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Communication Systems Maths Practice

This resource covers topics such as linear functions, reciprocal functions, function transformations, metric prefixes, and simultaneous equations. Learn to work with quantities and functions algebraically and graphically. Develop skills in writing and graphing equations of lines, substitution in linear equations, and solving simultaneous equations. Use the provided resources to practice and improve your mathematical abilities in communication systems. Click to start your math practice today!

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Communication Systems Maths Practice

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  1. Communication Systems Maths Practice Check your knowledge and practice your skills on: Scientific notation and metric prefixes Linear equations Function notation and transformations Simultaneous equations

  2. Quick Guide • Work through this guide in Present mode • Review the maths learning outcomes on the next slide. • Click the links to move between slides. • The sample Q’s are a guide only. If you need help, notes, looking at the solutions and working back, or a lot of thinking, to answer the Q’s correctly - then you should definitely do the practice

  3. Resources used so far • MathBeth worksheet 1 • MathBeth worksheet 2

  4. Students will know Students will be able to • Linear functions may be of the form y=mx + c or may be written as ky + cx = d • Reciprocal functions are of the form y=k/x • The shape and features of reciprocal functions • Function notation • Functions transformations (translation both up and down; reflection in x-axis, y-axis, and x=y?; dilation (stretching) and compression (squeezing) • The solution to a pair of simultaneous linear equations is the point of intersection of the two lines: • Use technology to construct and interpret graphs of linear functions • Substitute values into and solve reciprocal functions • Work with quantities, quantity symbols, unit names, unit symbols and metric prefixes • Work with function notation and identify function transformations • Work with measurements involving metric prefixes and convert them to standard units • Algebraically and graphically solve pairs of simultaneous equations with 2 variables and 2 unknowns Click to start

  5. Slope

  6. Linear equations Can you write the equation of a line if you are given its graph? (click for solutions to all 3 lines)Click to start Yes - all over it!!! Red line y = 2x + 5 Blue line y= ½x + 3 Green line y = 2 Click here I think I might need to practice Click here

  7. Equations of lines from graphs • MathBeth worksheet 1 • MathBeth worksheet 2 • Khan academy - equation from graph 4 or 5 practice Q’s • Khan academy - equation of line from 2 points 4 or 5 practice Q’s

  8. Linear equations Can you graph a line given its equation?Click to start Sketch the following lines: • y=x-2 • 4y+2x=8 • x=2 (click for graphs to all 3 lines) Yes - all over it!!! I think I need to check and practice

  9. Linear equations Can you substitute into and rearrange linear equations to find values? Click to start Yes - all over it!!! If y = ⅓(x - 7) • Find y when x is 2 • Find x when y is 2 Click here y=- 5/3 x=13 I think I might need to practice Click here

  10. Linear equations Can you find the equation of a line from 2 points Yes - all over it!!! Current and voltage are measured electrical circuit I think I need to check and practice

  11. Linear equations Can you write the equation of a line if you are given its graph?Click to start Yes - all over it!!! I think I need to check and practice

  12. Kirchoff’s Voltage Law Sum of voltages around a circuit loop = 0 Vbattery - Vresistor= 0 as Vresistor=I*R = 180*I Vbattery -180*I = 0 Vbattery I Vresistor

  13. Kirchhoff’s Current Law The sum of currents entering a junction (or node) are equal to the sum of currents leaving the junction. In the example: I1 = I2 + I3

  14. Kirchoff’s Voltage Law Loop 1 Starting at the battery negative terminal. Vbattery - VR1 - VR3 = 0 6 - I1*R1 - (I1- I2)R3 = 0 6 - 5I1 - 2(I1 - I2 ) = 0 6 - 5I1 - 2I1 + 2I2 = 0 7I1 - 2I2 = 6 (equation 1) Loop 2 VR2 - VR3 = 0 5I2 - 2(I1- I2)= 0 5I2 - 2I1 + 2I2 = 0 - 2I1 + 7I2 = 0 (equation 2) Vbattery -180*I = 0 6 V I2 I R2 I1 R3 R1 The current in this branch is I1- I2

  15. Solving simultaneous equations We have 2 equations and two unknowns I1and I2 7I1 - 2I2 = 6 (equation 1) - 2I1 + 7I2 = 0 (equation 2) add 2(eqn 1) to 7 (eqn 2) (to cancel the I1 terms) 14I1 - 4I2 - 14I1 + 49I2 = 2*6 + 7*0 -4I2 + 49I2 = 12 45I2 = 12 I2 =12/45 A I2 = 4/15 A = 0.27 A To find I1 sub I2 = 4/15 A into eqn 1 or eqn 2 - 2I1 + 7 (4/15) = 0 2I1 = 28/15 I1 = 14/15 A = 0.93 A Branch current = I1- I2 = (14/15) - (4/15) = 11/15 A = 0.73 A

  16. Let’s Solve Simultaneous Equations -8x-10y = 24 Equation 1 6x+5y = 2 Equation 2 12x+10y = 4 Double Equation 2 4x+0y= 28 Add the equations together x = 28/4 = 7 Solve for x 5y = 2-6x = 2-6*7 Solve for y y=-40/5 = -9

  17. Solving simultaneous equations Solving simultaneous equations algebraically is not the only way…... DESMOS Activity To gain a better understanding of simultaneous equations try this: Link

  18. A Challenge Insert SPEC/METH Challenge. Introduction to Matrices: Link

  19. Finding equations of lines What will be the population of Sydney in 2030? Popn. 1.4 1.2 1.0 How many pieces of information are needed to uniquely determine a line? Two. Typically the information available is: • Two points the line passes through Between 2011 and 2016 the population of Sydney increased from 4.4 to 4.8 million • The slope of the line and a point it passes through The population of Sydney hit 4.8 million in 2016, an increase of 80,000 per year since 2011. (2018, 1.4) (2011, 1.2) 2011 2018 (Year)

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