Function Monotonicity

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 increasing?
   • A．$y=\log_{0.5}x$
   • B．$y=\left(\frac{1}{3}\right)^x$
   • C．$y=2x+1$
   • D．$y=\sin x$
   Show answer & solution

   Answer: C

   Answer: C $y=2x+1$ is a linear function with positive slope, so it is increasing. Choose C.
   See it in the full CSCA Math December 2025 Past Paper
2. CSCA Math April 2026 Past Paper
   Which function is decreasing on $( - \infty , + \infty )$ ?
   • A．$y = - x + 5$
   • B．$y = x ^ { 3 }$
   • C．$y = x ^ { 2 } + 1$
   • D．$y = - \frac { 1 } { x }$
   Show answer & solution

   Answer: A

   (A) Linear with slope $- 1 < 0$, decreasing on all of $\mathbb { R } \checkmark$. (B) $x ^ { 3 }$ is increasing on $\mathbb { R }$; (C) parabola is not monotonic; (D) undefined at $x = 0$, so not on all of $\mathbb { R }$; moreover on each piece $( - \infty , 0 )$ and $( 0 , + \infty )$ it is in fact increasing, since $y ^ { \prime } = \frac { 1 } { x ^ { 2 } } > 0$.
   Take the full CSCA Math April 2026 Past Paper — timed & graded
3. CSCA Math June 2026 Past Paper
   Which of the following functions is monotonically decreasing?
   • A．$y = e^{-x}$
   • B．$y = x^2 - 1$
   • C．$y = 100^x$
   • D．$y = \cos x$
   Show answer & solution

   Answer: A

   $y = e^{-x} = \left( \frac{1}{e} \right)^x$ with base $\frac{1}{e} < 1$ is monotonically decreasing, so (A) is correct. $y = x^2 - 1$ decreases on $(-\infty, 0)$ and increases on $(0, +\infty)$, so it is not monotonic; $y = 100^x$ has base greater than 1 and is increasing; $y = \cos x$ is periodic and not monotonic on its domain. Choose (A).
   Take the full CSCA Math June 2026 Past Paper — timed & graded