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Communication Systems Maths Practice

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. Quick Guide. Work through this guide in Present mode

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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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