Chile · Grado 11 · Practice Sheet 32

1. 1.

   Find the force needed to accelerate a 21 kg mass at 7.3 m/s².

   Formula:Newton's Second Law

   $F = ma$

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2. 2.

   A device runs at 191 V drawing 8.4 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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3. 3.

   Find the sum of the first 20 terms of an arithmetic series with first term a = 1 and common difference d = 7.

   Formula:Sum of an Arithmetic Series

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

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4. 4.

   A device runs at 113 V drawing 5.6 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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5. 5.

   A population of 5,700 grows 10% per year. Find its size after 8 years (nearest whole number).

   Formula:Exponential Growth

   $N = N_0 (1 + r)^{t}$

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6. 6.

   A device runs at 202 V drawing 7.9 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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7. 7.

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

   Formula:Sum of a Geometric Series

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

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8. 8.

   A 17 kg object moves at 18 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

   $KE = \tfrac{1}{2} m v^2$

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9. 9.

   Find the population standard deviation of: 18, 3, 11, 2, 5 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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10. 10.

    A wave has frequency 383 Hz and wavelength 0.92 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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11. 11.

    Find the population standard deviation of: 10, 6, 8, 6, 17 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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12. 12.

    A body starts at 19 m/s and accelerates at 5.1 m/s² for 3 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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13. 13.

    Find the population standard deviation of: 3, 17, 11, 19, 20 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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14. 14.

    Find the sum of the first 3 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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15. 15.

    Find the gravitational potential energy of a 7 kg object raised 21 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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16. 16.

    A cylinder has radius 5 cm and height 20 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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17. 17.

    Find the force needed to accelerate a 35 kg mass at 5.6 m/s².

    Formula:Newton's Second Law

    $F = ma$

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18. 18.

    Two masses 2,500 kg and 640 kg are 11 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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19. 19.

    Find the sum of the first 7 terms of an arithmetic series with first term a = 9 and common difference d = 1.

    Formula:Sum of an Arithmetic Series

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

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20. 20.

    A right-angled triangle has legs of 11 cm and 13 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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