Kenya · Grade 11 · Practice Sheet 30

1. 1.

   Find the population standard deviation of: 4, 4, 11, 9, 2 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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2. 2.

   A force of 105 N moves an object 29 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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3. 3.

   A device runs at 104 V drawing 3.8 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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4. 4.

   A wave has frequency 121 Hz and wavelength 1.28 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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5. 5.

   Find the population standard deviation of: 3, 15, 16, 5, 15 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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6. 6.

   Find the force needed to accelerate a 55 kg mass at 5.4 m/s².

   Formula:Newton's Second Law

   $F = ma$

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7. 7.

   A 28 kg object moves at 2 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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8. 8.

   A right-angled triangle has legs of 3 cm and 7 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

   $c = \sqrt{a^2 + b^2}$

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9. 9.

   A wave has frequency 331 Hz and wavelength 2.28 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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10. 10.

    A triangle has sides a = 5 cm and b = 5 cm with an included angle C = 45°. 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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11. 11.

    Find the gravitational potential energy of a 30 kg object raised 5 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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12. 12.

    An object with initial velocity 7 m/s accelerates at 1.9 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.

    Find the population standard deviation of: 7, 14, 12, 3, 19 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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14. 14.

    A force of 307 N acts on an area of 5.3 m². Find the pressure.

    Formula:Pressure

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

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15. 15.

    A cone has base radius 3 cm and height 9 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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16. 16.

    Find the sum of the first 6 terms of a geometric series with first term a = 1 and common ratio r = 4.

    Formula:Sum of a Geometric Series

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

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17. 17.

    Find the momentum of a 14 kg object moving at 21 m/s.

    Formula:Momentum

    $p = mv$

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18. 18.

    A force of 91 N moves an object 4 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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19. 19.

    A right-angled triangle has legs of 8 cm and 6 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

    $c = \sqrt{a^2 + b^2}$

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20. 20.

    A force of 430 N acts on an area of 8.7 m². Find the pressure.

    Formula:Pressure

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

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