New Zealand · Year 7 · Practice Sheet 34

1. 1.

   A car travels 210 km in 7 hours. Find its average speed.

   Formula:Speed

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

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2. 2.

   A right-angled triangle has legs of 9 cm and 10 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 24 equally likely marbles, of which 1 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 triangle has a base of 22 cm and a height of 21 cm. Find its area.

   Formula:Area of a Triangle

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

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5. 5.

   A rectangle is 33 cm long and 28 cm wide. Find its area.

   Formula:Area of a Rectangle

   $A = l \times w$

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6. 6.

   Find the circumference of a circle whose radius is 28 m. (Use π ≈ 3.14159)

   Formula:Circumference of a Circle

   $C = 2\pi r$

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7. 7.

   Find the mean (average) of these numbers: 65, 16, 93, 32, 95, 52.

   Formula:Arithmetic Mean

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

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8. 8.

   A rectangle is 26 cm long and 10 cm wide. Find its area.

   Formula:Area of a Rectangle

   $A = l \times w$

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9. 9.

   A value changes from 20 to 163. 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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10. 10.

    Find the perimeter of a rectangle measuring 8 m by 4 m.

    Formula:Perimeter of a Rectangle

    $P = 2(l + w)$

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11. 11.

    Solve for x: 2x + 14 = 20.

    Formula:Solving a Linear Equation

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

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12. 12.

    A rectangle is 37 cm long and 14 cm wide. Find its area.

    Formula:Area of a Rectangle

    $A = l \times w$

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13. 13.

    Solve for x: 8x + 17 = 41.

    Formula:Solving a Linear Equation

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

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14. 14.

    A train moves at 42 km/h for 1.9 hours. How far does it travel?

    Formula:Distance from Speed & Time

    $d = v \times t$

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15. 15.

    A rectangle is 25 cm long and 24 cm wide. Find its area.

    Formula:Area of a Rectangle

    $A = l \times w$

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16. 16.

    A bag has 27 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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17. 17.

    A right-angled triangle has legs of 12 cm and 13 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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18. 18.

    A triangle has a base of 26 cm and a height of 20 cm. Find its area.

    Formula:Area of a Triangle

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

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19. 19.

    Find the perimeter of a rectangle measuring 29 m by 8 m.

    Formula:Perimeter of a Rectangle

    $P = 2(l + w)$

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20. 20.

    A right-angled triangle has legs of 9 cm and 8 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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