Peru · Grado 11 · Practice Sheet 8

1. 1.

   A force of 54 N moves an object 16 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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2. 2.

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

   Formula:Sum of a Geometric Series

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

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3. 3.

   A device runs at 17 V drawing 1.5 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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4. 4.

   Find the gravitational potential energy of a 23 kg object raised 35 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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5. 5.

   Find the momentum of a 38 kg object moving at 16 m/s.

   Formula:Momentum

   $p = mv$

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6. 6.

   A force of 29 N moves an object 17 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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7. 7.

   Two masses 7,900 kg and 150 kg are 4 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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8. 8.

   Solve using the quadratic formula: x² + 3x − 4 = 0.

   Formula:Quadratic Formula

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

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9. 9.

   Find the force needed to accelerate a 23 kg mass at 6.9 m/s².

   Formula:Newton's Second Law

   $F = ma$

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10. 10.

    A right-angled triangle has legs of 20 cm and 6 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

    $c = \sqrt{a^2 + b^2}$

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11. 11.

    A wave has frequency 25 Hz and wavelength 2.49 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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12. 12.

    Two masses 5,400 kg and 610 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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13. 13.

    A cone has base radius 7 cm and height 5 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 gravitational potential energy of a 22 kg object raised 20 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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15. 15.

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

    Formula:Sum of a Geometric Series

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

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16. 16.

    Find the population standard deviation of: 20, 6, 6, 15, 14 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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17. 17.

    In a triangle, a = 14, b = 17 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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18. 18.

    Find the sum of the first 8 terms of a geometric series with first term a = 1 and common ratio r = 2.

    Formula:Sum of a Geometric Series

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

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19. 19.

    A device runs at 62 V drawing 6.2 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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20. 20.

    Find the momentum of a 23 kg object moving at 24 m/s.

    Formula:Momentum

    $p = mv$

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