Final Review Topics The final is comprehensive and will cover sections: 1.1-­‐1.9, 2.1-­‐2.6, 3.1-­‐3.5, 7.1-­‐7.4, 8.1-­‐8.4, 9.1-­‐9.3, & 9.5. NO calculators will be allowed for this exam. You should bring your uID, a pencil and eraser. Scratch paper will be provided. Big Ideas from Math 1050 I. Functions: a. Definition b. Notation c. Ways to represent 1. Numeric (table) 2. Graphically 3. Algebraic (equation) d. Domain (& Implied Domain), Range e. Intercepts: x-­‐intercepts and y-­‐intercepts f. Operations with functions i. Add/Subtract, Multiply, Divide ii. Simplifying difference quotient g. Composition of functions h. Inverse of a function i. Symmetries i. Even vs. odd functions ii. x-­‐axis symmetry (not a function) j. Types of Functions (Library of Functions) i. Polynomial Functions 1. Lines 2. Parabolas 3. Higher degree Polynomials ii. Absolute Value iii. Square Root iv. Rational Functions v. Exponential Functions vi. Logarithmic Functions vii. Greatest Integer (Other Step Functions) k. Graphing Functions i. Transformations 1. Shifts 2. Reflection 3. Stretch/Shrink ii. Asymptotes 1. Horizontal 2. Vertical 3. Slant II. Systems of Equations (What does it mean to be a solution to a system?) a. Linear b. Non-­‐linear III. Sequence and Series a. Definition, Notation, & general Vocabulary b. Arithmetic i. Recursive & Iterative Formulas ii. Finite Series c. Geometric i. Recursive & Iterative Formulas ii. Finite Series iii. Infinite Series (When can we find the infinite sum?) d. Binomial Theorem i. Counting ii. Pascal’s Triangle IV. Tools: a. Coordinate Plane i. Calculate distance ii. Calculate midpoint iii. Calculate average rate of change iv. Graphs of relations b. Solving Equations i. Linear 1. Slope formula 2. Slope-­‐Intercept form 3. Point-­‐Slope form 4. Write the equation of a line (given 2 pieces of information) ii. Quadratic 1. Vertex (Standard) form 2. Minimum/maximum 3. Axis of symmetry 4. Factoring 5. Complete the Square 6. Quadratic Formula 7. Write the equation of a parabola (given vertex and another point or three points) iii. Higher Order Polynomial 1. End behavior 2. Zeros a. Number of zeros (Fundamental Theorem of Algebra) b. Rational Zeros Test c. Descartes Rule of Signs d.
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Upper/Lower Bound rules Factoring Complex zeros Zeros, factors, x-­‐intercepts iv. Rational v. Radical vi. Exponential vii. Logarithmic Polynomial Division i. Long Division ii. Synthetic Division 1. Remainder Theorem (related to evaluating a function at x=k) iii. Useful for finding Slant Asymptotes (Remember – Asymptotes are lines!) iv. Sometimes useful when factoring or finding zeros of a function Partial Fractions (related to Linear Systems) Complex Numbers i. Definition (i2=-­‐1) ii. Standard Form iii. Powers of imaginary unit i iv. Conjugates v. Operations (Add/Subtract, Multiply, Divide) Matrices i. Related to Linear Systems 1. Augmented Matrix and Row Operations 2. Matrix equations and Using the Inverse of a Matrix ii. As an Algebra 1. Scalar Multiplication 2. Adding/Subtracting 3. Matrix Multiplication 4. Inverse of a Matrix 5. Determinant of a Matrix Properties of Logs & Exponents i. Condensing Logs Expressions ii. Expanding Logs Expressions iii. Simplify Exponential Expression iv. Evaluate Log Expressions V. Models a. Simple Interest (LINEAR) b. Compound Interest (Exponential) c. Exponential Growth or Decay d. Logarithmic e. Logistic Growth f. Gaussian Practice Problems… p. 276-­‐277 #1-­‐23, 25-­‐27, 30-­‐31, 36-­‐40, 42 p. 720-­‐721 #1-­‐4, 8-­‐17, 22-­‐27, 29, 32, 33 p. 117-­‐121 #5, 25, 27, 41, 43, 55, 61, 63, 73, 75, 79, 85, 87, 117, 119, 123, 125, 131, 133, 135, 147, 149 p. 208-­‐211 #5, 23, 31, 33, 35, 37, 47, 51, 55, 63, 67, 73, 75, 83, 85, 89, 91, 93, 95, 101, 111, 113, 115, 129, 131 p. 271-­‐274 #11, 23, 35, 47, 49, 57, 83, 85, 91, 97, 99, 101, 111, 125, 127, 145 p. 563-­‐566 #7, 19, 37, 41, 49, 51, 57 p. 632-­‐636 #5, 13, 19, 21, 37, 41, 49, 53, 57, 69, 73, 85, 89, 95, 103, 105 p. 715-­‐718 #1, 7, 11, 14, 19, 21, 35, 41, 47, 57, 65, 75, 95, 103, 107