Bangladesh · Class 11 · Practice Sheet 36

1. 1.

   A cylinder has radius 13 cm and height 21 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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2. 2.

   Find the sum of the first 5 terms of a geometric series with first term a = 4 and common ratio r = 4.

   Formula:Sum of a Geometric Series

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

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3. 3.

   A force of 118 N moves an object 35 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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4. 4.

   A triangle has sides a = 9 cm and b = 17 cm with an included angle C = 90°. 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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5. 5.

   Find the momentum of a 45 kg object moving at 8 m/s.

   Formula:Momentum

   $p = mv$

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6. 6.

   An object has mass 102.6 g and volume 38 cm³. Find its density.

   Formula:Density

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

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7. 7.

   An object with initial velocity 0 m/s accelerates at 2.8 m/s² for 6 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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8. 8.

   In a triangle, a = 17, b = 8 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 force needed to accelerate a 30 kg mass at 0.8 m/s².

   Formula:Newton's Second Law

   $F = ma$

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10. 10.

    Find the gravitational potential energy of a 24 kg object raised 26 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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11. 11.

    A device runs at 17 V drawing 4.6 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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12. 12.

    A population of 7,600 grows 8% per year. Find its size after 4 years (nearest whole number).

    Formula:Exponential Growth

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

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13. 13.

    Find the population standard deviation of: 19, 18, 14, 14, 20 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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14. 14.

    A right-angled triangle has legs of 14 cm and 6 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

    $c = \sqrt{a^2 + b^2}$

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15. 15.

    An object with initial velocity 11 m/s accelerates at 2.3 m/s² for 8 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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16. 16.

    A population of 5,600 grows 2% per year. Find its size after 5 years (nearest whole number).

    Formula:Exponential Growth

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

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17. 17.

    A body starts at 18 m/s and accelerates at 2.3 m/s² for 12 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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18. 18.

    A wave has frequency 229 Hz and wavelength 1.28 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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19. 19.

    A cone has base radius 2 cm and height 10 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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20. 20.

    A body starts at 8 m/s and accelerates at 4.7 m/s² for 5 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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