Germany · Klasse 12 · Practice Sheet 28

1. 1.

   Solve using the quadratic formula: x² + 1x + 0 = 0.

   Formula:Quadratic Formula

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

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2. 2.

   €1,600 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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3. 3.

   A current of 6.5 A flows through a 60 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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4. 4.

   An object with initial velocity 1 m/s accelerates at 2.7 m/s² for 4 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

   $s = ut + \tfrac{1}{2}at^2$

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5. 5.

   A body starts at 20 m/s and accelerates at 3.3 m/s² for 2 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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6. 6.

   A wave has frequency 749 Hz and wavelength 0.24 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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7. 7.

   An object with initial velocity 3 m/s accelerates at 2.8 m/s² for 4 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

   $s = ut + \tfrac{1}{2}at^2$

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8. 8.

   Two masses 4,800 kg and 310 kg are 16 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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9. 9.

   Find the sum of the first 7 terms of an arithmetic series with first term a = 6 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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10. 10.

    Find the sum of the first 4 terms of a geometric series with first term a = 6 and common ratio r = 3.

    Formula:Sum of a Geometric Series

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

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11. 11.

    A force of 38 N moves an object 23 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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12. 12.

    €500 is invested at 3% 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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13. 13.

    A force of 251 N acts on an area of 8 m². Find the pressure.

    Formula:Pressure

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

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14. 14.

    Find the sum of the first 19 terms of an arithmetic series with first term a = 6 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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15. 15.

    A device runs at 208 V drawing 8.4 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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16. 16.

    A body starts at 9 m/s and accelerates at 3.4 m/s² for 2 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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17. 17.

    A cone has base radius 8 cm and height 17 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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18. 18.

    A wave has frequency 862 Hz and wavelength 0.6 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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19. 19.

    Find the population standard deviation of: 5, 2, 18, 5, 5 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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20. 20.

    Find the momentum of a 60 kg object moving at 8 m/s.

    Formula:Momentum

    $p = mv$

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