Nepal · Class 11 · Practice Sheet 7

1. 1.

   In a triangle, a = 7, b = 18 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 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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3. 3.

   An object has mass 62.4 g and volume 26 cm³. Find its density.

   Formula:Density

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

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4. 4.

   A wave has frequency 315 Hz and wavelength 3.91 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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5. 5.

   A force of 216 N acts on an area of 9.2 m². Find the pressure.

   Formula:Pressure

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

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6. 6.

   Find the sum of the first 10 terms of an arithmetic series with first term a = 2 and common difference d = 2.

   Formula:Sum of an Arithmetic Series

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

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7. 7.

   An object has mass 102.4 g and volume 16 cm³. Find its density.

   Formula:Density

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

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8. 8.

   A triangle has sides a = 10 cm and b = 10 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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9. 9.

   Find the population standard deviation of: 12, 10, 2, 12, 10 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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10. 10.

    A 32 kg object moves at 2 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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11. 11.

    A triangle has sides a = 7 cm and b = 16 cm with an included angle C = 30°. 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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12. 12.

    Find the force needed to accelerate a 27 kg mass at 6.5 m/s².

    Formula:Newton's Second Law

    $F = ma$

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13. 13.

    Find the momentum of a 40 kg object moving at 17 m/s.

    Formula:Momentum

    $p = mv$

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14. 14.

    In a triangle, a = 7, b = 8 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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15. 15.

    Find the volume of a sphere of radius 6 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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16. 16.

    Find the gravitational potential energy of a 22 kg object raised 11 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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17. 17.

    A 2 kg object moves at 2 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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18. 18.

    A force of 458 N acts on an area of 6 m². Find the pressure.

    Formula:Pressure

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

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19. 19.

    Find the force needed to accelerate a 56 kg mass at 2.6 m/s².

    Formula:Newton's Second Law

    $F = ma$

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20. 20.

    A device runs at 236 V drawing 2.9 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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