examday

Official papers

Official 2019 Paper 2 · Q18

Paper 2Logic & proofAlgebra

Consider the following inequality:

(∗):a∣x∣+1≤∣x−2∣(*):\quad a|x|+1\leq|x-2|

where aa is a real constant.

Which one of the following describes the complete set of values of aa such that (∗)(*) is true for all real xx?

Aa≤32a\leq\frac32
Ba≤1a\leq1
Ca≤12a\leq\frac12
Da≤0a\leq0
Ea≤−12a\leq-\frac12
Fa≤−1a\leq-1
Ga≤−32a\leq-\frac32
HThere are no such values of aa.

Read the questions freely. Sign in to check your answer, see the worked solution and save your progress.

Sign in to check your answerPractise the whole paper →