

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17. 17.

    A value changes from 179 to 159. 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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18. 18.

    ¥1,500 is invested at 7.5% simple interest per year for 3 years. Find the interest earned.

    Formula:Simple Interest

    $I = \dfrac{P \times r \times t}{100}$

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19. 19.

    A car travels 510 km in 6 hours. Find its average speed.

    Formula:Speed

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

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20. 20.

    Find the perimeter of a rectangle measuring 24 m by 4 m.

    Formula:Perimeter of a Rectangle

    $P = 2(l + w)$

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