New Zealand · Year 8 · Practice Sheet 48

1. 1.

   A circle has a radius of 16 cm. Find its area. (Use π ≈ 3.14159)

   Formula:Area of a Circle

   $A = \pi r^2$

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2. 2.

   Find the mean (average) of these numbers: 27, 31, 55, 38.

   Formula:Arithmetic Mean

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

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3. 3.

   Find the circumference of a circle whose radius is 8 m. (Use π ≈ 3.14159)

   Formula:Circumference of a Circle

   $C = 2\pi r$

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4. 4.

   $3,000 is invested at 3% 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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5. 5.

   A bag has 29 equally likely marbles, of which 19 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.

   A value changes from 96 to 223. 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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7. 7.

   A bag has 25 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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8. 8.

   A car travels 290 km in 5 hours. Find its average speed.

   Formula:Speed

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

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9. 9.

   A current of 0.6 A flows through a 60 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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10. 10.

    What is 10% of 370?

    Formula:Percentage of a Quantity

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

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11. 11.

    $4,400 is invested at 5% simple interest per year for 5 years. Find the interest earned.

    Formula:Simple Interest

    $I = \dfrac{P \times r \times t}{100}$

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12. 12.

    A right-angled triangle has legs of 15 cm and 18 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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13. 13.

    Solve for x: 8x + 13 = 61.

    Formula:Solving a Linear Equation

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

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14. 14.

    A car travels 522 km in 6 hours. Find its average speed.

    Formula:Speed

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

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15. 15.

    A train moves at 80 km/h for 1.5 hours. How far does it travel?

    Formula:Distance from Speed & Time

    $d = v \times t$

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16. 16.

    A force of 290 N acts on an area of 5.3 m². Find the pressure.

    Formula:Pressure

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

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17. 17.

    A right-angled triangle has legs of 12 cm and 8 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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18. 18.

    A circle has a radius of 21 cm. Find its area. (Use π ≈ 3.14159)

    Formula:Area of a Circle

    $A = \pi r^2$

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19. 19.

    A car travels 126 km in 3 hours. Find its average speed.

    Formula:Speed

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

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20. 20.

    A cylinder has radius 10 cm and height 18 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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