South Korea · Grade 11 · Practice Sheet 45

1. 1.

   Find the population standard deviation of: 20, 17, 14, 11, 12 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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2. 2.

   A current of 1.2 A flows through a 35 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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3. 3.

   A wave has frequency 450 Hz and wavelength 2.08 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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4. 4.

   A triangle has sides a = 17 cm and b = 12 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.

   Find the sum of the first 20 terms of an arithmetic series with first term a = 10 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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6. 6.

   A triangle has sides a = 7 cm and b = 18 cm with an included angle C = 90°. 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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7. 7.

   A cone has base radius 5 cm and height 22 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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8. 8.

   Two masses 7,600 kg and 780 kg are 13 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.

   An object has mass 56.4 g and volume 12 cm³. Find its density.

   Formula:Density

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

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10. 10.

    A triangle has sides a = 9 cm and b = 6 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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11. 11.

    In a triangle, a = 11, b = 11 and the included angle C = 80°. 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 device runs at 238 V drawing 3.8 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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13. 13.

    Find the gravitational potential energy of a 31 kg object raised 2 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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14. 14.

    A device runs at 198 V drawing 8.5 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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15. 15.

    Solve using the quadratic formula: x² + 7x + 12 = 0.

    Formula:Quadratic Formula

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

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16. 16.

    In a triangle, a = 5, b = 17 and the included angle C = 50°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

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17. 17.

    A current of 2.7 A flows through a 26 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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18. 18.

    Find the force needed to accelerate a 16 kg mass at 3.9 m/s².

    Formula:Newton's Second Law

    $F = ma$

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19. 19.

    A device runs at 37 V drawing 1.7 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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20. 20.

    Find the momentum of a 19 kg object moving at 25 m/s.

    Formula:Momentum

    $p = mv$

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