Taiwan · Grade 7 · Practice Sheet 18

1. 1.

   A right-angled triangle has legs of 12 cm and 12 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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2. 2.

   One item costs NT$ 5.77. Find the total cost of 10 items.

   Formula:Total Cost

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

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3. 3.

   Solve for x: 3x + 19 = 52.

   Formula:Solving a Linear Equation

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

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4. 4.

   A car travels 364 km in 7 hours. Find its average speed.

   Formula:Speed

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

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5. 5.

   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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6. 6.

   A bag has 30 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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7. 7.

   A triangle has a base of 9 cm and a height of 30 cm. Find its area.

   Formula:Area of a Triangle

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

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8. 8.

   Find the area of a square with side length 29 cm.

   Formula:Area of a Square

   $A = s^2$

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9. 9.

   Solve for x: 9x + 9 = 63.

   Formula:Solving a Linear Equation

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

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10. 10.

    A rectangle is 10 cm long and 11 cm wide. Find its area.

    Formula:Area of a Rectangle

    $A = l \times w$

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11. 11.

    NT$ 4,800 is invested at 4% 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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12. 12.

    NT$ 168 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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13. 13.

    Convert 11.52 kilometres into metres.

    Formula:Metric Length Conversion

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

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14. 14.

    Find 4/5 of 25.

    Formula:Fraction of a Quantity

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

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15. 15.

    A value changes from 58 to 71. 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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16. 16.

    Find 2/3 of 60.

    Formula:Fraction of a Quantity

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

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17. 17.

    One item costs NT$ 14.83. Find the total cost of 19 items.

    Formula:Total Cost

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

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18. 18.

    A right-angled triangle has legs of 15 cm and 20 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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19. 19.

    A rectangle is 14 cm long and 4 cm wide. Find its area.

    Formula:Area of a Rectangle

    $A = l \times w$

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20. 20.

    Find 2/8 of 40.

    Formula:Fraction of a Quantity

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

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