Taiwan · Grade 7 · Practice Sheet 24

1. 1.

   A right-angled triangle has legs of 14 cm and 11 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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2. 2.

   A value changes from 146 to 242. 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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3. 3.

   Solve for x: 8x + 17 = 105.

   Formula:Solving a Linear Equation

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

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4. 4.

   Find 1/3 of 15.

   Formula:Fraction of a Quantity

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

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5. 5.

   NT$ 4,300 is invested at 6% simple interest per year for 6 years. Find the interest earned.

   Formula:Simple Interest

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

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6. 6.

   A value changes from 52 to 239. 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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7. 7.

   Solve for x: 2x + 14 = 32.

   Formula:Solving a Linear Equation

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

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8. 8.

   One item costs NT$ 13.67. Find the total cost of 11 items.

   Formula:Total Cost

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

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9. 9.

   Find the area of a square with side length 21 cm.

   Formula:Area of a Square

   $A = s^2$

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10. 10.

    NT$ 84 is shared in the ratio 2 : 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.

    NT$ 1,500 is invested at 6% simple interest per year for 6 years. Find the interest earned.

    Formula:Simple Interest

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

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12. 12.

    A car travels 246 km in 6 hours. Find its average speed.

    Formula:Speed

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

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13. 13.

    A right-angled triangle has legs of 13 cm and 17 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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14. 14.

    A rectangle is 10 cm long and 22 cm wide. Find its area.

    Formula:Area of a Rectangle

    $A = l \times w$

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15. 15.

    Find the perimeter of a rectangle measuring 28 m by 31 m.

    Formula:Perimeter of a Rectangle

    $P = 2(l + w)$

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16. 16.

    A train moves at 78 km/h for 5.8 hours. How far does it travel?

    Formula:Distance from Speed & Time

    $d = v \times t$

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17. 17.

    A triangle has a base of 26 cm and a height of 5 cm. Find its area.

    Formula:Area of a Triangle

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

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18. 18.

    NT$ 155 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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19. 19.

    A value changes from 62 to 124. 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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20. 20.

    A right-angled triangle has legs of 13 cm and 20 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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