Mongolia · Grade 12 · Practice Sheet 30

1. 1.

   Find the population standard deviation of: 14, 4, 7, 5, 16 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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2. 2.

   Find the momentum of a 48 kg object moving at 25 m/s.

   Formula:Momentum

   $p = mv$

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3. 3.

   Find the sum of the first 8 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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4. 4.

   A wave has frequency 602 Hz and wavelength 3.51 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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5. 5.

   A current of 3.4 A flows through a 55 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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6. 6.

   Find the sum of the first 3 terms of a geometric series with first term a = 7 and common ratio r = 4.

   Formula:Sum of a Geometric Series

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

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7. 7.

   A triangle has sides a = 17 cm and b = 6 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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8. 8.

   In a triangle, a = 11, b = 13 and the included angle C = 70°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

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9. 9.

   Find the force needed to accelerate a 58 kg mass at 8.2 m/s².

   Formula:Newton's Second Law

   $F = ma$

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10. 10.

    A wave has frequency 326 Hz and wavelength 2.81 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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11. 11.

    Two masses 3,800 kg and 200 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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12. 12.

    A wave has frequency 429 Hz and wavelength 1.58 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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13. 13.

    A 29 kg object moves at 7 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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14. 14.

    A device runs at 58 V drawing 0.9 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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15. 15.

    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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16. 16.

    Find the sum of the first 3 terms of a geometric series with first term a = 7 and common ratio r = 4.

    Formula:Sum of a Geometric Series

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

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17. 17.

    A current of 1.2 A flows through a 33 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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18. 18.

    A force of 486 N acts on an area of 2.9 m². Find the pressure.

    Formula:Pressure

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

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19. 19.

    A triangle has sides a = 5 cm and b = 13 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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20. 20.

    A device runs at 196 V drawing 7.4 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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