Austria · Klasse 12 · Practice Sheet 5

1. 1.

   A wave has frequency 99 Hz and wavelength 3.58 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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2. 2.

   Two masses 4,300 kg and 850 kg are 17 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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3. 3.

   A population of 7,700 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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4. 4.

   A device runs at 156 V drawing 0.6 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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5. 5.

   €3,200 is invested at 5% 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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6. 6.

   A triangle has sides a = 6 cm and b = 14 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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7. 7.

   An object with initial velocity 15 m/s accelerates at 3 m/s² for 9 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

   $s = ut + \tfrac{1}{2}at^2$

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8. 8.

   Find the volume of a sphere of radius 2 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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9. 9.

   A wave has frequency 452 Hz and wavelength 2.14 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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10. 10.

    A force of 62 N moves an object 40 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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11. 11.

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

    Formula:Exponential Growth

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

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12. 12.

    Find the volume of a sphere of radius 10 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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13. 13.

    A device runs at 197 V drawing 8.3 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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14. 14.

    A current of 0.9 A flows through a 59 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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15. 15.

    Solve using the quadratic formula: x² − 1x − 12 = 0.

    Formula:Quadratic Formula

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

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16. 16.

    A force of 61 N moves an object 13 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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17. 17.

    A body starts at 3 m/s and accelerates at 5 m/s² for 11 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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18. 18.

    Find the sum of the first 13 terms of an arithmetic series with first term a = 3 and common difference d = 1.

    Formula:Sum of an Arithmetic Series

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

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19. 19.

    Find the gravitational potential energy of a 25 kg object raised 7 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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20. 20.

    A device runs at 212 V drawing 8 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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