Nepal · Class 11 · Practice Sheet 48

1. 1.

   Find the sum of the first 7 terms of a geometric series with first term a = 2 and common ratio r = 2.

   Formula:Sum of a Geometric Series

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

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2. 2.

   A population of 3,900 grows 8% per year. Find its size after 8 years (nearest whole number).

   Formula:Exponential Growth

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

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3. 3.

   A wave has frequency 135 Hz and wavelength 1.81 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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4. 4.

   A body starts at 20 m/s and accelerates at 5.9 m/s² for 12 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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5. 5.

   A device runs at 114 V drawing 8.1 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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6. 6.

   A wave has frequency 49 Hz and wavelength 3.43 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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7. 7.

   A force of 44 N acts on an area of 2.2 m². Find the pressure.

   Formula:Pressure

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

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8. 8.

   A cylinder has radius 7 cm and height 16 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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9. 9.

   Find the sum of the first 7 terms of an arithmetic series with first term a = 5 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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10. 10.

    Find the force needed to accelerate a 25 kg mass at 8.4 m/s².

    Formula:Newton's Second Law

    $F = ma$

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11. 11.

    Find the gravitational potential energy of a 49 kg object raised 22 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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12. 12.

    A wave has frequency 629 Hz and wavelength 2.78 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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13. 13.

    An object has mass 39.1 g and volume 23 cm³. Find its density.

    Formula:Density

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

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14. 14.

    A current of 5.4 A flows through a 48 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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15. 15.

    Find the sum of the first 4 terms of a geometric series with first term a = 1 and common ratio r = 3.

    Formula:Sum of a Geometric Series

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

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16. 16.

    Find the population standard deviation of: 13, 17, 7, 9, 8 (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 8 m/s and accelerates at 1.7 m/s² for 6 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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18. 18.

    A device runs at 180 V drawing 7.6 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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19. 19.

    Find the volume of a sphere of radius 3 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

    $V = \tfrac{4}{3} \pi r^3$

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20. 20.

    A cone has base radius 12 cm and height 13 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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