Exponents and Exponential Functions

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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.
   Antwort & Lösungsweg anzeigen

   Antwort: B

   Answer: B The base $\frac{1}{2}$ is between 0 and 1, so the exponential function is decreasing. Choose B.
   In der vollständigen CSCA Math December 2025 Past Paper ansehen
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 $\mathbf{R}$
   Antwort & Lösungsweg anzeigen

   Antwort: 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.
   Die komplette CSCA Math January 2026 Past Paper bearbeiten – mit Zeit & Bewertung
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．$a < 1$
   Antwort & Lösungsweg anzeigen

   Antwort: B

   Exponential $a ^ { x }$ (with $a > 0 , a \neq 1$ ) is decreasing iff $0 < a < 1$.
   Die komplette CSCA Math April 2026 Past Paper bearbeiten – mit Zeit & Bewertung