New Zealand · Year 7 · Practice Sheet 27

1. 1.

   Find 1/8 of 64.

   Formula:Fraction of a Quantity

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

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2. 2.

   A triangle has a base of 22 cm and a height of 18 cm. Find its area.

   Formula:Area of a Triangle

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

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3. 3.

   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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4. 4.

   Solve for x: 3x + 18 = 39.

   Formula:Solving a Linear Equation

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

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5. 5.

   Find the area of a square with side length 26 cm.

   Formula:Area of a Square

   $A = s^2$

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6. 6.

   A rectangle is 14 cm long and 24 cm wide. Find its area.

   Formula:Area of a Rectangle

   $A = l \times w$

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7. 7.

   What is 75% of 180?

   Formula:Percentage of a Quantity

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

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8. 8.

   A bag has 17 equally likely marbles, of which 5 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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9. 9.

   A triangle has a base of 12 cm and a height of 17 cm. Find its area.

   Formula:Area of a Triangle

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

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10. 10.

    Solve for x: 3x + 8 = 23.

    Formula:Solving a Linear Equation

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

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11. 11.

    A rectangle is 17 cm long and 9 cm wide. Find its area.

    Formula:Area of a Rectangle

    $A = l \times w$

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12. 12.

    A right-angled triangle has legs of 3 cm and 13 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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13. 13.

    $208 is shared in the ratio 5 : 3. Find each share.

    Formula:Dividing in a Ratio

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

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14. 14.

    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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15. 15.

    Find the mean (average) of these numbers: 41, 54, 60, 82, 93.

    Formula:Arithmetic Mean

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

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16. 16.

    Find the area of a square with side length 3 cm.

    Formula:Area of a Square

    $A = s^2$

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17. 17.

    A value changes from 116 to 100. 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.

    $3,800 is invested at 7.5% simple interest per year for 4 years. Find the interest earned.

    Formula:Simple Interest

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

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19. 19.

    A right-angled triangle has legs of 7 cm and 9 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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20. 20.

    A value changes from 173 to 72. 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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