Math 1010 Final Review Know How to… Simplify Add/Subtract Multiply Divide Solve COORDINATE PLANE LINES FACTORING GRAPHING EXPONENTS LOGS Expressions … including: Polynomial, Rational, and Radical Expressions Complex Factions Polynomials Rational Expressions Radical Expressions Polynomials Rational Expressions Radical Expressions Polynomials (Long/Synthetic Division) Rational Expressions Radical Expressions Equations & Inequalities in 1-­‐variable (this includes absolute values) 2x2 linear systems of equations Polynomial Equations by factoring Rational Equations Radical Equations Quadratic Equations (finding all real and complex solutions) Exponential Equations Logarithmic Equations Vocab. (origin, x-­‐axis, y-­‐axis, quadrants,…) Calculate distance mid-­‐point slope of a line Graph a line Write the equation of a line, given… a point on the line and the slope two points on the line a point on the line and the equation of a parallel line a point on the line and the equation of a perpendicular line Factor patterns (perfect squared trinomial, difference of squares, difference/sum of cubes) trinomials with leading coefficient of 1 trinomials with leading coefficient not 1 by grouping with the aide of division and a given factor Recognize a basic library of functions Transformations (vertical/horizontal shifts & reflections) Graph an equation using a table (t-­‐chart) Rules of Exponents Evaluate Logarithms Properties of Logs (Expand/Condense Logarithms) Other Big Ideas… •
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Labels for numbers (Real, Rational, Irrational, Complex, Integer, Natural, Whole…) Know the rules for fractions (Add/Subtract, Multiply, Divide, Simplifying…) Evaluate Real Number expressions using order of operations •
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Be familiar with vocabulary used during semester. Expressions vs. Equations What does it mean to be a SOLUTION? Functions (definition, domain, range, notation, composite, inverse, …) Problem Solving •
Library of Functions… Function Absolute Value Polynomials Constant €
Identity € + b ) General Linear Form ( y = mx
Square General Quadratic Form: €
y = ax 2 + bx + c €
Cube €
€
Rational (fraction of polynomials) Radical Square Root €
€
Cube Root €
Transcendental Functions Exponential €
(has a horizontal asymptote) Logarithmic (has a vertical asymptote) €
€
Equation y = x Domain Range y = c y = x y = x 2 y = x3
f (x)
y=
g(x)
y = x y = 3 x y = a x y = log a x Chapter 1 (1.1-­1.5) Classifying Real Numbers & Subsets of Real Numbers Operations with Real Numbers (add, subtract, multiply, divide, and exponents) Evaluating expressions (and order of operations) Simplifying expressions Verbal and Algebraic expressions (“translating”) Chapter 2 (2.1-­2.5) Understand what it means to be a solution of an equation or inequality. Solving equations and inequalities in one variable (including absolute value equations) Problem Solving (mixture problems, rate problems, work problems, percent problems) Chapter 3 (3.1-­3.4 & 3.6-­3.7) Understand what it means to be a solution of an equation in two variables. The coordinate plane Calculate distance, midpoint, and slope Writing the equation of a line Graphing a line Graphing functions using a table or transformations Functions, Domain/Range, Function notation Chapter 4 (4.1-­4.3) Understand what it means to be a solution for a system of equations Solve 2x2 systems by substitution or elimination Solve 3x3 systems Write a 2x2 or 3x3 system of equations given a “story” Chapter 5 (5.1-­5.6) Know the rules of exponents Polynomial vocabulary (standard form, degree, leading coefficient, constant term) Add/Subtract Polynomials Multiply Polynomials Know the patterns (perfect sq. trinomial, difference of squares, difference/sum of cubes) FACTOR Polynomials Solving Polynomial Equations (Zero Factor Property) Chapter 6 (6.1-­6.6) Simplify Rational Expressions (don’t forget about restrictions) Multiply/Divide Rational Expressions Add/Subtract Rational Expressions Simplify Complex Fractions Long Division & Synthetic Division of Polynomials Factor a polynomial completely with the help of division Solve Rational Equations (Remember to check solutions) Chapter 7 (7.1-­7.6) Rules of Exponents, some new rules relating to rational exponents Simplify Radical Expressions Add/Subtract Radical Expressions Multiply/Divide Radical Expressions (vocab. – conjugate) Solve Radical Equations (Remember to check solutions) Complex Numbers (the imaginary unit i) Chapter 8 (8.1-­8.3) Solve quadratic equations (factoring, square root property, completing the square, Quad. Formula) Chapter 9 (9.1-­9.6) Composite and Inverse Functions Exponential & Logarithmic Functions (recognize from eq. or graph, domain, range, asymptotes) Know properties of Logs Evaluate Logs (without calculator) Expand/Condense Logs Solve Exponential & Logarithmic Equations