New Zealand · Year 7 · Practice Sheet 1

1. 1.

   A right-angled triangle has legs of 14 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.

   A car travels 735 km in 7 hours. Find its average speed.

   Formula:Speed

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

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3. 3.

   Find the perimeter of a rectangle measuring 9 m by 13 m.

   Formula:Perimeter of a Rectangle

   $P = 2(l + w)$

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4. 4.

   Convert 4.09 kilometres into metres.

   Formula:Metric Length Conversion

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

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5. 5.

   Find the circumference of a circle whose radius is 27 m. (Use π ≈ 3.14159)

   Formula:Circumference of a Circle

   $C = 2\pi r$

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6. 6.

   Find the area of a square with side length 11 cm.

   Formula:Area of a Square

   $A = s^2$

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7. 7.

   $63 is shared in the ratio 4 : 3. 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 bag has 20 equally likely marbles, of which 3 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.

   Convert 8.18 kilometres into metres.

   Formula:Metric Length Conversion

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

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10. 10.

    Find 3/4 of 36.

    Formula:Fraction of a Quantity

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

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11. 11.

    $700 is invested at 6% 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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12. 12.

    One item costs $21.6. Find the total cost of 6 items.

    Formula:Total Cost

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

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13. 13.

    A car travels 160 km in 2 hours. Find its average speed.

    Formula:Speed

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

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14. 14.

    A value changes from 152 to 213. 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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15. 15.

    Solve for x: 7x + 8 = 43.

    Formula:Solving a Linear Equation

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

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16. 16.

    Find the mean (average) of these numbers: 57, 67, 25, 70, 57, 75.

    Formula:Arithmetic Mean

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

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17. 17.

    A bag has 15 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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18. 18.

    Find the perimeter of a rectangle measuring 17 m by 35 m.

    Formula:Perimeter of a Rectangle

    $P = 2(l + w)$

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19. 19.

    A train moves at 77 km/h for 2.7 hours. How far does it travel?

    Formula:Distance from Speed & Time

    $d = v \times t$

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20. 20.

    Find the perimeter of a rectangle measuring 25 m by 16 m.

    Formula:Perimeter of a Rectangle

    $P = 2(l + w)$

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