Shears Math 121/122/126 Makeup Tests Descriptions
Makeup tests are subject to updates so check back here right before you take a test. If you miss a test or an exam or are unhappy with your results, you may be allowed to replace it with a makeup test/exam. You are only allowed upto two makeup tests (and one makeup exam for math 126) excluding the final. You are not allowed to retake the final exam. The qualifications to take a makeup test/exam include scoring a 100% on the corresponding unit(s) WebAssign or D2L graded homework and takehome skills assignments. You may be asked to show me completed textbook and worksheet homework and/or discuss concepts related to the unit with me. The goal here is for you to actually do better on the makeup test/exam. If you do better on the makeup, the makeup score will replace your original score. If you do worse on the makeup test/exam, your scores will be averaged. It is best if you do well on all homework before the original test and all review problems before the original exam, so you can do well and not need to take a makeup test/exam. Most makeup tests/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).
Your test will include all or some of the topics listed in the descriptsions below and it will be a full length test that takes somewhere between 1 and 2 hours to complete.
Math 121 Unit 0 Makeup Test Review
- 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.
- Be able to simplify expressions involving compound fractions and radicals including rationalize denominators.
- Be able to add, subtract, mutliply, and divide rational expressions.Know all of the techniques of factoring and be able to apply mulitple techniques to a variety of problems.
- Be able to solve application problems involving:
- Be able to simplify expressions involving the complex number i to get the expression in a+bi form.
- Understand Absolute Value as a Distance problems.
- Be able to solve simple inequalities.
- Be able to solve inequalities involving absolute value.
- Be able to solve equations involving radicals.
- Know interval notation.
- Know scientific notation.
- Be able to simplify algebraic expressions involving absolute value when you know just enough information to determine the sign of the expression.
- Know the properites of numbers: associative, distributive, and commutative.
- Know the sets of numbers: Natural Numbers, Whole Numbers, Integers, Real Numbers, and Complex Numbers.
- Know what intersection and union mean and be able to find both when given sets of numbers or objects, or given subsets of real numbers as intervals.
Math 121/126 Unit 1 Makeup Test Review
- Be able to simplify rational expressions that involve factoring out common factors and reducing. Many of these expressions look messy at a glance.
- 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 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.
- Be able to find the standard equation of a circle given endpoints of a diameter or by completing the square on the general equation. Note this invovles several other skills such as find the distance beteen two ponts and finding a midpoint, as well as knowing what a tangent line is.
- Be able to find a point on a line or an axis that is equal distance from two given points.
- 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, or a point and a perpendicular line, or a description such as the set of all points equal ditance from two given points aka the perpendicular bisector. (sec. 1.10)
- Know how to calculate the net change and the average rate of change when you are not provided with the
formula or the definition.
Math 121/126 Unit 2 Makeup Test Review
- Know how to graphically recognize relationship symmetry with respect to the x-axis, the
y-axis, and the origin.
- Know how to justify relationship symmetry alebraically.
- Know how to graphically tell and how to algebraically justify whether a function is even, odd, or neither even nor odd.
- 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
- Know how to identify the domains of algebra and composition of functions given graphically.
- Know how to find the inverse function algebraically.
- Give the graph of a one to one function, be able to draw the graph or select the graph from some choices of the inverse function.
- Be able to identify the domain and range of a function and a functions inverse, when the inverse is a function.
- 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.
- Given a function's points or table of values and a set of transformations, know how to find the new set of points or table of values for the transformed function.
- Given 2 functions equations, graphs, or one function in terms of the other, be able to use words to identify the tranformations needed to get from one function to the other.
- Be able to convert a quadratic equation from general form to standard
form and identify the vertex and axis of symetry to draw the graph.
- 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. Also be able to do this in reverse: given the equation, be able to identify the zeros, their multiplicities, the end behavior, and the y-intercept, and use all of this to draw 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.
- Be able to estimate the solution to a rational inequality by using the graphing feature of your calculator.
- Be able to use the leading and constant terms of a polynomial to identify end behavior, whether the polynomial crosses the y-axis above or below the x-axis, the potential rational zeros of that polynomial, and the potential number of extrema.
- Know how to do long division and synthetic division, interpret the results, and apply it to factoring
- 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:
y → ____ as x → ∞ or
y → ____ as x → 2-
when the information is given from a graph or an equation.
- 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.
Math 121/126 Unit 4 Makeup Test Review
- Know the domain and range of logs and exponential functions and their shapes.
- 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.
Math 122/126 Unit 5 Makeup Test Review
- Be able to solve right triangles.
- Be able to solve application problems involving right triangles.
- Know your way around a unit circle. I.e. given a point, be able to find other points relative to it in terms of the angle they land at and the angle should be in terms of the original angle and π, etc. For example given that the P(α) = (a, b), then P(π/2 - α) = (b, a). Also, given that P(β) = (3/5, 4/5), then P(π − β) = (-3/5, 4/5). You should be able to plot these points on a unit circle.
- Know the exact values of the trig functions at key values on the unit circle.
- Be able to find the angle between a line and the x-axis when the line is given in y=mx + b form.
