Equations of Lines

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
   The inclination angle of the line $y=\sqrt{3}x+10$ is ( ).
   • A．$45^\circ$
   • B．$30^\circ$
   • C．$120^\circ$
   • D．$60^\circ$
   Show answer & solution

   Answer: D

   Answer: D The slope is $\sqrt{3}$. Thus $\tan\theta=\sqrt{3}$, so $\theta=60^\circ$. Choose D.
   See it in the full CSCA Math December 2025 Past Paper
2. CSCA Math March 2026 Past Paper
   The inclination angle of the line $x + \sqrt { 3 } \cdot y - 2 = 0$ is
   • A．$150 ^ { \circ }$
   • B．$60 ^ { \circ }$
   • C．$30 ^ { \circ }$
   • D．$120 ^ { \circ }$
   Show answer & solution

   Answer: A

   Slope $k = - 1 / \sqrt { 3 } = - \sqrt { 3 } / 3$. $\tan \theta = - \sqrt { 3 } / 3$ gives inclination angle $\theta = 150 ^ { \circ }$.
   Take the full CSCA Math March 2026 Past Paper — timed & graded
3. CSCA Math April 2026 Past Paper
   The slope of the line through $A ( - 1,1 )$ and $B ( 2,3 )$ is
   • A．$- \frac { 3 } { 2 }$
   • B．$- \frac { 2 } { 3 }$
   • C．$\frac { 3 } { 2 }$
   • D．$\frac { 2 } { 3 }$
   Show answer & solution

   Answer: D

   $k = \frac { y _ { 2 } - y _ { 1 } } { x _ { 2 } - x _ { 1 } } = \frac { 3 - 1 } { 2 - ( - 1 ) } = \frac { 2 } { 3 }$.
   Take the full CSCA Math April 2026 Past Paper — timed & graded