France · Classe 9 · Practice Sheet 12

1. 1.

   A bag has 22 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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2. 2.

   A force of 44 N moves an object 35 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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3. 3.

   A wave has frequency 242 Hz and wavelength 3.55 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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4. 4.

   Find the force needed to accelerate a 3 kg mass at 7.7 m/s².

   Formula:Newton's Second Law

   $F = ma$

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5. 5.

   An object has mass 180.6 g and volume 21 cm³. Find its density.

   Formula:Density

   $\rho = \dfrac{m}{V}$

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6. 6.

   A car travels 258 km in 6 hours. Find its average speed.

   Formula:Speed

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

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7. 7.

   A device runs at 6 V drawing 1.5 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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8. 8.

   A wave has frequency 674 Hz and wavelength 2.06 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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9. 9.

   A circle has a radius of 9 cm. Find its area. (Use π ≈ 3.14159)

   Formula:Area of a Circle

   $A = \pi r^2$

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10. 10.

    Find the momentum of a 25 kg object moving at 17 m/s.

    Formula:Momentum

    $p = mv$

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11. 11.

    A force of 202 N acts on an area of 9.9 m². Find the pressure.

    Formula:Pressure

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

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12. 12.

    A device runs at 25 V drawing 5.3 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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13. 13.

    A value changes from 33 to 176. 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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14. 14.

    Find the momentum of a 52 kg object moving at 17 m/s.

    Formula:Momentum

    $p = mv$

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15. 15.

    A value changes from 88 to 53. 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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16. 16.

    €3,300 is invested at 3% compound interest per annum for 3 years. Find the final amount (to 2 d.p.).

    Formula:Compound Interest

    $A = P\left(1 + \dfrac{r}{100}\right)^{t}$

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17. 17.

    A cone has base radius 10 cm and height 13 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

    $V = \tfrac{1}{3} \pi r^2 h$

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18. 18.

    A right-angled triangle has legs of 5 cm and 19 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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19. 19.

    Find the force needed to accelerate a 32 kg mass at 5.2 m/s².

    Formula:Newton's Second Law

    $F = ma$

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20. 20.

    Solve for x: 4x + 13 = 57.

    Formula:Solving a Linear Equation

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

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