1Preface
1164.3 Determinant
21. Equations and Inequalities
1174.3.1 Introduction
31.1 Linear Equation in One Variable
1184.3.2 Properties of Determinant
41.1.1 Definition
1194.3.3 Minors
51.1.2 Solving Linear Equation in one Variable
1204.3.4 Cofactors
61.2 Quadratic Equations in One Variable
121Exercise Set 4.3
71.2.1 Definition
1224.4 Inverse of a Matrix
81.2.2 Solving Quadratic Equations in one Variable
1234.4.1 Introduction
91.3 Applications of Linear and Quadratic Equations in one Variable: 1.3.1 Introduction
1244.4.2 Computing Inverse of a Matrix using Adjoint
101.4 Dealing with Inequalities
1254.4.3 Properties of Adjoint and Inverse
111.4.1 Linear Inequalities in one variable
1264.4.4 Computing Inverse of a Matrix using Gauss-Jordan Method
121.4.2 Properties of Inequalities
127Exercise Set 4.4
131.4.3 Compound Inequalities
1284.5 Solving System of Equations Using Matrices
141.4.3 Absolute-value Inequalities
1294.5.1 Introduction
151.5 Linear Equations in Two Variables
1304.5.2 System of Linear Equations in Two Variables
161.5.1 Definition
1314.5.3 System of Linear Equations in Three Variables
171.5.2 Solving Linear equation in two Variables
1324.5.4 Inconsistent & Dependent Systems
181.5.3 System of Linear Equation in two Variables
1334.5.5 Cramer’s Rule for Solving System of Linear Equations in two variables
191.5.4 Solution of a System of Linear Equations
1344.5.6 Cramer’s Rule for Solving System of Linear Equations in three Variables
20Exercise Set 1.5
1354.6 Applications of System of Linear Equations: 4.6.1 Introduction
211.6 Linear Equations in Three Variables
136References
221.6.1 Definition
1375. Functions and Relations
231.6.2 Solution of a linear equation in three variables
1385.1 The Rectangular Coordinate System and Graphing Utilities
241.6.3 System of Linear Equations in 3 Variables
1395.1.1 Plot points on a Rectangular Coordinate System
251.6.4 Solution of System of Linear Equations in three Variables
1405.1.2 The Distance and Midpoint Formulas
261.7 Applications of System of Linear Equations in Two and Three Variables: 1.7.1 Introduction
1415.1.3 Graph Equations by Plotting Points
271.8 System of Non-Linear Equations in two Variables
1425.1.4 Identify x and y-Intercepts
281.8.1 Introduction
143Exercise Set 5.1
291.8.2 Solution of Non- Linear Equations
1445.2 Circles
301.9 Inequalities in Two Variables
1455.2.1 Write an Equation of a Circle in Standard Form
311.9.1 Introduction
1465.2.2 Write the General Form of an Equation of a Circle
321.9.2 Solution of Linear Inequality in Two Variables
147Exercise Set 5.2
331.9.3 System of Linear Inequalities in Two Variables
1485.3 Functions and Relations
34References
1495.3.1 Determine Whether a Relation is a Function
352. Polynomial and Rational Functions
1505.3.2 Apply Function Notation
362.1 Introduction to Polynomials
1515.3.3 Determine the x and y-intercepts of a Function Defined by y = f(x)
372.1.1 Definition
1525.3.4 Determine Domain and Range of a Function
382.1.2 Properties of Polynomials
153Exercise Set 5.3
392.1.3 Degree of Polynomial
1545.4 Linear Equations in Two Variables and Linear Functions
402.1.4 The leading term Test
1555.4.1 Graph Linear Equations in Two Variables
412.1.5 Zeros and Multiplicities of Zero
1565.4.2 Determine the Slope of a Line
422.1.6 Graphing of the Polynomial
1575.4.3 Apply the Slope – Intercept Form of a Line
432.2 Multiplication of Polynomials
1585.4.4 Compute Average Rate of Change
442.2.1 Product of the Monomials
159Exercise Set 5.4
452.6.2 Product of a Monomial and a Polynomial
1605.5 Applications of Linear Equations and Modeling
462.2.3 Multiplying two Binomials
1615.5.1 Apply the Point – Slope Formula
472.2.4 Product of two Binomials by Foil Method
1625.5.2 Determine the Slopes of Parallel and Perpendicular Lines
482.2.5 Squaring of Binomials
1635.5.3 Create a Linear Function in an Application
492.2.6 Product of Higher order Polynomials
1645.6 Transformations of Graphs
502.3 Evaluation and some more Algebra of Polynomials
1655.6.1 Recognize Basic Functions
512.3.1 Division of two Polynomials
1665.6.2 Apply Vertical and Horizontal Translations
522.3.2 Evaluating the Polynomial
1675.6.3 Apply Vertical and Horizontal Shrinking and Stretching
532.3.3 Addition of Polynomials with Different Variables
1685.6.4 Apply Reflections across the x and y- Axes
542.4 Factoring of Polynomial
1695.6.5 Summarize Transformations of Graphs
