SAJC Chapter 1 Equations Teachers 2021

SAJC 2021 H1 Mathematics Chapter 1: Equations Page 1 of 54 (Pure Mathematics) Chapter 1: Equations Objectives At the end of the chapter, you should be able to: (a) solve quadratic equations using factorisation, completing the square, formula, sketching of graph and a GC; (b) understand and use the conditions for a quadra tic equation to have (i) two real and distinct roots, (ii) two real and equal roots, (iii) no real roots; (c) understand and use the conditions for a quadratic equation to be always positive (or always negative); (d) formulate a quadratic equation from a pro blem situation and interpret the solutio n in the context of the problem; (e) solve a pair of simultaneous equations, one linear and one quadratic, by substitution; (f) formulate a system of linear equations from a problem situation; (g) find the solution of a system of linear equations using a Graphing Calculator. Content 1.1 Quadratic Functions 1.1.1 Solving Quadratic Equations 1.1.2 Nature of Roots of a Quadratic Equation 1.1.3 Conditions for Quadratic Expression to be always positive (or always negative) 1.1.4 Intersection Problems Leading to Quadratic Equations 1.2 Simultaneous Linear and Quadratic Equations in Two Unknowns 1.2.1 Solving Simultaneous Linear and Quadratic Equations in Two Unknowns 1.2.2 Application questions 1.3 Systems of linear equation (SOLE) 1.3.1 Using Graphing Calculator to solve SOLE 1.3.2 Modelling a System of Linear Equations to Solve Practical Problems References 1. New Additional Mathematics, Ho Soo Thong (Msc, Dip Ed), Khor Nyak Hiong (Bsc, Dip Ed) 2. New Syllabus Additional Mathematics (7th Edition), Shinglee Publishers Ptd Ltd

SAJC 2021 H1 Mathematics Chapter 1: Equations Page 2 of 54 1.1 Quadratic Functions The expression   2f x ax bx c   , where 0a , is called a quadratic function. When the graph of the function 2y ax bx c   is drawn, two types of graphs are obtained, depending on the value of a. 0a U shape 0a Inverted – U shape Note: 1. a is the coefficient of 2x b is the coefficient of x c is the coefficient of 0x (also known as the constant term or the term independent of x) 2. If 0a , the curve has a minimum point at X. For example, in 22 7 4y x x   , 2a , 7b , 4c . Since 20a , the curve is U shape and has a minimum point. If 0a , the curve has a maximum point at Y. For example, in 2 69y x x   , 1a , 6b , 9c . Since 10a  , the curve is Inverted – U shape and has a maximum point. 3. The shape of a quadratic function is symmetrical about its minimum or maximum point. 1.1.1 Solving Quadratic Equations The general form of a quadratic equation is 2 0ax bx c   , 0a . There are five methods of solving a quadratic equation, namely: (a) Factorisation (b) Completin