Nepal · Class 11 · Practice Sheet 44

1. 1.

   An object has mass 148.5 g and volume 33 cm³. Find its density.

   Formula:Density

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

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2. 2.

   A force of 109 N moves an object 6 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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3. 3.

   An object has mass 128.1 g and volume 21 cm³. Find its density.

   Formula:Density

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

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4. 4.

   Rs 1,000 is invested at 3% compound interest per annum for 2 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 population of 8,500 grows 10% per year. Find its size after 8 years (nearest whole number).

   Formula:Exponential Growth

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

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6. 6.

   Find the population standard deviation of: 12, 9, 18, 20, 18 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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7. 7.

   Find the momentum of a 5 kg object moving at 13 m/s.

   Formula:Momentum

   $p = mv$

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8. 8.

   In a triangle, a = 9, b = 14 and the included angle C = 100°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

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9. 9.

   Find the momentum of a 6 kg object moving at 16 m/s.

   Formula:Momentum

   $p = mv$

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10. 10.

    A cylinder has radius 7 cm and height 23 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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11. 11.

    A wave has frequency 471 Hz and wavelength 1.51 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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12. 12.

    Find the sum of the first 16 terms of an arithmetic series with first term a = 7 and common difference d = 4.

    Formula:Sum of an Arithmetic Series

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

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13. 13.

    A cylinder has radius 11 cm and height 14 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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14. 14.

    Find the sum of the first 19 terms of an arithmetic series with first term a = 10 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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15. 15.

    A triangle has sides a = 20 cm and b = 10 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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16. 16.

    Find the force needed to accelerate a 58 kg mass at 7.4 m/s².

    Formula:Newton's Second Law

    $F = ma$

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17. 17.

    A wave has frequency 498 Hz and wavelength 2.8 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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18. 18.

    An object has mass 46.2 g and volume 11 cm³. Find its density.

    Formula:Density

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

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19. 19.

    A 7 kg object moves at 9 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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20. 20.

    Find the volume of a sphere of radius 8 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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