ASR Standard Curves Lecture Notes

JC1 H2 Mathematics Chapter 01: Standard Curves Standard Curves C01 – 1 ANDERSON SERANGOON JUNIOR COLLEGE 2026 JC1 H2 MATHEMATICS CHAPTER 01: STANDARD CURVES Lesson Objectives At the end of the chapter, you should be able to ▪ relate the following equations: y = |x|, 22 22 1xy ab+= , 22 22 1xy ab−= , 22 22 1yx ba−= and equations of parabolas with their graphs, identifying their characteristics such as symmetry, axial intercepts, turning points, asymptotes and restrictions on the possible values of x and/or y. ▪ use the graphic calculator to graph a curve with equations stated above. ▪ sketch simple parametric equations, and convert parametric equation into its Cartesian equation. Pre-Requisites You should already know: Standard graphs learnt previously at the O -Levels, such as straight line s, quadratic curve s, circles, the logarithmic curve (i.e. lnyx= ) and the exponential curve (i.e. exy= ). Pre-Lesson Activity • Watch video ‘Using the Conics App’ on https://education.ti.com/en/resources/test- preparation#lightbox=Test-Prep-tips-for-TI-84-Plus-CE to familarise with GC keystrokes. • Read Section 1 and complete exercises (1) to (3). (1) Find the equation of the line which passes through the point (2, ‒3) and makes an angle of π 3 with the positive x-axis. [Solution] [y = 3 2 3 3x −− ] (2) Sketch the graph of 1 24e x y=− , giving the exact coordinates where the curve cuts the axes, and the equation of the asymptotes. State any increasing and/or decreasing properties. [Solution] [(4ln 2, 0), (0, 3), y = 4] (3) Sketch the curve of 2 42y x x=− + − , indicating the coordinates of intercepts and the turning point. [GC steps in Annex 1]

JC1 H2 Mathematics Chapter 01: Standard Curves Standard Curves C01 – 2 Section 1: Standard Curves 1.1 Polynomial Curves Type of Graph Common Form of Equation Graph Straight Lines ▪ y = mx + c; or ▪ ( )00y y m x x− = − , where m is the gradient, c is the y-intercept and ( )00,xy is a point on the line. Note (1) 10 10 or tanyym xx −= −  , where  is the angle that the line makes with the positive x- axis in the anti-clockwise direction. (2) Vertical line: xh= Horizontal line: yk= Quadratic Curves ▪ y = ax2 + bx + c (a  0) a > 0 a < 0 Cubic Curves ▪ y = ax3 + bx2 + cx + d (a  0) a < 0 a > 0  y m > 0 • x c x • y  O m < 0 c Note: tanm=  Equivalence - is a relationship that express the equality of 2 math objects. In this case, the gradient of a straight line can be represented when you have either 1. coordinates of 2 points, or 2. Angle that the line makes with the positive x-axis. BIG IDEA

JC1 H2 Mathematics