Ecuador · Grado 12 · Practice Sheet 39

1. 1.

   Find the gravitational potential energy of a 41 kg object raised 3 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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2. 2.

   Solve using the quadratic formula: x² + 1x − 12 = 0.

   Formula:Quadratic Formula

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

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3. 3.

   An object with initial velocity 1 m/s accelerates at 1.1 m/s² for 4 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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4. 4.

   Two masses 7,400 kg and 420 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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5. 5.

   Find the population standard deviation of: 15, 6, 13, 20, 15 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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6. 6.

   Find the volume of a sphere of radius 12 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

   $V = \tfrac{4}{3} \pi r^3$

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7. 7.

   In a triangle, a = 10, b = 5 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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8. 8.

   Two masses 8,500 kg and 570 kg are 20 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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9. 9.

   A force of 241 N acts on an area of 5.1 m². Find the pressure.

   Formula:Pressure

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

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10. 10.

    A current of 5.4 A flows through a 44 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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11. 11.

    A force of 88 N moves an object 26 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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12. 12.

    A triangle has sides a = 7 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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13. 13.

    A current of 2.7 A flows through a 60 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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14. 14.

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

    A device runs at 75 V drawing 0.6 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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16. 16.

    Find the gravitational potential energy of a 25 kg object raised 30 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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17. 17.

    A device runs at 38 V drawing 0.4 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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18. 18.

    In a triangle, a = 13, b = 7 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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19. 19.

    A cone has base radius 6 cm and height 10 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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20. 20.

    Find the momentum of a 4 kg object moving at 29 m/s.

    Formula:Momentum

    $p = mv$

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