Math Analysis - Trimester 1 - Final Exam Checklist
General Information
The inverse of a 2x2 matrix and the sign matrix will be provided, but you will need to know when and how to use them.
The exam will be similar to the previous exams, expect one question on just about everything.
There will be NO SPARE CALCULATORS OR PENCILS. Please be prepared for the exam.
Be prepared to show your work.
You will be allowed a 3”x2.5” note card on the exam. I will provide you with one in class.
Chapter 1 – Functions
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Know the difference between a relation and a function
Be able to write out the domain and range of a relation
Be able to find the domain of rational (fraction) functions and square root functions
Functions (Evaluate) – Know how to evaluate a function for a number or other function
Functions (Operations) – Know how to add, subtract, multiply, and divide functions (using both notations)
Functions (Composition) – Know how to evaluate a composition at a number or for x (using both notations)
Lines (Graphing) – Know how to graph functions using both the intercepts and the slope/intercept
Lines (Writing) – Know how to write the equation of a line using the slope and a point or two points
Lines (Special Cases) – Know how to write the equation for parallel and perpendicular lines. Spot coinciding lines
Lines (Inequalities) – Know how to graph linear inequalities (solid/dashed lines and shading)
Chapter 2 – Systems and Matrices
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Systems (General) – Know what type of solutions are allowed in systems of equations
Systems (Graphing) – Know how to solve a system of equations by graphing two lines
Systems (Substitution) – Know how to solve a system using substitution
Systems (Elimination) – Know how to solve a system of equations using elimination
Systems (Three Variable) – Know how to solve a system of three equations using double elimination
Matrices (General) – Dimension, elements, and equality
Matrices (Operations) – Compatibility in addition and multiplication. Addition, multiplication, and distribution
Matrices (Determinants) – Know how to find a 2x2 and 3x3 determinant
Matrices (Inverses) – Know how to recognize if an inverse exists, if matrices are inverses, and find a 2x2 inverse
Matrices (Systems) – Solve a 2x2 systems using augmented matrices and inverse matrices
Chapters 4 – Polynomials, Factors, and Roots
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Know how to factor quadratic and quadratic-type polynomials
Know how to factor 4-term polynomials by grouping
Fundamental Theorem of Algebra (FTA) – Know how many real and imaginary roots a polynomial can have
FTA – Know how to write a polynomial in factored and expanded form given real and/or imaginary roots
Remainder and Factor Theorem – Be able to recognize a root of a function based on division
Remainder and Factor Theorem – Be able to factor a polynomial using long and synthetic division
Rational Root Theorem – Be able to use the leading and constant term to determine possible rational real roots
Descartes’ Rule of Signs – Be able to use f(x) and f(-x) to determine possible root combinations