- Be able to use the definition of radians to find either an arc length, radius, or an angle when given the other two. The angle could be given or asked for in radians or degrees.
- Be able to solve an application problem where you need to find an angular velocity, linear speed, and/or revolutions per unit time.
- Given the trig function of an angle and an interval that the angle is in or the sign of another trig function, be able to find the angle.
- Be able to find the trig functions of an angle when one trig function is given and the quadrant that the angle lands in is given.
- Given a trig function at one point on the unit circle, be able to find other trig functions at other points on the unit circle by using the symmetries of the circle.
- Given a trig function's value and another trig function's sign, be able to find the values of other trig functions.
Math 122/126 Unit 6 Makeup Test Review
- Be able to find the essential information of a trig graph from its equation such as amplitude, period, and phase shift.
- Be able to match trig functions to their graphs with basic transformations.
- Be able to graph special cases or match a special case graph to its equation. The special cases that we studied this semester are the addition of ordinates case and the multiplication or ordinates case.
- Understand even and odd functions and be able to apply that concept to trig functions.
- Be able to find inverse trig function values both exactly by hand and approximately with a calculator.
- Be able to factor a trig expression and simplify using an identity.
- Given an equation involving x and a trig function, be able to write another trig function in terms of x.
- Be able to apply the sum, difference, double, and/or half angle formula to find a trig function at a specified value exactly.
- Given information about a trig function of an angle and what quadrant it is in, be able to find another trig function of double or half of the angle.
- Be able to evaluate composed trig functions and inverse trig functions. You should also be able to do this when there is a sum or difference of trig functions involved as well as when there is a half or double angle formula involved. You should be able to do this with numbers or just expressions in terms of a variable.
- Be able to manipulate trig expressions and prove trig identities.
- Be able to solve a triangle for all possible solutions given three pieces of information.
- Be able to find the area of a triangle.
Math 122/126 Unit 7 Makeup Test Review
- Be able to solve trig equations involving finding all solutions and solutions in a specified interval exactly when possible and using a calculator when it is not possible. Even when you are using a calculator you need to know how to get the rest of the solutions after you find the first solutions with your calculator.
- Be able to convert a complex number given in a + bi form to trigonometric form (rcis θ) and vice versa.
- Be able to graph complex numbers.
- Be able to apply the properties of multiplication and division of complex numbers in trigonometric form to multiply or divide two complex numbers and simplify the result.
- Be able to find the angle between two given vectors and to represent it graphically.
- Be able to to identify a point on a polar grid with both positive and negative r values.
- Be able to convert a rectangular point to a polar point and vice versa.
- Be able to convert a polar equation into a rectangular equation or vice-versa.
- Be able to solve a vector equation for a specified vector when the other vectors in the equation are given. Also be able to represent this vector sum graphically on a rectangular grid.
- Be able to solve application problems. Your reading skills should be good enough that you can draw a picture from the descirption and then use your triangle solving skills or vector skills to find the needed information to answer the question.
- Be able to solve application problems with matrices and your calculator.
- Be able to translate a partially reduced row echelon matrix back into a set of equations and solve the rest of the way by hand.
- Know how to get a specified zero in a 2 by 3 matrix and be able to tell how to get that zero using row notation as follows:
- Be able to come up with a set of parametric equations from a given rectangular linear equation with restrictions on how the points are traced out by specific values of t.
- Be able to graph in the x-y plane a graph that is generated from a set of parametric equations. You may use your calculator to assist.
- Be able to convert a set of parametric equations involving trig functions, to a rectangular equation.
- Be able to find the equation of a conic section when given some information about the conics characteristics such as focus or foci, directrix or sum constant or difference constant, etc.
- Be able to put a conic equation given in general form into standard form and know what kind of conic it is.
- When given a conic equation in standard form, be able to tell where its key characteristics are located.
- Be able to come up with the equation of a conic when its information is given to you in a manner similar to its definition, e.g. "The set of all points in a plane that are ...."
- Expect to see an application problem involving a conic section.
- Be able to graph or match graphs of conic equations.
Math 122/126 Unit 9 Makeup Test Review
- Be able to find terms of a recursively defined sequence.
- Be able to find terms fo an explicitly defined sequence.
- Understand summation notation and be able to evaluate a simple summation by hand.
- Understand summation properties and be able to evaluate a summation using the properties of summation for both simple and complicated problems.
- Be able to find a specific term of a binomial expansion.
- Be able to use Pascal's Triangle or the Binomial
Theorem to completely expand a binomial expression raised to a power.
- Be able to identify arithmetic and geometric sequences and be able to find recursive and explicit formulas for such sequences.
- Be able to calculate finite and infinite sums for arithimetic and geometric sequences when they exist. Know when a sequence has a sum and when it does not.
- Understand factorial and combination notation and be able to evaluate expressions involving those notations.
- Be able to solve application problems that involve finite or infinite arithmetic or geometric sequences.
- Be able to solve a variety of counting problems.
Math 126 Exam 1 Review |
Math 126 Exam 2 Review |
Math 126 Exam 3 Review
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Last Update: November 27, 2017