Austria · Klasse 12 · Practice Sheet 41

1. 1.

   A force of 252 N acts on an area of 0.9 m². Find the pressure.

   Formula:Pressure

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

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2. 2.

   A population of 6,700 grows 10% per year. Find its size after 2 years (nearest whole number).

   Formula:Exponential Growth

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

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3. 3.

   A device runs at 232 V drawing 6.5 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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4. 4.

   Solve using the quadratic formula: x² − 6x + 8 = 0.

   Formula:Quadratic Formula

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

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5. 5.

   Find the gravitational potential energy of a 3 kg object raised 35 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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6. 6.

   Find the momentum of a 39 kg object moving at 27 m/s.

   Formula:Momentum

   $p = mv$

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7. 7.

   A cone has base radius 5 cm and height 7 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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8. 8.

   Find the volume of a sphere of radius 8 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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9. 9.

   A force of 6 N moves an object 16 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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10. 10.

    A triangle has sides a = 5 cm and b = 18 cm with an included angle C = 45°. 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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11. 11.

    Find the force needed to accelerate a 14 kg mass at 1.8 m/s².

    Formula:Newton's Second Law

    $F = ma$

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12. 12.

    Find the gravitational potential energy of a 17 kg object raised 39 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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13. 13.

    A device runs at 119 V drawing 0.8 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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14. 14.

    Find the gravitational potential energy of a 36 kg object raised 25 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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15. 15.

    A 14 kg object moves at 18 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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16. 16.

    A wave has frequency 818 Hz and wavelength 2.37 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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17. 17.

    Find the gravitational potential energy of a 45 kg object raised 24 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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18. 18.

    Solve using the quadratic formula: x² + 5x + 6 = 0.

    Formula:Quadratic Formula

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

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19. 19.

    Find the sum of the first 16 terms of an arithmetic series with first term a = 3 and common difference d = 8.

    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 146 Hz and wavelength 1.12 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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