Past Papers’ Solutions | Assessment & Qualification Alliance (AQA) | AS & A level | Mathematics 6360 | Pure Core 1 (6360-MPC1) | Year 2011 | June | Q#7

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Question

Solve each of the following inequalities:

a.  

b.  

Solution

a.
 

b.
 

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  & .

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 equation  is a quadratic equation representing upwards  opening parabola.

Therefore conditions for  are;

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