Austria · Klasse 12 · Practice Sheet 31

1. 1.

   A current of 6.8 A flows through a 60 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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2. 2.

   Find the force needed to accelerate a 30 kg mass at 4.7 m/s².

   Formula:Newton's Second Law

   $F = ma$

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3. 3.

   Find the sum of the first 8 terms of a geometric series with first term a = 3 and common ratio r = 4.

   Formula:Sum of a Geometric Series

   $S_n = \dfrac{a(r^{n} - 1)}{r - 1}$

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4. 4.

   A force of 241 N acts on an area of 7.6 m². Find the pressure.

   Formula:Pressure

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

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5. 5.

   Find the momentum of a 59 kg object moving at 21 m/s.

   Formula:Momentum

   $p = mv$

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6. 6.

   A force of 57 N moves an object 21 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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7. 7.

   A force of 413 N acts on an area of 0.9 m². Find the pressure.

   Formula:Pressure

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

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8. 8.

   Find the sum of the first 5 terms of a geometric series with first term a = 6 and common ratio r = 2.

   Formula:Sum of a Geometric Series

   $S_n = \dfrac{a(r^{n} - 1)}{r - 1}$

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9. 9.

   A wave has frequency 346 Hz and wavelength 4.2 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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10. 10.

    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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11. 11.

    Two masses 7,500 kg and 640 kg are 6 m apart. Find the gravitational force between them. (G = 6.674×10⁻¹¹)

    Formula:Newton’s Law of Gravitation

    $F = G\dfrac{m_1 m_2}{r^2}$

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12. 12.

    A population of 6,800 grows 5% per year. Find its size after 6 years (nearest whole number).

    Formula:Exponential Growth

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

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13. 13.

    A 2 kg object moves at 21 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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14. 14.

    Solve using the quadratic formula: x² − 5x + 0 = 0.

    Formula:Quadratic Formula

    $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

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15. 15.

    Find the volume of a sphere of radius 9 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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16. 16.

    Find the force needed to accelerate a 25 kg mass at 5.6 m/s².

    Formula:Newton's Second Law

    $F = ma$

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17. 17.

    A triangle has sides a = 11 cm and b = 11 cm with an included angle C = 120°. 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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18. 18.

    A wave has frequency 552 Hz and wavelength 3.81 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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19. 19.

    Find the sum of the first 16 terms of an arithmetic series with first term a = 11 and common difference d = 4.

    Formula:Sum of an Arithmetic Series

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

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20. 20.

    A wave has frequency 652 Hz and wavelength 0.88 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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