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Exercises - Not covered in Syllabus

Module by: Rory Adams, Free High School Science Texts Project, Heather Williams. E-mail the authors

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.
    Figure 1
    Figure 1 (MG12C14_001.png)
    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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