Bahrain · Grade 12 · Practice Sheet 14

1. 1.

   Find the sum of the first 20 terms of an arithmetic series with first term a = 9 and common difference d = 8.

   Formula:Sum of an Arithmetic Series

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

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2. 2.

   A force of 73 N moves an object 35 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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3. 3.

   A wave has frequency 601 Hz and wavelength 0.44 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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4. 4.

   Find the sum of the first 19 terms of an arithmetic series with first term a = 12 and common difference d = 4.

   Formula:Sum of an Arithmetic Series

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

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5. 5.

   A force of 27 N moves an object 33 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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6. 6.

   A population of 4,500 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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7. 7.

   Find the force needed to accelerate a 41 kg mass at 8.5 m/s².

   Formula:Newton's Second Law

   $F = ma$

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8. 8.

   Two masses 2,200 kg and 430 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.

   Find the force needed to accelerate a 14 kg mass at 6.5 m/s².

   Formula:Newton's Second Law

   $F = ma$

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10. 10.

    Find the sum of the first 5 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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11. 11.

    In a triangle, a = 16, b = 16 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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12. 12.

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

    Formula:Gravitational Potential Energy

    $PE = mgh$

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13. 13.

    A force of 106 N moves an object 23 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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14. 14.

    A population of 8,900 grows 5% per year. Find its size after 8 years (nearest whole number).

    Formula:Exponential Growth

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

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15. 15.

    A device runs at 184 V drawing 4.9 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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16. 16.

    Find the gravitational potential energy of a 26 kg object raised 39 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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17. 17.

    Two masses 6,700 kg and 500 kg are 14 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 force needed to accelerate a 51 kg mass at 8.8 m/s².

    Formula:Newton's Second Law

    $F = ma$

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19. 19.

    A device runs at 34 V drawing 4.2 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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20. 20.

    A wave has frequency 617 Hz and wavelength 4.14 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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