Argentina · Grado 12 · Practice Sheet 46

1. 1.

   In a triangle, a = 7, b = 9 and the included angle C = 60°. 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.

   Find the population standard deviation of: 3, 4, 8, 11, 19 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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3. 3.

   Find the gravitational potential energy of a 47 kg object raised 36 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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4. 4.

   A device runs at 130 V drawing 8.4 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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5. 5.

   Find the force needed to accelerate a 8 kg mass at 2.9 m/s².

   Formula:Newton's Second Law

   $F = ma$

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6. 6.

   Find the momentum of a 40 kg object moving at 28 m/s.

   Formula:Momentum

   $p = mv$

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7. 7.

   A 39 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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8. 8.

   Solve using the quadratic formula: x² + 3x − 10 = 0.

   Formula:Quadratic Formula

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

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9. 9.

   An object with initial velocity 4 m/s accelerates at 4.2 m/s² for 7 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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10. 10.

    A wave has frequency 457 Hz and wavelength 2.25 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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11. 11.

    A force of 92 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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12. 12.

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

    Formula:Quadratic Formula

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

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13. 13.

    A cone has base radius 4 cm and height 24 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.

    Find the population standard deviation of: 3, 14, 19, 14, 5 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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15. 15.

    Two masses 4,000 kg and 530 kg are 19 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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16. 16.

    A force of 342 N acts on an area of 5.6 m². Find the pressure.

    Formula:Pressure

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

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17. 17.

    A body starts at 5 m/s and accelerates at 3.5 m/s² for 5 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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18. 18.

    An object with initial velocity 2 m/s accelerates at 2.7 m/s² for 7 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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19. 19.

    Find the momentum of a 20 kg object moving at 15 m/s.

    Formula:Momentum

    $p = mv$

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20. 20.

    Find the force needed to accelerate a 55 kg mass at 6 m/s².

    Formula:Newton's Second Law

    $F = ma$

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