### Shears Math 121 Makeup Tests

Makeup tests are subject to updates so check back here right before you take a test. If you miss an exam or unhappy with your results of a regular exam, you may be allowed to replace it with a makeup exam. You are only allowed upto two makeup exams per semester. You are not allowed to retake the final exam. The qualifications to take a makeup exam include scoring a 100% on the corresponding unit graded homework in WebAssign or D2L quizzes. If you do better on the makeup exam, the makeup score will replace your original score. Most makeup exams will be given at the Assessment Center (for online and main campus classes) or at the LCC East testing center (for classes held at LCC East only). Each makeup exam is designed to be taken in one 2 hour block of time. Make sure you take care of personal needs and that you have picture identification with you when you go to take the exam. Testing centers generally do not allow students to take bathroom breaks in the middle of an exam.

Your exam will include all or some of the topics listed in the descriptsions below.

#### Makeup Test 1

- Know the difference between different types of numbers: Complex, Reals, Rationals, Irrationals, Integers, Whole Numbers, and Natural Numbers (sec. 1.1.)
- Given restrictions on a variable, be able to determine the sign of an expression involving that variable and then be able to simplify the absolute value of that expression.
- Know how to work with scientific notation. (sec. 1.2)
- Be able to identify what property of numbers is being used: distributive, associative, and communtative. (Sec. 1.1)
- Be able to translate absolute value as a distance mathematical expressions into words and vice versa.
- Be able to simplify all sorts of rational expressions that involve factors with positive, negative or integer exponents, terms that can be factored and factors that can be cancelled.
- Know all of the techniques of factoring and be able to apply mulitple techniques to a variety of problems.
- Be able to perform operations (addition, subtraction, division, mulitplication, and raise to a power) on rational expressions and factor and simplify to reduce your answer.
- Be able to simplify rational expressions that involve factoring out common factors and reducing. Many of these expressions look messy at a glance.
- Be able to solve a variety of equations for a specifed variable: literal, quadratic, equations that involve factoring, equations that involve just undoing whatever is being done to the variable.
- Be able to solve equations involving rational expressions, radical expressions,
- Be able to simplify epressions involving rational expressions and be able to rationalize denominators.
- Be able to find the standard equation of a circle given endpoints of a diameter or by completing the square on the general equation.
- Be able to solve application problems involving: geometrical (sec. 1.7), mixture (sec. 1.7), rate time - distance (sec. 1.7), time needed to do a job (sec. 1.7), variation (sec. 1.12), unit conversions, and percents.
- Be able to come up with an equation of a line, given 2 points on it, a point and a slope, a point and a parallel line, and a point and a perpendicular line. (sec. 1.10)
- Be able to simplify expressions involving complex numbers.
- Be able to solve equations and inequalities involving absolute values. (sec. 1.5 and 1.8)

#### Makeup Test 2

- Know how to work with function notation and be able to use function notation to evaluate and simplify a function with various types of input values or expressions.
- Know how to calculate the difference quotient when provided with the formula.
- Know how to calculate the net change and the average rate of change when you are not provided with the formula or the definition.
- Know how to identify whether a relation is a function. This applies to relations defined in words, graphically, in an equation, and with a chart or a mapping image.
- Know how to evaluate the domain of algebraic functions involving roots and fractions.
- Know how to work with linear functions and what a linear function is.
- Given a graph involving linear functions, know how to come up with the equation.
- Be able to use linear functions and linear inequalities to represent and solve application problems.
- Know how to graph piecewise defined functions and to get information from a piecewise defined function's graph or definition. Given the graph, be able to come up with the piecewise equation.
- Know how to read a graph and answer questions about where it is increasing, decreasing, and constant as well as where it has local extrema and what those extremeat are.
- Know how to graphically recognize relationship symmetry with respect to the
*x*-axis, the*y*-axis, and the origin and how to justify that symmetry alebraically. - Know how to tell and how to justify whether a function is even, odd, or neither even nor odd algebriacally.
- Given a point on a graph and some information about a relation's or a function's symmetry or even/oddness or transformations, be able to come up with another point on the graph.
- Know how to perform algebra and composition of functions and how to identify the domains of the result.
- Know how to perform algebra and composition of functions at specified values when the functions are given graphically.
- Know how to identify the domains of algebra and composition of functions given graphically
- Know how to find the inverse function and how the graph of a function and the inverse function relate to each other.
- Given a set of transformations, know how a function equation is affected, and how the graph is affected and how to write one function in terms of another function.
- Given 2 graphs where one is gotten by transforming the other, be able to write an equation for one in terms of the other.

#### Makeup Test 3

- Be able to complete the square to convert a quadratic equation from general form to standard form and identify the vertex and axis of symetry.
- Be able to come up with an equation of a polynomial (quadratic and higher degree)when you can identify the zeros, the shapes near the zeros, and one other point on the graph.
- Be able to come up with an equation of a quadratic funcion from the graph when you can identify the vertex and one other point.
- Be able to solve a rational inequality by getting zero on one side and getting the other side completely factored in both the numerator and the denominator.
- Given a polynomial in factored form know how to use the zeros and their multiplicity and how to find the
*y*-intercept to draw a graph of the polynomial with the proper shape near the zeros, the proper axis intercepts, and the proper end behavior. - Be able to use the leading and constant terms of a polynomial to identify end behavior graphically and/or
with limit notation, whether the polynomial crosses above or below the
*x*-axis, and all of the potential rational zeros of that polynomial. - Be able to use leading and constant terms to identify the potential number of extrema, the end behavior,
and the
*y*-intercept. - Know how to do long division and synthetic division, interpret the results, and apply it to factoring a polynomial.
- Know how to use the Intermidiate Value Theorem and when to apply it.
- Know how to fill in the blanks when given the following type notation:
or*y*→ ____ as*x*→ ∞ when the information is given from a graph or an equation.*y*→ ____ as*x*→ 2^{-} - Know how to use the Remainder and Factor Thereoms.
- Know what a conjugate pair is and when to use it.
- Be able to give details about a rational function and use the details to draw the graph.
- Know how the degree of the numerator and denominator gives you a horizontal or slanted asymptote and how to find that asymptote.
- Know how to find the vertical asymptotes and when you get a hole instead of an asymptote.

#### Makeup Test 4

- Know the domain and range of logs and exponential functions.
- Know what values are acceptable for a base of a log or exponential function.
- Know the shape of a basic and exponential and logarithmic graph for both when the base is greater than 1 and less than one.
- Know how to solve both challenging and easy equations involving exponential and logarthmic functions.
- Be able to apply transformations to a log or exponential graph.
- Know the definition of a log and how to convert a logarithmic equation to an exponential equation and vice versa.
- Know the properties of logs and how to expand and how to collapse a log.
- Be able to come up with the formula for a simple growth or decay problem such as those in the handout: Exponential Story Problems
- Be able to come up with the formula for exponetial growth and decay problems. Understand doubling time and half-life.
- Be able to solve application problems involving compound interest. Know the formula or be able to come up with it.
- Understand what APY (annual percentage yeild) is and how it relates to compound interest.
- Be able to use Newton's Law of Cooling to answer questions about an object that is cooling. You may need to use the description of the law and some given information to come up with the equation or you might be given the equation.