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# Exercises - Not covered in Syllabus

## Exercises - Not covered in Syllabus

1. [IEB, Nov. 2001, HG]
1. Sketch two curves which will enable you to solve |x-2||x|-1|x-2||x|-1 graphically.
2. Calculate the point(s) of intersection of the two curves, and hence, or otherwise, write down the solution set to the inequality above.
2. [IEB, Nov. 2002, HG] Evaluate without using a calculator: |2x-1|-|-5x||2x-1|-|-5x|    given that x=-1x=-1
3. [IEB, Nov. 2003, HG] In the figure below, two graphs are shown:
f(x)=ax2+bx+c and g(x)=|x+c|f(x)=ax2+bx+c and g(x)=|x+c|
(1)
x=-1x=-1 is the equation of the axis of symmetry of the parabola. ff contains the points (2; 0) and (4; -8), and PP is the turning point of gg.
1. Find the values of aa, bb and cc.
2. Find the length of MNMN if MNMN is perpendicular to the yy-axis and MNMN produced passes through the yy-intercept of f(x)f(x) and g(x)g(x).
3. Determine the equation of the graph that results when g(x)g(x) is reflected about the line x=1x=1.
4. [IEB, Nov. 2003, HG]
1. Sketch the graph of f(x)=x3-9x2+24x-20f(x)=x3-9x2+24x-20, showing all intercepts with the axes and turning points.
2. Find the equation of the tangent to f(x)f(x) at x=4x=4.
3. Sketch the graph of y=|f(x)|y=|f(x)| on a new set of axes, giving coordinates of the turning points and intercepts with the axes.
5. [IEB, Nov. 2004, HG] Solve: 18|x-3|18|x-3|
6. [IEB, Nov. 2005, HG] Solve for xx:   25|1-2x|=5425|1-2x|=54
7. [IEB, Nov. 2005, HG] If f(x)=|4-x|f(x)=|4-x|, find the value of f'(3)f'(3).

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