New Zealand · Year 8 · Practice Sheet 33

1. 1.

   A current of 6.9 A flows through a 13 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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2. 2.

   A bag has 10 equally likely marbles, of which 2 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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3. 3.

   A value changes from 199 to 42. 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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4. 4.

   A triangle has a base of 40 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 car travels 651 km in 7 hours. Find its average speed.

   Formula:Speed

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

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6. 6.

   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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7. 7.

   A force of 47 N acts on an area of 8.1 m². Find the pressure.

   Formula:Pressure

   $P = \dfrac{F}{A}$

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8. 8.

   A train moves at 78 km/h for 5.6 hours. How far does it travel?

   Formula:Distance from Speed & Time

   $d = v \times t$

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9. 9.

   Find the mean (average) of these numbers: 63, 84, 73, 59, 37.

   Formula:Arithmetic Mean

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

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10. 10.

    A bag has 17 equally likely marbles, of which 13 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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11. 11.

    A car travels 204 km in 6 hours. Find its average speed.

    Formula:Speed

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

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12. 12.

    A bag has 9 equally likely marbles, of which 5 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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13. 13.

    Find the mean (average) of these numbers: 53, 13, 85, 52.

    Formula:Arithmetic Mean

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

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14. 14.

    What is 15% of 100?

    Formula:Percentage of a Quantity

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

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15. 15.

    $55 is shared in the ratio 3 : 2. Find each share.

    Formula:Dividing in a Ratio

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

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16. 16.

    A current of 5.6 A flows through a 42 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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17. 17.

    A right-angled triangle has legs of 20 cm and 18 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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18. 18.

    Solve for x: 4x + 10 = 54.

    Formula:Solving a Linear Equation

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

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19. 19.

    A bag has 24 equally likely marbles, of which 6 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.

    Solve for x: 9x + 2 = 101.

    Formula:Solving a Linear Equation

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

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