Question 2 - A-Level Maths

Given that \(a\) and \(b\) are real numbers, find a counterexample to disprove the statement that, if \(a > b\), then \(a ^ { 2 } > b ^ { 2 }\).
A student writes the statement that \(\sin x ^ { \circ } = 0.5 \Longleftrightarrow x ^ { \circ } = 30 ^ { \circ }\).
1. Explain why this statement is incorrect.
2. Write a corrected version of this statement.
Prove that the sum of four consecutive multiples of 4 is always a multiple of 8 .