New Zealand · Year 7 · Practice Sheet 25

1. 1.

   A value changes from 103 to 186. 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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2. 2.

   A right-angled triangle has legs of 19 cm and 6 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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3. 3.

   A bag has 21 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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4. 4.

   A car travels 268 km in 4 hours. Find its average speed.

   Formula:Speed

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

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5. 5.

   A bag has 10 equally likely marbles, of which 4 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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6. 6.

   Find the area of a square with side length 7 cm.

   Formula:Area of a Square

   $A = s^2$

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7. 7.

   A rectangle is 37 cm long and 9 cm wide. Find its area.

   Formula:Area of a Rectangle

   $A = l \times w$

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8. 8.

   A right-angled triangle has legs of 11 cm and 19 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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9. 9.

   One item costs $3.01. Find the total cost of 10 items.

   Formula:Total Cost

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

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10. 10.

    A rectangle is 31 cm long and 11 cm wide. Find its area.

    Formula:Area of a Rectangle

    $A = l \times w$

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11. 11.

    Solve for x: 4x + 14 = 42.

    Formula:Solving a Linear Equation

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

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12. 12.

    Find the circumference of a circle whose radius is 10 m. (Use π ≈ 3.14159)

    Formula:Circumference of a Circle

    $C = 2\pi r$

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13. 13.

    Find the perimeter of a rectangle measuring 29 m by 27 m.

    Formula:Perimeter of a Rectangle

    $P = 2(l + w)$

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14. 14.

    Convert 4.23 kilometres into metres.

    Formula:Metric Length Conversion

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

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15. 15.

    Find the area of a square with side length 14 cm.

    Formula:Area of a Square

    $A = s^2$

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16. 16.

    Find the circumference of a circle whose radius is 23 m. (Use π ≈ 3.14159)

    Formula:Circumference of a Circle

    $C = 2\pi r$

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17. 17.

    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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18. 18.

    Find the perimeter of a rectangle measuring 28 m by 4 m.

    Formula:Perimeter of a Rectangle

    $P = 2(l + w)$

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19. 19.

    Find the circumference of a circle whose radius is 6 m. (Use π ≈ 3.14159)

    Formula:Circumference of a Circle

    $C = 2\pi r$

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20. 20.

    Find the mean (average) of these numbers: 66, 19, 29, 30, 77, 55.

    Formula:Arithmetic Mean

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

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