Mongolia · Grade 11 · Practice Sheet 40

1. 1.

   A cylinder has radius 2 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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2. 2.

   Find the population standard deviation of: 4, 10, 5, 17, 15 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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3. 3.

   A population of 5,600 grows 3% per year. Find its size after 5 years (nearest whole number).

   Formula:Exponential Growth

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

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4. 4.

   A force of 28 N moves an object 28 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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5. 5.

   A cone has base radius 5 cm and height 5 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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6. 6.

   Find the population standard deviation of: 17, 14, 12, 9, 7 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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7. 7.

   A triangle has sides a = 13 cm and b = 7 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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8. 8.

   An object has mass 151.8 g and volume 46 cm³. Find its density.

   Formula:Density

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

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9. 9.

   A device runs at 162 V drawing 0.9 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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10. 10.

    Find the momentum of a 35 kg object moving at 29 m/s.

    Formula:Momentum

    $p = mv$

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11. 11.

    A force of 23 N moves an object 30 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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12. 12.

    A current of 2.6 A flows through a 58 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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13. 13.

    In a triangle, a = 10, b = 6 and the included angle C = 50°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

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14. 14.

    A triangle has sides a = 16 cm and b = 13 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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15. 15.

    An object has mass 160.6 g and volume 22 cm³. Find its density.

    Formula:Density

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

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16. 16.

    Two masses 8,300 kg and 730 kg are 17 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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17. 17.

    Find the gravitational potential energy of a 38 kg object raised 40 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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18. 18.

    A device runs at 33 V drawing 1.7 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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19. 19.

    Find the force needed to accelerate a 50 kg mass at 7.6 m/s².

    Formula:Newton's Second Law

    $F = ma$

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20. 20.

    An object has mass 210 g and volume 35 cm³. Find its density.

    Formula:Density

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

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