Important Notes:
For Paper 1 (Objective Questions), the questions asked are usually related to the shapes and positions of basic graphs of LINEAR, QUADRATIC, CUBIC and RECIPROCAL FUNCTIONS.
Students are expected to be able to identify:
a) the shape of graph given a type of functionThe different types of functions for Paper 1, SPM Mathematics:
Linear y = mx + c m = gradient c = y-intercept | Quadratic y = ax2 + bx + c Note : Paper 1 limits to y = ax2 + c | Cubic y = ax3 +bx2 +cx + d Note : Paper 1 limits to y = ax3 + c | Reciprocal y =1 x |
 |  |  |  |
Note : This module concentrates on graph sketching, the skills needed for Paper 1. For details on how to plot graphs please refer to the other related modules (eg. Chapter 12 – The Straight Line – on how to draw / plot straight lines) | |||
19.0 Back to Basic
I. Linear Graphs : can be represented by the equation y = mx + c.
· m is the gradient
· c the y-intercept, ie, the place where the straight line cuts the y-axis.
II. The general form of a Quadratic Function is f(x) = ax2 + bx + c; a, b, c are constants and a ≠ 0.
Characteristics of a quadratic function:
· Involves one variable only,
· The highest power of the variable is 2.
III. The general form of a Cubic Function is f(x) = ax3 + bx2 + cx + d ; a, b, c and d are constants and a ≠ 0.
Characteristics of a cubic function:
· Involves one variable only,
· The highest power of the variable is 3.
IV. The simple Reciprocal Function is of the form y = 
, where a is a constant.
, where a is a constant.19.1 To Identify The Type Of Function Given Its Equation
Example 1
No. | Linear y = mx + c | Quadratic y = ax2 + bx + c | Cubic y = ax3 + bx2 + cx + d | Reciprocal y = |
1. | y = x | y = x2 + 2x -3 | y = x3 + 2x2 + 3x – 4 | y =  |
2. | y = 2x + 3 | y = x2 + 2 | y = x3 – 3 | y =  |
3. | y = 3x – 4 | y = 4 – 3x2 | y = 4 – 3x3 | xy = 4 |
4. | y = 5 | y = 3x2 | y = 2x3 | y =  |
5. | x+ y = 4 | y = 3 – 4x + 5x2 | y = 1 – 2x + 5x3 | y =  |
