Algebraic Proof Quiz

1. Which symbol shows that a statement is true for all values of the variable?

• A. $=$
• B. $\equiv$
• C. $\approx$
• D. $\neq$

2. Which expression represents any odd number, where $n$ is an integer?

• A. $2n$
• B. $n^2$
• C. $2n + 1$
• D. $n + 2$

3. A student proves 'the sum of two consecutive integers is odd' by testing only $n = 4$, giving $4 + 5 = 9$. Why is this not a valid proof?

• A. 9 is not actually an odd number
• B. It only checks one specific case, not every integer
• C. The student should have used a decimal instead
• D. Consecutive integers cannot be added together

4. To disprove the statement 'squaring a number always makes it bigger', which value gives the best counter-example?

• A. $5$
• B. $-1$
• C. $0.5$
• D. $100$

5. Prove that the sum of three consecutive integers $n$, $n+1$, $n+2$ is always a multiple of 3. Which simplified expression correctly completes this proof?

• A. $3n + 2$
• B. $3n + 3 = 3(n+1)$
• C. $n^3 + 3$
• D. $3n - 1$