India · Class 12 · Practice Sheet 15

1. 1.

   Find the sum of the first 20 terms of an arithmetic series with first term a = 9 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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2. 2.

   A population of 7,700 grows 3% per year. Find its size after 6 years (nearest whole number).

   Formula:Exponential Growth

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

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3. 3.

   A wave has frequency 337 Hz and wavelength 1.32 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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4. 4.

   A body starts at 15 m/s and accelerates at 4.9 m/s² for 7 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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5. 5.

   A force of 98 N moves an object 18 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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6. 6.

   A triangle has sides a = 6 cm and b = 5 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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7. 7.

   A 11 kg object moves at 21 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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8. 8.

   Find the momentum of a 28 kg object moving at 3 m/s.

   Formula:Momentum

   $p = mv$

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9. 9.

   A device runs at 19 V drawing 9.5 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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10. 10.

    In a triangle, a = 10, b = 7 and the included angle C = 40°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

    $c = \sqrt{a^2 + b^2 - 2ab\cos C}$

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11. 11.

    Find the sum of the first 14 terms of an arithmetic series with first term a = 10 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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12. 12.

    An object with initial velocity 7 m/s accelerates at 2.8 m/s² for 10 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

    $s = ut + \tfrac{1}{2}at^2$

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13. 13.

    A force of 12 N moves an object 28 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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14. 14.

    Find the gravitational potential energy of a 3 kg object raised 36 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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15. 15.

    Find the force needed to accelerate a 47 kg mass at 6.7 m/s².

    Formula:Newton's Second Law

    $F = ma$

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16. 16.

    Find the sum of the first 12 terms of an arithmetic series with first term a = 5 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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17. 17.

    Solve using the quadratic formula: x² + 5x + 6 = 0.

    Formula:Quadratic Formula

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

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18. 18.

    Two masses 7,300 kg and 200 kg are 9 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 a geometric series with first term a = 3 and common ratio r = 3.

    Formula:Sum of a Geometric Series

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

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20. 20.

    A wave has frequency 43 Hz and wavelength 4.86 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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