Portugal · Ano 12 · Practice Sheet 46

1. 1.

   In a triangle, a = 15, b = 5 and the included angle C = 110°. 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 wave has frequency 625 Hz and wavelength 3.89 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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3. 3.

   A device runs at 140 V drawing 7.5 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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4. 4.

   Find the momentum of a 53 kg object moving at 19 m/s.

   Formula:Momentum

   $p = mv$

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5. 5.

   A cone has base radius 3 cm and height 8 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.

   A device runs at 126 V drawing 6.8 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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7. 7.

   Find the momentum of a 60 kg object moving at 7 m/s.

   Formula:Momentum

   $p = mv$

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8. 8.

   A wave has frequency 708 Hz and wavelength 2.53 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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9. 9.

   A force of 61 N acts on an area of 1.6 m². Find the pressure.

   Formula:Pressure

   $P = \dfrac{F}{A}$

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10. 10.

    Find the population standard deviation of: 13, 9, 14, 5, 20 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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11. 11.

    Solve using the quadratic formula: x² − 4x − 5 = 0.

    Formula:Quadratic Formula

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

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12. 12.

    Find the force needed to accelerate a 45 kg mass at 6.9 m/s².

    Formula:Newton's Second Law

    $F = ma$

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13. 13.

    A cone has base radius 11 cm and height 19 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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14. 14.

    A device runs at 135 V drawing 5.9 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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15. 15.

    Find the gravitational potential energy of a 27 kg object raised 27 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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16. 16.

    A 27 kg object moves at 25 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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17. 17.

    Find the gravitational potential energy of a 33 kg object raised 30 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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18. 18.

    A 3 kg object moves at 7 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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19. 19.

    Solve using the quadratic formula: x² − 9x + 20 = 0.

    Formula:Quadratic Formula

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

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20. 20.

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