Pakistan · Class 11 · Practice Sheet 13

1. 1.

   Find the population standard deviation of: 19, 14, 18, 3, 5 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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2. 2.

   ₨2,700 is invested at 3% compound interest per annum for 5 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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3. 3.

   A body starts at 4 m/s and accelerates at 5.3 m/s² for 4 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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4. 4.

   Find the momentum of a 29 kg object moving at 7 m/s.

   Formula:Momentum

   $p = mv$

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5. 5.

   In a triangle, a = 18, b = 13 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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6. 6.

   A force of 41 N moves an object 34 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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7. 7.

   A current of 3.7 A flows through a 26 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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8. 8.

   A cone has base radius 12 cm and height 19 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

   $V = \tfrac{1}{3} \pi r^2 h$

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9. 9.

   Find the population standard deviation of: 11, 14, 6, 9, 8 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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10. 10.

    A population of 8,300 grows 5% per year. Find its size after 5 years (nearest whole number).

    Formula:Exponential Growth

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

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11. 11.

    Solve using the quadratic formula: x² − 9x + 18 = 0.

    Formula:Quadratic Formula

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

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12. 12.

    A cylinder has radius 13 cm and height 7 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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13. 13.

    A force of 79 N moves an object 25 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 force needed to accelerate a 27 kg mass at 5.2 m/s².

    Formula:Newton's Second Law

    $F = ma$

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15. 15.

    Find the momentum of a 20 kg object moving at 23 m/s.

    Formula:Momentum

    $p = mv$

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16. 16.

    A body starts at 17 m/s and accelerates at 2.4 m/s² for 4 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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17. 17.

    A wave has frequency 258 Hz and wavelength 1.73 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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18. 18.

    A force of 53 N moves an object 15 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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19. 19.

    Find the gravitational potential energy of a 16 kg object raised 25 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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20. 20.

    A wave has frequency 47 Hz and wavelength 1.19 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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