Amath notes

Additional Mathematics SA2 Overall Revision Notes Chapters 1 – 2 ( ) Simultaneous Equations, Indices, Surds, Logarithms Chapter 1: Simultaneous Equations There are 3 methods in solving simultaneous linear equations: 1.) Substitution Method 2.) Elimination Method 3.) Graphical Method There are several steps to follow: 1.) Express one unknown in terms of another unknown (avoid fractional expressions) 2.) Substitute this newly – formed equation into the non-linear equation 3.) Solve for the unknown 4.) Use the linear equation to find the other unknown. Chapter 2.1: Surds ( )( ) and . Rationalising Denominator: Multiply the square root to both numerator and denominator. m n mn mm nn a m b m a b m a b a b a b a b k c d k a c b d              Chapter 2.2: Indices mnn mn m n n n n mm m n m n m mm m mnn m n m n m a a a a xa x aa a b ab a a a a abb a a a a a a ) ( ) ( 1 1 ) ( ) ( ) ( 0                   When a > 1 xnaa xn   Chapter 2.3: Logarithms

Additional Mathematics SA2 Overall Revision Notes Chapters 3 - 4 Quadratic Functions and Inequalities Sum and Product of Roots 2In Sum of roots Product of roots ax bx c b a c a       We can use the sum and product of roots to write an equation. 2 (sum of roots) (product of roots) 0xx   Discriminant and Nature of Roots Intersection Terms Crosses / Cuts 2 points of intersection, 2 real/distinct roots/ discriminant more than 0. Touches / tangent 1 point of intersection, 2 real/equal roots/ discriminant = 0. Does not intersect / meet 0 points of intersection, no real roots, discriminant < 0. Meet Discriminant more than or equal to 0. Quadratic Inequality ( )( ) 0, or ( )( ) 0, x a x b x a x b x a x b a x b           Chapter 8: Linear Law The graph of a linear equation Y = mX + c is a straight line with gradient m and y intercept c. There are 2 parts to solving linear law questions: Draw a straight line graph to determine gradient and y-intercept, and to find the equation of the straight line. Key Steps: 1.) Force the equation into the form of Y = mX + c. 2.) Take some experimental values of x and y and compute the corresponding values of X and Y. 3.) Use these computed values to plot the points on a graph with X and Y axis. 4.) Draw a line passing through the plotted points. Always have more space at the lower end of graph for the line to cut the Y axis for Y-intercept. 5.) Obtain the Gradient and the Y-intercept. Note: In Y = mX + c (a): Y must not have any coefficient, (b): mX is part constant and part variable. (c): c must not contain any variable X and Y.

Additional Mathematics SA2 Overall Revision Notes Chapters 3 - 4 Polynomials/Partial Fractions Polynomial An expression that is a sum o