Pakistan · Class 11 · Practice Sheet 25

1. 1.

   Find the sum of the first 14 terms of an arithmetic series with first term a = 5 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.

   A wave has frequency 591 Hz and wavelength 0.85 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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3. 3.

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

   Formula:Quadratic Formula

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

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4. 4.

   ₨500 is invested at 4% compound interest per annum for 5 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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5. 5.

   A body starts at 1 m/s and accelerates at 1.1 m/s² for 10 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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6. 6.

   Two masses 3,700 kg and 340 kg are 20 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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7. 7.

   A device runs at 156 V drawing 0.6 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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8. 8.

   A cone has base radius 10 cm and height 21 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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9. 9.

   A force of 157 N acts on an area of 3.5 m². Find the pressure.

   Formula:Pressure

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

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10. 10.

    Find the sum of the first 5 terms of a geometric series with first term a = 5 and common ratio r = 2.

    Formula:Sum of a Geometric Series

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

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11. 11.

    A device runs at 59 V drawing 6 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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12. 12.

    A force of 69 N moves an object 3 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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13. 13.

    A population of 5,300 grows 5% per year. Find its size after 2 years (nearest whole number).

    Formula:Exponential Growth

    $N = N_0 (1 + r)^{t}$

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14. 14.

    Find the momentum of a 27 kg object moving at 28 m/s.

    Formula:Momentum

    $p = mv$

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15. 15.

    ₨4,000 is invested at 5% compound interest per annum for 3 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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16. 16.

    A current of 4.6 A flows through a 60 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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17. 17.

    An object has mass 142 g and volume 20 cm³. Find its density.

    Formula:Density

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

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18. 18.

    A 14 kg object moves at 18 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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19. 19.

    A device runs at 141 V drawing 0.5 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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20. 20.

    Find the momentum of a 50 kg object moving at 18 m/s.

    Formula:Momentum

    $p = mv$

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