Austria · Klasse 11 · Practice Sheet 47

1. 1.

   A right-angled triangle has legs of 19 cm and 14 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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2. 2.

   Find the gravitational potential energy of a 31 kg object raised 29 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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3. 3.

   A device runs at 176 V drawing 3.7 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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4. 4.

   €1,600 is invested at 6% 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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5. 5.

   A current of 3.8 A flows through a 7 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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6. 6.

   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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7. 7.

   A triangle has sides a = 8 cm and b = 11 cm with an included angle C = 45°. 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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8. 8.

   Find the population standard deviation of: 9, 4, 11, 18, 4 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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9. 9.

   A device runs at 180 V drawing 9.4 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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10. 10.

    An object has mass 170.5 g and volume 31 cm³. Find its density.

    Formula:Density

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

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11. 11.

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

    Formula:Sum of a Geometric Series

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

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12. 12.

    Find the population standard deviation of: 11, 16, 6, 5, 6 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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13. 13.

    Find the momentum of a 59 kg object moving at 11 m/s.

    Formula:Momentum

    $p = mv$

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14. 14.

    Find the population standard deviation of: 19, 16, 2, 20, 18 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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15. 15.

    A population of 2,100 grows 5% per year. Find its size after 8 years (nearest whole number).

    Formula:Exponential Growth

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

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16. 16.

    Find the sum of the first 18 terms of an arithmetic series with first term a = 6 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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17. 17.

    A wave has frequency 285 Hz and wavelength 4.06 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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18. 18.

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

    Formula:Sum of a Geometric Series

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

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19. 19.

    A force of 103 N acts on an area of 6.3 m². Find the pressure.

    Formula:Pressure

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

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20. 20.

    Find the momentum of a 44 kg object moving at 18 m/s.

    Formula:Momentum

    $p = mv$

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