Exponents and Exponential Functions

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 statement about $y=\left(\frac{1}{2}\right)^x$ is correct?
   • A．It is increasing.
   • B．It is decreasing.
   • C．It is symmetric about the origin.
   • D．It is symmetric about the $x$-axis.
   Show answer & solution

   Answer: B

   Answer: B The base $\frac{1}{2}$ is between 0 and 1, so the exponential function is decreasing. Choose B.
   See it in the full CSCA Math December 2025 Past Paper
2. CSCA Math January 2026 Past Paper
   About the exponential function $y=a^x$ ($a>0$, $a\neq1$), which statement is incorrect?
   • A．The range is $(0,+\infty)$
   • B．The graph passes through $(0,1)$
   • C．The function is increasing on its domain
   • D．The domain is $\mathbf{R}$
   Show answer & solution

   Answer: C

   Answer: C For $y=a^x$, the domain is $\mathbf{R}$, the range is $(0,+\infty)$, and the graph passes through $(0,1)$. It is increasing only when $a>1$ and decreasing when $0<a<1$, so statement C is not always true.
   Take the full CSCA Math January 2026 Past Paper — timed & graded
3. CSCA Math April 2026 Past Paper
   Function $y = a ^ { x }$ is decreasing on $\mathbb { R }$ when
   • A．$a > 0$
   • B．$0 < a < 1$
   • C．$a > 1$
   • D．$a < 1$
   Show answer & solution

   Answer: B

   Exponential $a ^ { x }$ (with $a > 0 , a \neq 1$ ) is decreasing iff $0 < a < 1$.
   Take the full CSCA Math April 2026 Past Paper — timed & graded