Germany · Klasse 11 · Practice Sheet 46

1. 1.

   A device runs at 170 V drawing 2.8 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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2. 2.

   Solve using the quadratic formula: x² + 4x + 0 = 0.

   Formula:Quadratic Formula

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

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3. 3.

   Find the momentum of a 32 kg object moving at 16 m/s.

   Formula:Momentum

   $p = mv$

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4. 4.

   Find the population standard deviation of: 18, 8, 6, 20, 8 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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5. 5.

   Find the force needed to accelerate a 27 kg mass at 2 m/s².

   Formula:Newton's Second Law

   $F = ma$

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6. 6.

   Find the gravitational potential energy of a 27 kg object raised 10 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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7. 7.

   A current of 0.6 A flows through a 28 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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8. 8.

   A 25 kg object moves at 11 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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9. 9.

   A device runs at 167 V drawing 5.9 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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10. 10.

    Find the population standard deviation of: 18, 13, 15, 9, 6 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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11. 11.

    In a triangle, a = 8, b = 8 and the included angle C = 100°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

    $c = \sqrt{a^2 + b^2 - 2ab\cos C}$

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12. 12.

    A body starts at 5 m/s and accelerates at 2 m/s² for 8 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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13. 13.

    Find the sum of the first 7 terms of a geometric series with first term a = 5 and common ratio r = 4.

    Formula:Sum of a Geometric Series

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

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14. 14.

    A cone has base radius 7 cm and height 16 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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15. 15.

    Find the gravitational potential energy of a 50 kg object raised 16 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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16. 16.

    A wave has frequency 187 Hz and wavelength 1.41 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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17. 17.

    Find the momentum of a 35 kg object moving at 4 m/s.

    Formula:Momentum

    $p = mv$

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18. 18.

    Two masses 3,900 kg and 360 kg are 19 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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19. 19.

    A force of 106 N moves an object 19 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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20. 20.

    €2,800 is invested at 6% compound interest per annum for 2 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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