Colombia · Grado 12 · Practice Sheet 24

1. 1.

   Find the population standard deviation of: 20, 12, 9, 7, 4 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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2. 2.

   A cone has base radius 3 cm and height 6 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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3. 3.

   A wave has frequency 79 Hz and wavelength 4.22 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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4. 4.

   Find the population standard deviation of: 19, 11, 13, 8, 13 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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5. 5.

   A wave has frequency 502 Hz and wavelength 2.61 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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6. 6.

   Find the population standard deviation of: 3, 2, 17, 12, 15 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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7. 7.

   A wave has frequency 517 Hz and wavelength 0.82 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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8. 8.

   A force of 42 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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9. 9.

   A 12 kg object moves at 19 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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10. 10.

    A current of 1.3 A flows through a 46 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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11. 11.

    An object with initial velocity 1 m/s accelerates at 2.7 m/s² for 5 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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12. 12.

    $3,200 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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13. 13.

    Find the sum of the first 3 terms of a geometric series with first term a = 2 and common ratio r = 4.

    Formula:Sum of a Geometric Series

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

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14. 14.

    Two masses 5,700 kg and 240 kg are 7 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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15. 15.

    Find the force needed to accelerate a 50 kg mass at 1.9 m/s².

    Formula:Newton's Second Law

    $F = ma$

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16. 16.

    Find the gravitational potential energy of a 21 kg object raised 29 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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17. 17.

    Find the force needed to accelerate a 10 kg mass at 2.1 m/s².

    Formula:Newton's Second Law

    $F = ma$

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18. 18.

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

    Formula:Quadratic Formula

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

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19. 19.

    Find the volume of a sphere of radius 7 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

    $V = \tfrac{4}{3} \pi r^3$

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20. 20.

    Find the population standard deviation of: 19, 3, 6, 10, 14 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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