New Zealand · Year 7 · Practice Sheet 48

1. 1.

   A bag has 17 equally likely marbles, of which 9 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: 4x + 9 = 37.

   Formula:Solving a Linear Equation

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

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3. 3.

   Find the perimeter of a rectangle measuring 26 m by 20 m.

   Formula:Perimeter of a Rectangle

   $P = 2(l + w)$

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4. 4.

   A triangle has a base of 19 cm and a height of 8 cm. Find its area.

   Formula:Area of a Triangle

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

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5. 5.

   A circle has a radius of 25 cm. Find its area. (Use π ≈ 3.14159)

   Formula:Area of a Circle

   $A = \pi r^2$

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6. 6.

   Solve for x: 4x + 1 = 21.

   Formula:Solving a Linear Equation

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

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7. 7.

   $238 is shared in the ratio 2 : 5. Find each share.

   Formula:Dividing in a Ratio

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

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8. 8.

   A rectangle is 26 cm long and 19 cm wide. Find its area.

   Formula:Area of a Rectangle

   $A = l \times w$

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9. 9.

   Find 2/3 of 24.

   Formula:Fraction of a Quantity

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

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10. 10.

    Find the mean (average) of these numbers: 92, 70, 33, 45, 26.

    Formula:Arithmetic Mean

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

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11. 11.

    A right-angled triangle has legs of 11 cm and 20 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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12. 12.

    Find the area of a square with side length 27 cm.

    Formula:Area of a Square

    $A = s^2$

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13. 13.

    A rectangle is 25 cm long and 6 cm wide. Find its area.

    Formula:Area of a Rectangle

    $A = l \times w$

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14. 14.

    A car travels 315 km in 5 hours. Find its average speed.

    Formula:Speed

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

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15. 15.

    A value changes from 82 to 174. 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.

    What is 50% of 120?

    Formula:Percentage of a Quantity

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

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17. 17.

    One item costs $11.81. Find the total cost of 13 items.

    Formula:Total Cost

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

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18. 18.

    Find the perimeter of a rectangle measuring 21 m by 6 m.

    Formula:Perimeter of a Rectangle

    $P = 2(l + w)$

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19. 19.

    A right-angled triangle has legs of 14 cm and 8 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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20. 20.

    Find the mean (average) of these numbers: 54, 23, 14, 18, 10, 58.

    Formula:Arithmetic Mean

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

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