New Zealand · Year 7 · Practice Sheet 36

1. 1.

   Find the perimeter of a rectangle measuring 34 m by 23 m.

   Formula:Perimeter of a Rectangle

   $P = 2(l + w)$

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2. 2.

   Solve for x: 4x + 7 = 15.

   Formula:Solving a Linear Equation

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

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3. 3.

   A rectangle is 26 cm long and 20 cm wide. Find its area.

   Formula:Area of a Rectangle

   $A = l \times w$

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4. 4.

   Find the mean (average) of these numbers: 38, 11, 22, 73.

   Formula:Arithmetic Mean

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

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5. 5.

   Convert 8.7 kilometres into metres.

   Formula:Metric Length Conversion

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

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6. 6.

   What is 5% of 230?

   Formula:Percentage of a Quantity

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

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7. 7.

   Find the perimeter of a rectangle measuring 31 m by 14 m.

   Formula:Perimeter of a Rectangle

   $P = 2(l + w)$

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8. 8.

   What is 50% of 570?

   Formula:Percentage of a Quantity

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

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9. 9.

   $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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10. 10.

    $108 is shared in the ratio 1 : 5. Find each share.

    Formula:Dividing in a Ratio

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

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11. 11.

    Solve for x: 4x + 16 = 36.

    Formula:Solving a Linear Equation

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

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12. 12.

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

    Formula:Area of a Square

    $A = s^2$

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13. 13.

    A bag has 30 equally likely marbles, of which 12 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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14. 14.

    A rectangle is 21 cm long and 15 cm wide. Find its area.

    Formula:Area of a Rectangle

    $A = l \times w$

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15. 15.

    A right-angled triangle has legs of 4 cm and 9 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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16. 16.

    A triangle has a base of 10 cm and a height of 27 cm. Find its area.

    Formula:Area of a Triangle

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

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17. 17.

    A circle has a radius of 22 cm. Find its area. (Use π ≈ 3.14159)

    Formula:Area of a Circle

    $A = \pi r^2$

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18. 18.

    $93 is shared in the ratio 1 : 2. 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 bag has 17 equally likely marbles, of which 16 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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20. 20.

    What is 20% of 460?

    Formula:Percentage of a Quantity

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

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