Ecuador · Grado 12 · Practice Sheet 24

1. 1.

   Find the sum of the first 4 terms of a geometric series with first term a = 5 and common ratio r = 2.

   Formula:Sum of a Geometric Series

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

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2. 2.

   A 34 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.

   Solve using the quadratic formula: x² − 1x − 6 = 0.

   Formula:Quadratic Formula

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

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4. 4.

   Find the momentum of a 2 kg object moving at 11 m/s.

   Formula:Momentum

   $p = mv$

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5. 5.

   A body starts at 15 m/s and accelerates at 5.2 m/s² for 5 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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6. 6.

   Solve using the quadratic formula: x² + 0x − 16 = 0.

   Formula:Quadratic Formula

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

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7. 7.

   A triangle has sides a = 16 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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8. 8.

   Find the force needed to accelerate a 30 kg mass at 4.1 m/s².

   Formula:Newton's Second Law

   $F = ma$

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9. 9.

   A force of 6 N moves an object 8 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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10. 10.

    Solve using the quadratic formula: x² + 2x − 8 = 0.

    Formula:Quadratic Formula

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

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11. 11.

    Find the gravitational potential energy of a 5 kg object raised 28 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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12. 12.

    Two masses 5,800 kg and 100 kg are 7 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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13. 13.

    Find the gravitational potential energy of a 21 kg object raised 8 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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14. 14.

    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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15. 15.

    Find the force needed to accelerate a 47 kg mass at 4.7 m/s².

    Formula:Newton's Second Law

    $F = ma$

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16. 16.

    A wave has frequency 275 Hz and wavelength 4.83 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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17. 17.

    Find the population standard deviation of: 9, 7, 20, 17, 14 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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18. 18.

    A current of 0.6 A flows through a 33 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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19. 19.

    A force of 137 N acts on an area of 2.7 m². Find the pressure.

    Formula:Pressure

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

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20. 20.

    A current of 0.6 A flows through a 43 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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