Chile · Grado 12 · Practice Sheet 37

1. 1.

   Find the gravitational potential energy of a 4 kg object raised 17 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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2. 2.

   A device runs at 69 V drawing 5.6 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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3. 3.

   Find the gravitational potential energy of a 18 kg object raised 7 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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4. 4.

   Solve using the quadratic formula: x² + 7x + 12 = 0.

   Formula:Quadratic Formula

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

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5. 5.

   A device runs at 142 V drawing 1.2 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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6. 6.

   Find the momentum of a 44 kg object moving at 8 m/s.

   Formula:Momentum

   $p = mv$

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7. 7.

   A device runs at 147 V drawing 8.5 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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8. 8.

   Find the population standard deviation of: 19, 13, 11, 12, 5 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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9. 9.

   Find the sum of the first 6 terms of a geometric series with first term a = 3 and common ratio r = 2.

   Formula:Sum of a Geometric Series

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

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10. 10.

    A force of 17 N moves an object 13 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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11. 11.

    Find the sum of the first 5 terms of an arithmetic series with first term a = 5 and common difference d = 2.

    Formula:Sum of an Arithmetic Series

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

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12. 12.

    Find the sum of the first 4 terms of a geometric series with first term a = 6 and common ratio r = 2.

    Formula:Sum of a Geometric Series

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

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13. 13.

    A wave has frequency 864 Hz and wavelength 3.85 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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14. 14.

    Find the force needed to accelerate a 37 kg mass at 6.5 m/s².

    Formula:Newton's Second Law

    $F = ma$

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15. 15.

    Solve using the quadratic formula: x² + 8x + 15 = 0.

    Formula:Quadratic Formula

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

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16. 16.

    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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17. 17.

    Two masses 8,000 kg and 450 kg are 18 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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18. 18.

    Find the sum of the first 4 terms of a geometric series with first term a = 1 and common ratio r = 3.

    Formula:Sum of a Geometric Series

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

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19. 19.

    Find the sum of the first 15 terms of an arithmetic series with first term a = 6 and common difference d = 6.

    Formula:Sum of an Arithmetic Series

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

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20. 20.

    Find the volume of a sphere of radius 11 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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