GAUTENG DEPARTMENT OF EDUCATION SENIOR SECONDARY INTERVENTION PROGRAMME MATHEMATICS GRADE 11 SESSION 20 (LEARNER NOTES)

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Barry Noah Green
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1 MATHEMATICAL MOELLING Learner Note: Mathematical modelling is the application of functions in the real world. ata is represented on a scatter plot and the trend of the data is modelled by a line or curve of best fit. SECTION A: TYPICAL EXAM QUESTIONS Question (5 minutes) The table below represents the number of people infected with a deadly new virus from the year 00 to 007. Year Number of infections (a) raw a scatter plot to represent this data. () (b) Explain whether a linear, quadratic or exponential curve would be a line or curve of best fit. () Page of 8

2 Question (5minutes) A parachutist jumps out of a helicopter and his height above ground level is estimated at various times after he opened his parachute. The following table gives the results of the observations where y measures his height above ground level in metres and t represents the time in seconds after he opened his parachute. t y (a) raw a scatter plot for the above information. () (b) escribe the curve of best fit. () (c) Use the scatter plot to estimate the height of the parachutist 5,5 seconds after he had opened his parachute. () Page of 8

3 Height above ground level (metres) SECTION B: SOLUTIONS AN HINTS Question (a) all points plotted correctly. () (b) Linear function answer Question (a) Scatter Plot of height above ground level SCATTER PLOT OF HEIGHT ABOVE vs time GROUN LEVEL VS TIME all points plotted correctly. () Time (seconds) (b) Exponential OR Qu answer Page 3 of 8

4 SECTION C: AITIONAL CONTENT NOTES Scatter plot diagrams Plotting data on a scatter plot diagram will show trends in the data. ata could follow a linear, quadratic or exponential trend. Linear Quadratic Exponential SECTION : HOMEWORK Question A motor company did research on how the speed of a car affects the fuel consumption of the vehicle. The following data was obtained: Speed in km/h Fuel consumption in l/00 km,5 0 8,4 9, 7,8 8,9 8,8 8,6 0, (a) Represent the data as a scatter plot. Page 4 of 8

5 Fuel consumption (l/00 km) Scatter plot of speed vs fuel consumption Speed (km/h) (b) Suggest whether a linear, quadratic or exponential function would best fit the dat () (c) What advice can the company give about the driving speed in order to keep the cost of fuel to a minimum? () SECTION E: SOLUTIONS TO SESSION 9 HOMEWORK (a) m AB m C y ( 4) ( x ( )) y 4 x y x m AB m C correct substitution into formula for equation of line yx (4) Page 5 of 8

6 (b) Equation of AB: Equation of C: y ( x 4) y x y x y x 3 x 3 x x 6 4x 4 5x 0 x y E(; ) (c) C( ; 4) E(; ) ( x; y) x 4 y and 4 x 4 4 y x 5 y 8 (5;8) 5 ( 4) 9 Now mac 3 4 ( ) 3 Equation of line required: y 8 3( x 5) y 8 3x5 y 3x 3 (d) x-intercept: 0 x x x (;0) Substitute (;0) into x y LHS x y 0 RHS (;0) lies on line AF y ( x 4) y x 3 3 x x x E(;) x 5 y 8 m AB m C correct substitution into formula for equation of line yx x Substitute (;0) LHS RHS (5) (6) Page 6 of 8

7 (a) ( 3) k ;3 ; k ;3 ; k 3 6 k k 4 (b) m m lines // AB C k ( 3) 3 3 k ( k 3) 5 k 6 k k m m lines (c) AB C k 3 5 k 3 0 k 3 0 k 3 m m lines // (d) AB BC k 3 ( 3) k 6 6 ( k) 6 k 8 k k 4 ( 3) k ;3 ; k 3 k 4 k ( 3) 3 3 k k 3 5 k 3 k 3 ( 3) k 4 Page 7 of 8

8 (e) C 5 And C ( 3) 3 k k k k k 0 k 6k 6 0 ( k8)( k ) k 8 or k C ( 3) 3 k k k 0 k 6k 6 0 ( k8)( k ) k 8 or k (5) The SSIP is supported by Page 8 of 8

Graphing and Writing Linear Equations Review 3.1, 3.3, & 4.4. Name: Date: Period:

Graphing and Writing Linear Equations Review.1,., 4.1-4. & 4.4 Algebra I Name: Date: Period: Quest Topics Section.1 linear versus nonlinear rewrite linear equations in standard form: Ax By C find and use