Solving Inequalities

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
   Given $a>b$, which statement is true?
   • A．$5a>5b$
   • B．$\frac{1}{a}<\frac{1}{b}$
   • C．$a^2>b^2$
   • D．$\sin a>\sin b$
   Show answer & solution

   Answer: A

   Answer: A Multiplying both sides of $a>b$ by the positive number 5 preserves the inequality, so $5a>5b$. Choose A.
   See it in the full CSCA Math December 2025 Past Paper
2. CSCA Math January 2026 Past Paper
   Let $a , b , c$ be three real numbers. Which of the following statements is correct? ( )
   • A．If $a > b$, then $a c > b c$
   • B．If $a > b$, then $a + c > b + c$
   • C．If $a c > b c$, then $a > b$
   • D．If $a > b$, then $a ^ { 2 } > b ^ { 2 }$
   Show answer & solution

   Answer: B

   Which inequality property is correct? If $\mathrm { a } > \mathrm { b }$, adding the same number c to both sides preserves the inequality: $\mathrm { a } + \mathrm { c } > \mathrm { b } + \mathrm { c }$.
   Take the full CSCA Math January 2026 Past Paper — timed & graded
3. CSCA Math March 2026 Past Paper
   Given $\mathrm { a } > \mathrm { b }$, which of the following must be true?
   • A．$a ^ { 3 } > b ^ { 3 }$
   • B．$| \mathrm { a } | > | \mathrm { b } |$
   • C．$a ^ { 2 } > b ^ { 2 }$
   • D．$| \mathrm { a } | < | \mathrm { b } |$
   Show answer & solution

   Answer: A

   $y = x ^ { 3 }$ is strictly increasing on $\mathbb { R }$. If $a > b$ then $a ^ { 3 } > b ^ { 3 }$. Options B, C, D can be disproved by counterexamples.
   Take the full CSCA Math March 2026 Past Paper — timed & graded