Core Pure -as Year 1- Unit Test 5 Algebra And Functions Guide

She flipped back. Question 6 (not mentioned yet) was a proof by contradiction involving a rational root of a cubic. She had left it till last. Prove that ( \sqrt{3} ) is irrational. She wrote: Assume ( \sqrt{3} = \frac{a}{b} ) in lowest terms. Then ( 3b^2 = a^2 ). So 3 divides ( a^2 ), so 3 divides ( a ). Let ( a = 3k ). Then ( 3b^2 = 9k^2 ) → ( b^2 = 3k^2 ). So 3 divides ( b^2 ), so 3 divides ( b ). Contradiction — ( a ) and ( b ) have a common factor 3, not lowest terms. Hence ( \sqrt{3} ) is irrational.

As she walked out, she thought: That wasn't a test. That was a rite of passage. core pure -as year 1- unit test 5 algebra and functions

Elena stared at the clock on the wall of Exam Hall 4. 9:02 AM. She had 58 minutes left. She flipped back