Pakistan · Class 11 · Practice Sheet 49

1. 1.

   In a triangle, a = 7, b = 5 and the included angle C = 100°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

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2. 2.

   A force of 110 N moves an object 36 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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3. 3.

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

   Formula:Sum of a Geometric Series

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

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4. 4.

   ₨2,100 is invested at 5% compound interest per annum for 4 years. Find the final amount (to 2 d.p.).

   Formula:Compound Interest

   $A = P\left(1 + \dfrac{r}{100}\right)^{t}$

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5. 5.

   Find the sum of the first 8 terms of a geometric series with first term a = 5 and common ratio r = 2.

   Formula:Sum of a Geometric Series

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

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6. 6.

   Find the sum of the first 19 terms of an arithmetic series with first term a = 6 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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7. 7.

   A device runs at 194 V drawing 2.7 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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8. 8.

   A population of 6,900 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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9. 9.

   Find the force needed to accelerate a 21 kg mass at 4.9 m/s².

   Formula:Newton's Second Law

   $F = ma$

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10. 10.

    Find the momentum of a 11 kg object moving at 3 m/s.

    Formula:Momentum

    $p = mv$

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11. 11.

    A force of 45 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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12. 12.

    A device runs at 142 V drawing 0.7 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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13. 13.

    Find the momentum of a 44 kg object moving at 3 m/s.

    Formula:Momentum

    $p = mv$

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14. 14.

    In a triangle, a = 13, b = 12 and the included angle C = 50°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

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15. 15.

    A current of 4.4 A flows through a 59 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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16. 16.

    A wave has frequency 304 Hz and wavelength 3.62 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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17. 17.

    Find the gravitational potential energy of a 40 kg object raised 23 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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18. 18.

    A wave has frequency 121 Hz and wavelength 0.25 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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19. 19.

    A force of 48 N moves an object 21 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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20. 20.

    A device runs at 60 V drawing 9.9 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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