Bangladesh · Class 11 · Practice Sheet 44

1. 1.

   In a triangle, a = 17, b = 15 and the included angle C = 70°. 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.

   A 22 kg object moves at 13 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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3. 3.

   Two masses 8,900 kg and 620 kg are 8 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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4. 4.

   Find the momentum of a 5 kg object moving at 22 m/s.

   Formula:Momentum

   $p = mv$

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5. 5.

   In a triangle, a = 16, b = 13 and the included angle C = 80°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

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6. 6.

   Find the population standard deviation of: 10, 16, 19, 15, 3 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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7. 7.

   A right-angled triangle has legs of 12 cm and 6 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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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.

   A current of 1.4 A flows through a 16 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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10. 10.

    A device runs at 171 V drawing 6.6 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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11. 11.

    Two masses 6,000 kg and 820 kg are 5 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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12. 12.

    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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13. 13.

    A right-angled triangle has legs of 9 cm and 8 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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14. 14.

    A triangle has sides a = 9 cm and b = 19 cm with an included angle C = 60°. 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.

    A device runs at 233 V drawing 2.3 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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16. 16.

    Solve using the quadratic formula: x² − 5x + 6 = 0.

    Formula:Quadratic Formula

    $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

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17. 17.

    A population of 8,700 grows 2% per year. Find its size after 7 years (nearest whole number).

    Formula:Exponential Growth

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

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18. 18.

    A 30 kg object moves at 19 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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19. 19.

    In a triangle, a = 15, b = 14 and the included angle C = 70°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

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20. 20.

    Find the force needed to accelerate a 56 kg mass at 4.8 m/s².

    Formula:Newton's Second Law

    $F = ma$

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