Module 2 · Algebra
Chapter 21: Modulus
Algebra
3 topics
What this chapter covers
The 3 topics below make up Modulus on the CAT. Click any topic to open its notes, examples and practice test.
Study material & tests
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📝 Chapter test
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Formula Reference Sheet
This chapter
Definition & core properties
| Piecewise definition | |x| = x if x ≥ 0, and −x if x < 0 |
|---|---|
| Square-root form | |x| = √(x²); also |x|² = x² |
| Distance on the line | |x − a| = distance between x and a |
| Product & quotient | |ab| = |a||b|; |a/b| = |a|/|b| (b ≠ 0) |
| Non-negativity | |x| ≥ 0, with |x| = 0 only when x = 0 |
Equations, inequalities & triangle rule
| Basic equation | |x| = c (c ≥ 0) ⇒ x = c or x = −c |
|---|---|
| Linear equation | |ax + b| = c ⇒ ax + b = ±c (needs c ≥ 0) |
| Less-than inequality | |x| ≤ c ⇒ −c ≤ x ≤ c (c ≥ 0) |
| Greater-than inequality | |x| ≥ c ⇒ x ≤ −c or x ≥ c |
| Triangle inequality | |a + b| ≤ |a| + |b|; |a − b| ≥ ||a| − |b|| |
CAT reference
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