CDS Mathematics · Teaching notes

Inequalities — CDS Elementary Mathematics

Inequalities has 13 past-year questions in CDS Elementary Mathematics, in 9 of the twenty-one sittings from 2016 (II) to 2026 (II). Five ask you to solve an inequality; the other eight, including both HARD items, turn on signs and comparisons, most of them as data-sufficiency questions. The first page covers solving linear and quadratic inequalities, the second reasoning with signs, powers and x + 1/x.

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Subtopic notes

Formula & revision sheet

3 formulas · 3 gotchas across all subtopics — the exam-eve cheat-sheet

Solving Inequalities

Formulas (1)

Linear and quadratic inequalities · Quadratic sign $(x - \alpha)(x - \beta) > 0 \iff x < \alpha \text{ or } x > \beta$

Watch out for (1)

'Or', not 'and', outside the roots
→ Linear and quadratic inequalities

Signs, Powers and Comparisons

Formulas (2)

What a statement forces about signs · Odd and even powers $x^{2k} \ge 0, \qquad \operatorname{sign}\!\left(x^{2k+1}\right) = \operatorname{sign}(x)$
x + 1/x and comparing expressions · AM–GM for x and 1/x $x + \dfrac{1}{x} \ge 2 \quad (x > 0)$

Watch out for (2)

Dividing by an unknown sign
→ What a statement forces about signs
'Only when' is a claim too
→ x + 1/x and comparing expressions

PYQ weightage by concept

3 concepts · 13 PYQs — where the marks actually sit, so you know what to drill first

Solving Inequalities5 PYQs · 38%

Concept	PYQs	Share
Linear and quadratic inequalities	5	38%

Signs, Powers and Comparisons8 PYQs · 62%

Concept	PYQs	Share
What a statement forces about signs	6	46%
x + 1/x and comparing expressions	2	15%

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