Austria · Klasse 11 · Practice Sheet 6

1. 1.

   Find the gravitational potential energy of a 15 kg object raised 10 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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2. 2.

   Find the sum of the first 7 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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3. 3.

   Find the momentum of a 35 kg object moving at 21 m/s.

   Formula:Momentum

   $p = mv$

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4. 4.

   A triangle has sides a = 7 cm and b = 8 cm with an included angle C = 60°. 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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5. 5.

   A population of 6,000 grows 3% per year. Find its size after 4 years (nearest whole number).

   Formula:Exponential Growth

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

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6. 6.

   Find the sum of the first 5 terms of an arithmetic series with first term a = 11 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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7. 7.

   A wave has frequency 883 Hz and wavelength 1.5 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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8. 8.

   Find the sum of the first 8 terms of an arithmetic series with first term a = 4 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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9. 9.

   A device runs at 23 V drawing 8.8 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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10. 10.

    Find the population standard deviation of: 20, 15, 3, 19, 20 (to 2 d.p.).

    Formula:Standard Deviation (Population)

    $\sigma = \sqrt{\dfrac{\sum (x - \bar{x})^2}{n}}$

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11. 11.

    A right-angled triangle has legs of 7 cm and 11 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

    $c = \sqrt{a^2 + b^2}$

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12. 12.

    Two masses 3,300 kg and 680 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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13. 13.

    Find the momentum of a 23 kg object moving at 26 m/s.

    Formula:Momentum

    $p = mv$

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14. 14.

    Two masses 3,500 kg and 770 kg are 20 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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15. 15.

    A force of 240 N acts on an area of 0.6 m². Find the pressure.

    Formula:Pressure

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

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16. 16.

    Find the force needed to accelerate a 3 kg mass at 3.6 m/s².

    Formula:Newton's Second Law

    $F = ma$

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17. 17.

    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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18. 18.

    A current of 3.2 A flows through a 42 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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19. 19.

    In a triangle, a = 7, 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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20. 20.

    Find the gravitational potential energy of a 42 kg object raised 26 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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