Germany · Klasse 11 · Practice Sheet 16

1. 1.

   A force of 301 N acts on an area of 5.9 m². Find the pressure.

   Formula:Pressure

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

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2. 2.

   A right-angled triangle has legs of 18 cm and 20 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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3. 3.

   Find the sum of the first 4 terms of a geometric series with first term a = 5 and common ratio r = 2.

   Formula:Sum of a Geometric Series

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

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4. 4.

   Find the momentum of a 41 kg object moving at 24 m/s.

   Formula:Momentum

   $p = mv$

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5. 5.

   Find the population standard deviation of: 3, 18, 6, 20, 13 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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6. 6.

   A cone has base radius 7 cm and height 12 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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7. 7.

   A force of 94 N moves an object 39 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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8. 8.

   A current of 1.5 A flows through a 27 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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9. 9.

   Find the sum of the first 10 terms of an arithmetic series with first term a = 8 and common difference d = 2.

   Formula:Sum of an Arithmetic Series

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

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10. 10.

    Find the population standard deviation of: 5, 17, 15, 5, 16 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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11. 11.

    Find the gravitational potential energy of a 25 kg object raised 38 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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12. 12.

    A population of 3,500 grows 2% per year. Find its size after 7 years (nearest whole number).

    Formula:Exponential Growth

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

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13. 13.

    Find the sum of the first 8 terms of an arithmetic series with first term a = 5 and common difference d = 3.

    Formula:Sum of an Arithmetic Series

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

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14. 14.

    Find the population standard deviation of: 6, 9, 11, 4, 19 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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15. 15.

    Find the sum of the first 7 terms of a geometric series with first term a = 1 and common ratio r = 4.

    Formula:Sum of a Geometric Series

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

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16. 16.

    An object has mass 120 g and volume 40 cm³. Find its density.

    Formula:Density

    $\rho = \dfrac{m}{V}$

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17. 17.

    Find the gravitational potential energy of a 30 kg object raised 14 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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18. 18.

    A device runs at 164 V drawing 1.3 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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19. 19.

    A wave has frequency 298 Hz and wavelength 2.32 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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20. 20.

    Two masses 6,400 kg and 830 kg are 5 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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