Sri Lanka · Grade 12 · Practice Sheet 27

1. 1.

   In a triangle, a = 5, b = 16 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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2. 2.

   Find the population standard deviation of: 18, 17, 6, 16, 20 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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3. 3.

   Two masses 4,900 kg and 120 kg are 3 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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4. 4.

   In a triangle, a = 18, b = 7 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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5. 5.

   A current of 3 A flows through a 37 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 7 terms of a geometric series with first term a = 3 and common ratio r = 3.

   Formula:Sum of a Geometric Series

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

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7. 7.

   Solve using the quadratic formula: x² − 2x − 15 = 0.

   Formula:Quadratic Formula

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

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8. 8.

   Find the force needed to accelerate a 30 kg mass at 8.2 m/s².

   Formula:Newton's Second Law

   $F = ma$

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9. 9.

   A force of 296 N acts on an area of 2.8 m². Find the pressure.

   Formula:Pressure

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

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10. 10.

    Rs 3,100 is invested at 8% compound interest per annum for 4 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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11. 11.

    An object with initial velocity 1 m/s accelerates at 3.7 m/s² for 9 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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12. 12.

    A device runs at 198 V drawing 3.4 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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13. 13.

    Find the momentum of a 26 kg object moving at 21 m/s.

    Formula:Momentum

    $p = mv$

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14. 14.

    A device runs at 206 V drawing 2.8 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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15. 15.

    A current of 6.2 A flows through a 36 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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16. 16.

    Find the sum of the first 3 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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17. 17.

    Find the momentum of a 51 kg object moving at 28 m/s.

    Formula:Momentum

    $p = mv$

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18. 18.

    A body starts at 12 m/s and accelerates at 5.6 m/s² for 3 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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19. 19.

    Solve using the quadratic formula: x² − 4x − 5 = 0.

    Formula:Quadratic Formula

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

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20. 20.

    A force of 83 N moves an object 7 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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