Australia · Year 12 · Practice Sheet 9

1. 1.

   Find the sum of the first 15 terms of an arithmetic series with first term a = 6 and common difference d = 5.

   Formula:Sum of an Arithmetic Series

   $S_n = \tfrac{n}{2}\left(2a + (n-1)d\right)$

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2. 2.

   A current of 1.7 A flows through a 36 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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3. 3.

   A population of 6,100 grows 8% per year. Find its size after 2 years (nearest whole number).

   Formula:Exponential Growth

   $N = N_0 (1 + r)^{t}$

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4. 4.

   A wave has frequency 168 Hz and wavelength 3.32 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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5. 5.

   A triangle has sides a = 11 cm and b = 6 cm with an included angle C = 90°. Find its area (to 2 d.p.).

   Formula:Area of a Triangle (Sine Rule)

   $A = \tfrac{1}{2} ab\sin C$

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6. 6.

   A device runs at 72 V drawing 5.7 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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7. 7.

   A current of 6.7 A flows through a 12 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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8. 8.

   Find the momentum of a 59 kg object moving at 27 m/s.

   Formula:Momentum

   $p = mv$

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9. 9.

   A force of 490 N acts on an area of 5.7 m². Find the pressure.

   Formula:Pressure

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

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10. 10.

    A wave has frequency 848 Hz and wavelength 4.79 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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11. 11.

    Find the gravitational potential energy of a 43 kg object raised 10 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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12. 12.

    A wave has frequency 476 Hz and wavelength 2.17 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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13. 13.

    A force of 334 N acts on an area of 9.6 m². Find the pressure.

    Formula:Pressure

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

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14. 14.

    Find the momentum of a 28 kg object moving at 29 m/s.

    Formula:Momentum

    $p = mv$

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15. 15.

    Find the volume of a sphere of radius 5 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

    $V = \tfrac{4}{3} \pi r^3$

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16. 16.

    A force of 144 N acts on an area of 6.2 m². Find the pressure.

    Formula:Pressure

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

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17. 17.

    A 24 kg object moves at 16 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

    $KE = \tfrac{1}{2} m v^2$

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18. 18.

    Find the momentum of a 34 kg object moving at 7 m/s.

    Formula:Momentum

    $p = mv$

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19. 19.

    A cone has base radius 7 cm and height 20 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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20. 20.

    A 3 kg object moves at 9 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

    $KE = \tfrac{1}{2} m v^2$

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