Which Mathematics Course Should You Take? August 22, 2018 Which mathematics course you should take depends on your current mathematics skill level

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1 Which Mathematics Course Should You Take? August, 018 Which mathematics course you should take depends on your current mathematics skill level and your intended major. This is a conversation you should have with your adviser, or contact Professor Robertson at droberts@umn.edu or for more information. In general, if you have successfully completed 3 years of high school mathematics, including introductory algebra, geometry, and intermediate algebra then you are officially ready to take a college-level mathematics course. However, having passed these prerequisite courses does not necessarily mean that you still know the material. If you are in doubt, contact your adviser to arrange for a mathematics placement test and also consult the Why Math Placement link at In the same way that it makes no sense to register for Spanish III if you do not remember Spanish I and II, registering for College Algebra or Precalculus if you do not remember high school algebra is a recipe for failure. If you need a review of high school algebra, consider CI 083 Algebra Review (0 credits, class size 5, computer mediated). This course covers the essentials of high school algebra including order of operations, simplifying epressions, solving linear equations and inequalities, solving absolute value equations and inequalities, X-Y graphing, introduction to relations and functions, equations of lines, solving systems of linear equations, integer and rational eponents, factoring polynomials, simplifying rational epressions (fractions), solving rational equations, and simplifying radical epressions. Earning an C or higher in this course should prepare you well enough for College Algebra or Precalculus. The following courses are the ones most liberal arts U students take as their first college-level mathematics course. Choose the course that is right for you in terms of your major and interests. Each of these courses satisfy the Mathematical Thinking Diversified Core portion of the Liberal Education requirements of the University of Minnesota. CI 1806 College Algebra through Modeling (3 credits, class size 30). In this course you will study college algebra and create mathematical models (equations and graphs) that describe real world data and situations. The models are used to make predictions, to evaluate errors, and to link observed phenomena with algebraic processes. The course is both theoretical and practical. It focuses on applications of linear, polynomial, rational, eponential, logarithmic, and logistic functions and includes some probability. For more information contact Professor Staats (staats@umn.edu). Math 1031 College Algebra and Probability (3 credits, class size 150). This is a third course in algebra and analytic geometry. Probability makes up about a third of the course. Instruction is by large lecture (MWF) and smaller discussion groups (Tu & Th). Smaller sections that meet two days per week are available in the evenings. For more information contact Professor Mosher (mosher@umn.edu). Math 1051 Precalculus I (3 credits, class size 150). This course eamines the behavior of functions including inverses, transformations, and compositions with particular attention to linear, quadratic, polynomial, rational, eponential, and logarithmic functions and their graphs. Instruction is by watching videos at home and then engaging in problem solving in large lecture (MWF) and smaller discussion groups (Tu & Th). For more information contact Professor Weimerskirch (weim004@umn.edu). After taking CI 1806 or Math 1031 or Math 1051 you will be prepared to take Math 1151 Precalculus II or Math 114 Short Calculus. However, Math 1051 is the best preparation for those two courses because it is specifically designed to lead students to calculus.

2 Which Mathematics Course Should You Take? page Problems You Should Be Able To Do Before Taking College-level Mathematics. 1. Simplify: Calculate the area of the shape shown. It is an equilateral triangle on top of a. The height of the is 4 feet. The perimeter of the entire shape is 14 feet. Round your answer to the nearest tenth. 3. Epand and simplify: 3 4. Factor completely: Reduce to lowest terms: Perform the indicated operations and simplify: Solve: Simplify completely: 4 3 y Rationalize the denominator and simplify: Find the equation of the line that passes through the points 3, and 1, 6. Answers: sq ft = y y y 4 The complete solutions are on the net 5 pages.

3 Which Mathematics Course Should You Take? page 3 Solutions to the Sample Problems 1. Follow the order of operations for simplifying arithmetic epressions: Step 1 Simplify epressions inside grouping symbols, which include parentheses ( ), a brackets [ ], the fraction bar, absolute value bars, and radicals n a. b Step Simplify eponents, roots, and absolute values. Step 3 Simplify multiplication and division, working left to right. Step 4 Simplify addition and subtraction, working left to right total = + triangle We know the formulas for areas: triangle = length width 1 base height To find the area of the we need to figure out the width. Since the triangle is equilateral, all three of its sides have the same length. So, let = length of a side of triangle.

4 Which Mathematics Course Should You Take? page 4 We are given the perimeter is 14 feet. We can write: Perimeter = sideof triangle + height of + widthof + height of + sideof triangle The width of the is the same as the base of the triangle, which is. So, we can write: Now we know the width of the is and the length is 4: = length width 4 8 To find the area of the triangle we need to know its base (it is = ) and its height. To find the height we note that we can form a right triangle where the hypotenuse is (length of the side of the triangle), the base is 1 (half the bottom side of the triangle) and the height, which we want to find h 3 h 3 h 3 h h Since h is a height, we ignore the negative root. So, we can write: triangle bh total7.7 triangle We cannot cube each term inside the parentheses. We must epand this and then use FOIL Factor completely: First, look for the factors that are common to each term. There are none. Since has the form a b c, find two integers whose product is a c and whose sum is b, replace the b term using these integers, and factor by grouping. For this problem a c = (10)( 18) = 180.

5 Which Mathematics Course Should You Take? page 5 Here are the pairs of positive integers factors whose product is 180: 1180, 90, 3 60, 4 45, 5 36, 6 30, 7 na, 8 na, 9 0, 10 18, 11 na, 1 15 The pair whose sum or difference is 3 is 1 and 15. That is, and Now, replace the middle term using the two integers we just found Now, factor by grouping: Factor the numerator and the denominator and then cancel common factors: Find the LCD by factoring each denominator and multiplying the largest group of each factor: LCD Now convert each fraction into an equivalent fraction but with the LCD as the denominator:

6 Which Mathematics Course Should You Take? page 6 7. First, find the LCD of all the terms. 6 = 3, 10 = 5, and is prime so the LCD is 3 5 = 30. Then, clear the fractions by multiplying each term by the LCD of all the fractions and solve using the properties of equality We can check this answer by replacing with 3 in the original equation and seeing if a true statement results ? ? Yes 8. First, write 3 as 5 so everything is in eponential form: 3 y y Since this is a 4th root, divide each eponent by 4. The quotients are the eponents of the factors outside the radical while the remainders are the eponents of the factors inside the radical. 5 : 5 4 1with remainder 1 y 16 9 : with remainder 0 : 9 4 with remainder 1 So, 3 y y y y y Multiply numerator and denominator by the conjugate of the denominator

7 Which Mathematics Course Should You Take? page First, find the slope: m y y y Net, find the y-intercept using the slope-intercept formula y m b and one of the given points. We will use 3,. y m b y b 3 b 6 b 4 b So, the equation of the line is y 4.