Pakistan · Class 11 · Practice Sheet 12

1. 1.

   Solve using the quadratic formula: x² − 3x − 4 = 0.

   Formula:Quadratic Formula

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

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2. 2.

   Find the force needed to accelerate a 24 kg mass at 7.3 m/s².

   Formula:Newton's Second Law

   $F = ma$

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3. 3.

   An object with initial velocity 8 m/s accelerates at 2.2 m/s² for 4 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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4. 4.

   A force of 24 N moves an object 39 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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5. 5.

   A current of 1.5 A flows through a 28 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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6. 6.

   Find the population standard deviation of: 14, 18, 19, 15, 5 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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7. 7.

   Solve using the quadratic formula: x² − 7x + 10 = 0.

   Formula:Quadratic Formula

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

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8. 8.

   A 15 kg object moves at 3 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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9. 9.

   Find the force needed to accelerate a 21 kg mass at 6 m/s².

   Formula:Newton's Second Law

   $F = ma$

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10. 10.

    An object with initial velocity 11 m/s accelerates at 1.1 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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11. 11.

    Find the sum of the first 8 terms of a geometric series with first term a = 3 and common ratio r = 2.

    Formula:Sum of a Geometric Series

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

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12. 12.

    A cylinder has radius 7 cm and height 12 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 458 N acts on an area of 0.6 m². Find the pressure.

    Formula:Pressure

    $P = \dfrac{F}{A}$

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14. 14.

    A cylinder has radius 4 cm and height 19 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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15. 15.

    Find the sum of the first 11 terms of an arithmetic series with first term a = 4 and common difference d = 5.

    Formula:Sum of an Arithmetic Series

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

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16. 16.

    A cylinder has radius 14 cm and height 13 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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17. 17.

    A wave has frequency 32 Hz and wavelength 1.09 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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18. 18.

    An object with initial velocity 7 m/s accelerates at 3.7 m/s² for 8 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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19. 19.

    A device runs at 190 V drawing 8.3 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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20. 20.

    A 26 kg object moves at 10 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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