Numerical Analysis

• Properties of real numbers
• The distributive property
• Division of real numbers
• Solving linear equations
• Solving equations using addition and subtraction
• Solving equations using multiplication and division
• Solving multi-step equations
• Solving equations with variables on both sides
• Linear equations and problem solving
• Solving decimal equations
• Formulas and functions
• Rates, ratios and percents
• Graphing linear equations and functions
• Coordinates and scatter plots
• Graphing linear equations
• Quick graphs using intercepts
• The slope of a line
• Direct variation
• Quick graphs using slope-intercept form
• Solving linear equations using graphs
• Functions and relations
• Writing linear equations
• Writing linear equations in slope-intercept form
• Writing linear equations given the slope and a point
• Writing linear equations given two points
• Fitting a line to data
• Point-slope form of a linear equation
• The standard form of a linear equation (ax+by=c)
• Predicting with linear models
• Solving and graphing linear inequalities
• Solving one-step linear inequalities
• Solving multi-step linear inequalities
• Solving compound inequalities
• Solving absolute-value equations and inequalities
• Graphing linear inequalities in two variables
• Systems of linear equations and inequalities
• Solving linear systems by graphing
• Solving linear systems by substitution
• Solving linear systems by linear combinations
• Applications of linear systems
• Special types of linear systems
• Exponents and exponential functions
• Multiplication properties of exponents
• Zero and negative exponents
• Division properties of exponents
• Scientific notation
• Exponential growth functions
• Exponential decay functions
• Quadratic equations and functions
• Graphing quadratic equations
• Solve quadratic equations by graphing
• Solve quadratic equations by factoring ax^2+bx+c=0
• Applications to real situations
• Polynomials and factoring
• Adding and subtracting polynomials
• Multiplying polynomials
• Solving polynomial equations in factored form
• Factoring x^2+bx+c and ax^2+bx+c
• Factoring using the distributive property
• Rational equations and functions
• Simplifying rational expressions
• Multiplying and dividing rational expressions
• Adding and subtracting rational expressions

• Function concepts
• Definition as a set of ordered pairs, as a rule, compared with relations
• Function notation
• Domain, range
• Independent and dependent variable
• Arithmetic operations on functions
• Inverse of a function
• Piecewise defined functions
• Composition
• Inverse functions

1.       Graphical meaning and in terms of ordered pairs

2.       How to compute

3.       Whether an inverse exists

• Even and odd functions
• The linear transformations and their effect on graphs
• Applications and modeling
• Linear functions and relations
• Slope-intercept and point-slope form
• Graphs and use of a coordinate system
• Geometric interpretation of slope and slope as a rate
• Solving linear equations
• Linear regression
• Linear inequalities in one and and two variables
• Absolute value equations and inequalities - solved by graphing
• Applications and modeling
• Systems of linear equations and inequalities
• Solving algebraically (substitution and elimination) and by graphing
• Use grapher to solve arbitrary systems (not necessarily linear)
• Linear programming
• Graphing in three variables
• Applications and modeling
• Matrix algebra
• Matrix concepts
• Terminology: row, column, identity, inverse
• Calculator use
• Operations
• Addition, subtraction and scalar multiplication.
• Multiplication by calculator
• Multiplication by hand
• Identity and inverse matrices
• Finding inverses by calculator
• Finding inverses using formulas and/or by hand
• Solve systems of equations
• Using row operations by hand
• Using inverses (to solve AX = B)
• Cramer's rule
• Selected applications and modeling: inventory, cost and profit, area of a triangle, equation of line, cryptography, transformations of the coordinate plane: size and scale, reflection, rotation.
• Quadratics
• Terminology: intercept, root, zero, solution.
• Graphing: roots, y-intercept, vertex, symmetric points, axis of symmetry.
• Vertex form
• Solving
• Common factor and quadratic factoring
• Completing the square
• Ways to find the vertex: vertex form, -b/2a, symmetry, graphing calculator
• The quadratic formula
• Relationship between factoring and the quadratic formula
• Relationship between discriminant and roots
• Complex arithmetic
• Arithmetic (add, subtract, multiply, divide) and conjugates
• The complex plane
• Absolute value and distance
• Solving quadratics with complex roots
• Finding a parabola from three points
• Applications and modeling e.g. motion, gravitational constant
• Polynomials
• Vocabulary: Degree, coefficient, leading coefficient, term, nth degree, term, constant term, root=solution=zero=x-intercept, complete factoring
• Multiplying, binomial theorem
• Factoring
• Common factor
• Difference of squares, perfect squares
• Sum and difference of cubes
• Long division algorithm
• Synthetic division
• Finding roots
• The factor/remainder theorem
• The rational roots theorem
• When complete factoring is possible
• Use of grapher to solve
• Theory of graphs and easy curve sketching
• End behavior
• Number of roots
• Turning points/changes in sign
• Finding a function from a graph
• Applications and modeling
• Powers, roots and radicals
• nth roots
• Solving radical equations by graphing
• Applications and modeling
• Rational equations and functions
• Inverse, joint and direct variation
• Solving rational equations by graphing
• Add, subtract, multiply and divide rational expressions
• Vertical asymptotes
• Applications and modeling
• Exponents and logarithms
• Basic laws of exponents, negative and rational exponents, roots
• Logarithm as the inverse of exponentiation
• Logarithmic notation
• Log rules (product, quotient, power and change of base rule)
• Solve exponential equations, with and without calculator
• Solve log equations, with and without calculator
• Find an exponential equation from two points
• Base e, ln
• Graphs of exponential and logarithmic functions
• Applications and modeling e.g. growth and decay, bank interest and depreciation, Ph, Richter scales.