Sri Lanka · Grade 12 · Practice Sheet 25

1. 1.

   Find the sum of the first 20 terms of an arithmetic series with first term a = 8 and common difference d = 6.

   Formula:Sum of an Arithmetic Series

   $S_n = \tfrac{n}{2}\left(2a + (n-1)d\right)$

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2. 2.

   In a triangle, a = 12, b = 13 and the included angle C = 60°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

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3. 3.

   Find the momentum of a 31 kg object moving at 6 m/s.

   Formula:Momentum

   $p = mv$

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4. 4.

   A 3 kg object moves at 6 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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5. 5.

   An object with initial velocity 15 m/s accelerates at 1.3 m/s² for 5 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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6. 6.

   Find the population standard deviation of: 15, 10, 2, 4, 7 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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7. 7.

   A wave has frequency 848 Hz and wavelength 2.44 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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8. 8.

   Find the force needed to accelerate a 55 kg mass at 6.5 m/s².

   Formula:Newton's Second Law

   $F = ma$

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9. 9.

   Find the sum of the first 8 terms of an arithmetic series with first term a = 2 and common difference d = 1.

   Formula:Sum of an Arithmetic Series

   $S_n = \tfrac{n}{2}\left(2a + (n-1)d\right)$

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10. 10.

    A device runs at 205 V drawing 8.8 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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11. 11.

    Find the force needed to accelerate a 54 kg mass at 6.4 m/s².

    Formula:Newton's Second Law

    $F = ma$

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12. 12.

    A wave has frequency 236 Hz and wavelength 2.03 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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13. 13.

    Find the gravitational potential energy of a 48 kg object raised 37 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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14. 14.

    An object with initial velocity 6 m/s accelerates at 3.5 m/s² for 8 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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15. 15.

    A force of 265 N acts on an area of 1.6 m². Find the pressure.

    Formula:Pressure

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

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16. 16.

    Find the population standard deviation of: 15, 18, 5, 10, 13 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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17. 17.

    A body starts at 19 m/s and accelerates at 3.5 m/s² for 8 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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18. 18.

    A current of 7.2 A flows through a 41 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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19. 19.

    A device runs at 38 V drawing 6.5 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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20. 20.

    A triangle has sides a = 16 cm and b = 8 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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