https://soh-cah-toa.pages.dev/tags/m18/ Recent content in M18 on SOH-CAH-TOA Hugo en-us Sun, 23 Aug 2026 21:19:38 +0700 https://soh-cah-toa.pages.dev/mark-schemes/mathematics/curved_graphs_ms/ Sun, 23 Aug 2026 21:19:38 +0700 https://soh-cah-toa.pages.dev/mark-schemes/mathematics/curved_graphs_ms/ <h1 id="curved-graphs-quiz-marking-scheme">Curved Graphs Quiz: Marking Scheme</h1> <blockquote> <p>This is the marking scheme for quiz: <a href="https://soh-cah-toa.pages.dev/quizzes/mathematics/curved_graphs_quiz/">M18 - Curved Graphs Quiz</a><br> Topic Guide: <a href="https://soh-cah-toa.pages.dev/guides/mathematics/curved_graphs/">M18 - Curved Graphs</a></p> </blockquote> <p><strong>Total: 40 marks</strong></p> <p>Accept equivalent notation and correct methods that produce a correct result.</p> <ol> <li><strong>A</strong> — $y=(x-2)^2-3$</li> <li><strong>B</strong> — reciprocal graph with two branches</li> <li><strong>B</strong> — $x=3$</li> <li><strong>C</strong> — tangent has the same gradient as the curve at the point of contact</li> </ol> <hr> <ol start="5"> <li>For $y=x^2-6x+5$: <ul> <li><strong>1 mark:</strong> Finds the axis of symmetry as $x=3$, using $x=-b/(2a)$ or an equivalent method.</li> <li><strong>2 marks:</strong> Finds the turning point as $(3,-4)$. <ul> <li>1 mark for substituting $x=3$ correctly.</li> <li>1 mark for obtaining $y=-4$ and stating the coordinates.</li> </ul> </li> <li><strong>1 mark:</strong> Identifies the turning point as a minimum because the coefficient of $x^2$ is positive.</li> </ul> </li> </ol> <hr> <ol start="6"> <li> <p>For $y=-3/x$:</p> https://soh-cah-toa.pages.dev/quizzes/mathematics/curved_graphs_quiz/ Sun, 23 Aug 2026 21:19:24 +0700 https://soh-cah-toa.pages.dev/quizzes/mathematics/curved_graphs_quiz/ <h1 id="curved-graphs-quiz">Curved Graphs Quiz</h1> <p><strong>Total: 40 marks</strong></p> <p>Answer all questions. Show working for Questions 5–8. Give exact answers where appropriate.</p> <h4 id="1-1-mark">1. [1 mark]</h4> <p>A quadratic function has its vertex at $(2,-3)$ and passes through $(4,1)$. Which equation represents the function?</p> <p>A. $y=(x-2)^2-3$</p> <p>B. $y=(x-2)^2+3$</p> <p>C. $y=2(x-2)^2-3$</p> <p>D. $y=(x+2)^2-3$ <br><br></p> <h4 id="2-1-mark">2. [1 mark]</h4> <p>What type of graph is represented by $y=\frac{1}{x}$?</p> <p>A. A straight line</p> <p>B. A reciprocal graph with two branches</p>