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Tim Gan Math

2015 A-Level H2 Mathematics

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Question 2Inequalities6 marks
  1. Sketch the curve with equation $y=\left| \frac{x+1}{1-x} \right|$, stating the equations of the asymptotes. On the same diagram, sketch the line with equation $y=x+2$.

    [3]

  2. Solve the inequality $\left| \frac{x+1}{1-x} \right| < x+2$.

    [3]

Solution step 1, image 1
Solution step 2, image 1
Solution step 2, image 2

Final Answer:

(i) Graph shown; (ii) -√3 < x ≤ -1 + √2 or x > √3