Austria · Klasse 12 · Practice Sheet 6

1. 1.

   A force of 108 N moves an object 17 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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2. 2.

   €600 is invested at 6% compound interest per annum for 2 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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3. 3.

   A device runs at 137 V drawing 9.2 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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4. 4.

   Find the momentum of a 35 kg object moving at 30 m/s.

   Formula:Momentum

   $p = mv$

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5. 5.

   Find the force needed to accelerate a 8 kg mass at 5.9 m/s².

   Formula:Newton's Second Law

   $F = ma$

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6. 6.

   A triangle has sides a = 12 cm and b = 15 cm with an included angle C = 30°. 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.

   A population of 3,800 grows 3% per year. Find its size after 3 years (nearest whole number).

   Formula:Exponential Growth

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

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8. 8.

   A device runs at 107 V drawing 3.9 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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9. 9.

   A wave has frequency 22 Hz and wavelength 4.16 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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10. 10.

    A device runs at 239 V drawing 7.4 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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11. 11.

    Two masses 4,900 kg and 780 kg are 8 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 current of 5.1 A flows through a 51 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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13. 13.

    Find the sum of the first 9 terms of an arithmetic series with first term a = 1 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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14. 14.

    Solve using the quadratic formula: x² + 2x − 8 = 0.

    Formula:Quadratic Formula

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

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15. 15.

    Find the sum of the first 19 terms of an arithmetic series with first term a = 1 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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16. 16.

    In a triangle, a = 10, b = 8 and the included angle C = 50°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

    $c = \sqrt{a^2 + b^2 - 2ab\cos C}$

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17. 17.

    Solve using the quadratic formula: x² − 2x − 15 = 0.

    Formula:Quadratic Formula

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

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18. 18.

    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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19. 19.

    A body starts at 12 m/s and accelerates at 3.6 m/s² for 10 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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20. 20.

    In a triangle, a = 18, b = 8 and the included angle C = 60°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

    $c = \sqrt{a^2 + b^2 - 2ab\cos C}$

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