NCEA+Level+1+Graphs

=Graphs 4 Credits on the 14th of November 2011= =External AS91028 Level 1 Credits 4= =Mathematics 1.3 Investigate relationships between tables, equations and graphs= [] NCEA Level 1 Past Papers [] =Option Line 4 resources:= Fast track p. 46 to 68 (this includes exponential and parabola's which ontrack does not) New Zealand Mathematics: Chap 12 Linear Graphs; Chapter 14 Quadratics; Chapter 17 page 492 to 502. =Option Line 2 resources:= Ontrack page 46 to 58 Gamma page 97 to 130 NCEA Level 1 Graphs Video Lessons Coordinates: [] [] [] Graphs: Applet Graphs SL 3 ways Applet Pip Parabola

=Subject content= =Linear (Straight Line: ontrack page 46 to 58)= •Linear equations (there are no powers, eg y=3x+2) •Simultaneous linear equations (2 linear equations might have one point of intersection, be the same line, or have no common points) •Linear graphs (can you move between tables - graphs - equations, y=mx+c year 10 revision, m is the gradient, (0,c) is the y intercept.) •Linear patterns (start with a pattern, create a table of points, graph the points, work out the equation of the pattern) =Quadratic (Parabolas: Gamma page 113 onwards)= •Graphing parabolas (27th of September) •Quadratic equations (these equations produce parabolas when graphed) •Quadratic patterns (start with a pattern, create a table of points, graph the points, work out the equation of the pattern) =Exponential ([|Growth and decay])= •Exponential equations and graphs (26th of September) =Gradient (rate of change)= •Interpreting gradients (the gradient represents the rate of change, so in a distance-time graph, it represents speed for example Applet Graphs Gradient as Speed)

Video Lessons are created and uploaded as I teach each topic. These are for students who are absent (in mind or in body) at the time of the lesson. =NCEA Level 1 Graphs Video Lessons=

=We will go over year 10 work first= Year 10 Graphs media type="youtube" key="3wAjpMP5eyo" height="345" width="560" =Key tips= •Graphs will involve only linear, quadratic and simple exponential functions. •Features could include x and y intercepts, maxima and minima, axes of symmetry, domain and range, and gradients of straight lines (rates of change). •An understanding of transformations of graphs is expected. •Use a ruler for drawing line graphs. •Look carefully at the scales on each axis. When working out the gradient do not simply count squares – remember to check how many units each grid line represents first. •Know the difference between 'intercept' and 'intersect'. An intercept is a point where the graph crosses the axes. Intersect means cross or meet. •Parabolas should be smooth curves with a rounded turning point (vertex). •Show your working clearly in correct mathematical steps. Give a full sentence stating your answer. •Answer the question in the context that is given. Use commonsense to check your answer. •Reread the question to check that you have answered the question asked. •A graph may be made up of two different functions (piecewise graph). It could be made up of two lines, or part of a parabola and a line. •Attempt all questions as evidence from higher level questions may be used in awarding credit for a lower grade.

We have 3.5 weeks to cover this topic: it will be fast paced

23rd September: Gradient, revise linear graphs Applet Gradient 1 Applet Gradient 2 Applet Graph Linear Applet Graphs SL 3 ways Applet Graph Patterns

26th of September Draw the x and y axis and on it plot y=2^x; y=3^x; y=4^x and y=5^x What do you observe? Applet Graphs Exponential or Applet Graphs Exponential 2

27th of September Graphing parabolas Applet Graph Paraboloa Modelling and Applet Pip Parabola Modelling Translations Applet Graphs Parabola and Applet Pip Parabola Applet Graphs Parabola Gamma pg 113 Option Line 4: NZ MATHS page 492 "E" exponential functions - 100 mice example

3rd October Option Line 2: From [] I can do check list from [] Option Line 4: Working from New Zealand Mathematics Page 309 Ex 11H Formulae by Pattern (induction) Page 318 Ex 12A Understanding Graphs (piece wise) Page 337 Ex 12I Applications of Linear Graphs Second Differences - use these to find the equation of patterns

4th October Option Line 2 and 4: Revised that linear patterns have a constant difference, quadratic patterns have a constant 2nd difference, and exponential patterns have the same 1st and 2nd difference. Looked at the x and y intercepts. Set x=0 to find the y intercept. Set y=0 to find the x intercepts. Option Line 4: Completing the square to get the form y=(x-a)^2 + b so the vertex is easy to plot (a,b) Also talked about the parabola having symmetry, so the x value of the vertex can be found half way between the 2 x intercepts. Of course not all parabolas intersect with the x axis! I have uploaded reminder videos to NCEA Level 1 Graphs Video Lessons

5th October Applet Graphs Gradient as Speed Option Line 4: Text Book page 310 to 314 (patterns and algebra). Chapter 14 Quadratic Functions page 377 to 404.

6th October Option Line 4: media type="custom" key="10732486" Option Line 2:

7th October Applet Graphs Test Applet Graphs Test 2

=Term Four= -25th October: We talked about attention to details in marking schedules. For example if you have a pattern where n takes the value of 1,2,3... then it should be graphed as points, not joined up as a line. If you are graphing continuous data you must add the line. This attention to detail can be the difference between Achieved, Merit and Excellence. -In General. We have covered the content, and need to put our new knowledge into practise. The focus is on doing as many examples as possible, the past papers are the best way to prepare. There are no shortcuts, this is a time for working hard. Making study plans, setting goals and keeping on task. Marking schedules are vital in guiding our knowledge of what is required. NCEA Level 1 Past Papers

Extra for experts: Applet All Graphs From []

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