Austria · Klasse 12 · Practice Sheet 33

1. 1.

   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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2. 2.

   A force of 104 N moves an object 33 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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3. 3.

   A wave has frequency 737 Hz and wavelength 0.54 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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4. 4.

   Find the sum of the first 6 terms of a geometric series with first term a = 2 and common ratio r = 3.

   Formula:Sum of a Geometric Series

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

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5. 5.

   Find the gravitational potential energy of a 23 kg object raised 36 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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6. 6.

   A device runs at 174 V drawing 3.1 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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7. 7.

   A wave has frequency 150 Hz and wavelength 2.2 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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8. 8.

   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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9. 9.

   A device runs at 125 V drawing 6.3 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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10. 10.

    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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11. 11.

    A device runs at 186 V drawing 3.5 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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12. 12.

    Find the force needed to accelerate a 54 kg mass at 0.7 m/s².

    Formula:Newton's Second Law

    $F = ma$

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13. 13.

    A 6 kg object moves at 4 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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14. 14.

    A triangle has sides a = 14 cm and b = 10 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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15. 15.

    Two masses 3,700 kg and 760 kg are 11 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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16. 16.

    €1,400 is invested at 4% compound interest per annum for 5 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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17. 17.

    In a triangle, a = 5, b = 11 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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18. 18.

    A wave has frequency 807 Hz and wavelength 3.06 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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19. 19.

    A force of 103 N moves an object 20 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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20. 20.

    Find the sum of the first 20 terms of an arithmetic series with first term a = 7 and common difference d = 7.

    Formula:Sum of an Arithmetic Series

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

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