United Arab Emirates · Grade 11 · Practice Sheet 12

1. 1.

   In a triangle, a = 7, b = 5 and the included angle C = 40°. 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 11 kg object moves at 14 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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3. 3.

   Two masses 3,400 kg and 660 kg are 12 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 sum of the first 6 terms of a geometric series with first term a = 8 and common ratio r = 4.

   Formula:Sum of a Geometric Series

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

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5. 5.

   Find the population standard deviation of: 13, 20, 4, 8, 12 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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6. 6.

   A device runs at 209 V drawing 9.5 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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7. 7.

   Find the gravitational potential energy of a 34 kg object raised 7 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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8. 8.

   A triangle has sides a = 17 cm and b = 12 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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9. 9.

   Find the sum of the first 9 terms of an arithmetic series with first term a = 7 and common difference d = 5.

   Formula:Sum of an Arithmetic Series

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

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10. 10.

    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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11. 11.

    An object has mass 102.2 g and volume 14 cm³. Find its density.

    Formula:Density

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

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12. 12.

    A force of 66 N moves an object 25 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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13. 13.

    Find the force needed to accelerate a 39 kg mass at 5.8 m/s².

    Formula:Newton's Second Law

    $F = ma$

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14. 14.

    A wave has frequency 416 Hz and wavelength 1.02 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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15. 15.

    A force of 21 N moves an object 39 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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16. 16.

    Find the momentum of a 47 kg object moving at 16 m/s.

    Formula:Momentum

    $p = mv$

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17. 17.

    A 26 kg object moves at 15 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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18. 18.

    A device runs at 81 V drawing 5.9 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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19. 19.

    A triangle has sides a = 7 cm and b = 13 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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20. 20.

    An object has mass 43.4 g and volume 31 cm³. Find its density.

    Formula:Density

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

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