552.4.1 Introduction
1705.7 Analyzing Graphs of Functions and Piecewise – Defined Functions
562.4.2 Factoring by Grouping
1715.7.1 Test for Symmetry
572.4.3 Factoring by Middle Term Splitting
1725.7.2 Identify Even and Odd Functions
582.5 Quadratic Equations and its Solutions
1735.7.3 Graph Piecewise – Defined Functions 5-22
592.5.1 Introduction
1745.7.4 Investigate Increasing, Decreasing, and Constant Behavior of a Function
602.5.2 Square Root Property
1755.7.5 Determine Relative Minima and Maxima of a Function
612.5.3 Completing the Square
1765.8 Algebra of Functions and Function Composition
622.5.4 Quadratic Formula
1775.8.1 Perform Operations on Functions
632.5.5 Vertex Form of Quadratic Equations
1785.8.2 Evaluate a Difference Quotient
642.5.6 Graph of a Quadratic Function in Vertex Form
1795.8.3 Compose and Decompose Functions
652.5.7 Vertex of Parabola
180References
662.6 Rational Functions
1816. Analytic Geometry
672.6.1 Introduction
1826.1 Coordinate Geometry
682.6.2 Asymptotes
1836.1.1 The Distance Formula
692.6.3 Graphing the Rational Function
1846.1.2 The Section Formula
702.7 Inequalities
1856.1.3 Slope of Line
712.7.1 Introduction
1866.1.4 Angle between the Lines
722.7.2 Polynomial Inequality
187Exercise Set 6.1
732.7.3 Rational Inequality
1886.2 Circle
742.8 Applications of Polynomials and Rational Equalities and Inequalities
1896.2.1 Circle with Centre at Origin
752.8.1 Applications of Polynomials
1906.2.2 Circles with Centre not at Origin
762.8.2 Applications of Polynomial and Rational Inequalities
1916.2.3 Parametric form of Circle
772.9 Variation
1926.2.4 Equation of a Tangent to a Circle
782.9.1 Direct Variation
1936.2.5 Equation of a Normal to a Circle
792.9.2 Inverse Variation
1946.2.6 Director Circle
802.9.3 Joint Variation
1956.3 Ellipse
812.9.4 Applications of Variations
1966.3.1 Ellipses with Centre at Origin
82References
1976.3.2 Ellipses with Centre not at Origin
833. Exponential and Logarithmic Functions
1986.3.3 Parametric form of Ellipse
843.1 Exponential function
1996.3.4 Auxiliary Circle
853.2 Graphing of exponential functions
2006.3.5 Equation of Tangent of an Ellipse
863.3 Compute the exponential function base e
2016.3.6 Equation of Normal
87Exercise Set 3.3
2026.3.7 Director Circle
883.4 Use of exponential functions in various applications
2036.3.8 Diameter and Conjugate Diameter of an Ellipse
893.4.1 Exponential Curve through two Points
2046.3.9 Equation of Chord with middle point of an Ellipse
903.4.2 Compound Interest using Exponential Functions
2056.3.10 Ellipse and its Applications
91Exercise Set 3.4
206Exercise Set 6.3
923.5 Logarithmic functions
2076.4 Parabola
933.6 Graphing of Logarithmic Functions
2086.4.1 Parabolas with Vertex at Origin
943.7 Conversion between Exponential & Logarithmic Functions
2096.4.2 Parabolas with Vertex not at Origin
953.8 Use of logarithmic functions in various applications
2106.4.3 Equation of the Tangent of a Parabola
963.9 Exponential & Logarithmic Equations
2116.4.4 Equation of Director Circle of a Parabola
973.9.1 Solving Exponential Equations
2126.4.5 Equation of a Normal to a Parabola
983.9.2 Solving Logarithmic Equations
2136.4.6 Equation of Chord of a Parabola
99References
2146.4.7 Equation of Diameter of a Parabola
1004. Matrices Determinants and its Applications
2156.4.8 Parabola and its Applications
1014.1 Elementary Row Operations
2166.5 Hyperbolas
1024.1.1 Introduction
2176.5.1 Hyperbolas with Centre at Origin
1034.1.2 Types of Matrices
2186.5.2 Hyperbolas with Centre not at Origin
1044.1.3 Equality of Matrices
2196.5.3 Parametric form of points of a Hyperbola
1054.1.4 Trace of Matrix
2206.5.4 Auxiliary circle of a Hyperbola
1064.1.5 Elementary Row Operations
2216.5.5 Equation of Tangent to a Hyperbola
1074.1.6 Augmented Matrix
2226.5.6 Equation of the Normal to the Hyperbola
1084.2 Arithmetic operation on matrices
2236.5.7 Equation of Director Circle to the Hyperbola
1094.2.1 Introduction
2246.5.8 Equations of chord with middle point at (x1, y1 ) on the Hyperbola
1104.2.2 Addition & Subtraction
2256.5.9 Equations of Diameter and Conjugate Diameter of the Hyperbola
1114.2.3 Transpose of a Matrix
2266.6 Rectangular Hyperbola : 6.6.1 Asymptotes
1124.2.4 Scalar Multiplication of a Matrix
227Exercise Set 6.6
1134.2.5 Matrix Multiplication
228References
1144.2.6 Special type of Matrices
229Index
115Exercise set 4.2
