Function Parity

How the real exam tests it

Questions from real CSCA papers that test this concept. Work each one out before you open the answer.

1. CSCA Math December 2025 Past Paper
   Which of the following functions is odd?
   • A．$y=\cos x$
   • B．$y=x+x^3$
   • C．$y=x^4$
   • D．$y=x\sin x$
   Show answer & solution

   Answer: B

   Answer: B For $f(x)=x+x^3$, $f(-x)=-f(x)$, so it is odd. Choose B.
   See it in the full CSCA Math December 2025 Past Paper
2. CSCA Math June 2026 Past Paper
   Which of the following statements about the odd function $y = f(x)$ is incorrect?
   • A．The domain of the function is symmetric about the origin
   • B．In the domain of the function, $f(-x) = f(x)$
   • C．The graph of the function is symmetric about the origin
   • D．In the domain of the function, $f(-x) = -f(x)$
   Show answer & solution

   Answer: B

   For an odd function, both the domain and the graph are symmetric about the origin, so (A) and (C) are true; by definition $f(-x) = -f(x)$, so (D) is true. Statement (B) is the property of an even function and is therefore the incorrect statement. Choose (B).
   Take the full CSCA Math June 2026 Past Paper — timed & graded