Past Papers’ Solutions  Edexcel  AS & A level  Mathematics  Core Mathematics 1 (C16663/01)  Year 2014  June  Q#3
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Question
Find the set of values of x for which
a.
b.
c. both and .
Solution
a.
We are given;
b.
We are required to solve the inequality;
We solve the following equation to find critical values of ;
Now we have two options;






Hence the critical points on the curve for the given condition are 3 & 12.
Standard form of quadratic equation is;
The graph of quadratic equation is a parabola. If (‘a’ is positive) then parabola opens upwards and its vertex is the minimum point on the graph.
If (‘a’ is negative) then parabola opens downwards and its vertex is the maximum point on the graph.
We recognize that it is an upwards opening parabola.
Therefore conditions for are;
c.
We have found in (a) for ;
We have found in (b) for ;
For both inequalities to be true the overlapping period of two sets of value of x is what will make them so;
Therefore;
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