SPS SPS SM 2021 January — Question 3 9 marks

Exam BoardSPS
ModuleSPS SM (SPS SM)
Year2021
SessionJanuary
Marks9
TopicInequalities
TypeCombined linear and quadratic inequalities
DifficultyModerate -0.8 This question involves routine algebraic manipulation of a simple linear inequality and a straightforward quadratic inequality, followed by finding the intersection of solution sets. All steps are standard textbook exercises requiring only basic technique with no problem-solving insight or novel approaches needed.
Spec1.02g Inequalities: linear and quadratic in single variable

3. a) Solve the linear inequality $$6 - 2 ( x + 2 ) < 10 .$$ b) Solve the quadratic inequality $$( x + 1 ) ^ { 2 } \geq 4 x + 9$$ c) Hence determine the range of values of \(x\) that satisfy both the inequalities of part (a) and part (b).

3.

a) Solve the linear inequality

$$6 - 2 ( x + 2 ) < 10 .$$

b) Solve the quadratic inequality

$$( x + 1 ) ^ { 2 } \geq 4 x + 9$$

c) Hence determine the range of values of $x$ that satisfy both the inequalities of part (a) and part (b).\\

\hfill \mbox{\textit{SPS SPS SM 2021 Q3 [9]}}