Mathematics

The math placement exam is used to place students into the math course that corresponds to their current math skill level. All entering freshmen and transfer students who have not yet obtained either a 23 subscore on the math portion of the ACT or a grade of "C" or better in a transfer math course are required to take this placement exam.

There is no charge to take the placement exam.

A subscore of 23 in the math portion of the ACT will place a student into College Algebra. The ACT is not used to place a student into any other level of Mathematics at SCC.

An ACT product called Compass is used as our placement tool. On this placement exam, the on-screen calculator may be used. However, knowledge of basic mathematical concepts including computation with fractions, decimals, and signed numbers is still a necessary pre-requisite skill. We recommend that all high school students continually review basic computation skills and take math their senior year in order to maintain and retain their math skills prior to entering college. The following Web sites provide practice exercises for preparing for our Compass placement exam. Try working these exercises without using your calculator.

1. http://www.testprepreview.com/ (Select Compass Practice, then choose appropriate modules)
2. www.act.org/compass/sample/ (Select mathematics then select content areas to view short sample tests OR select PDF versions which provide more sample questions)
3. www.cs.umsl.edu/PlacementTest/ (This is the University of Missouri-St. Louis Math Department Web page with practice exercises)
4. mathonline.missouri.edu (This math site is offered through the University of Missouri-Columbia and provides many sample tests)

A subscore of 23 in the math portion of the ACT will place a student into College Algebra. The ACT is not used to place a student into any other level of mathematics at SCC.

A score lower than 23 in the math portion of the ACT will require a student to take the placement exam at SCC.

In order to place into a higher-level math course than College Algebra, a student will need to take the placement exam or provide a transfer credit with a passing grade in the prerequisite course.

There is no charge for the placement exam.

The placement exam may be taken a second time if the student would like to try to place into a higher level course. If the desired placement is not obtained on this second attempt, the student can make a final appeal with the mathematics department chair. Please call the division office coordinator at 636-922-8496 to set up an appointment.

1. The American Mathematical Society
2. The Mathematical Association of America
3. The American Mathematical Association of Two-Year Colleges
4. The American Statistical Association

Pre-algebra is a basic course in mathematics which is designed to prepare the student for advancement into Beginning Algebra. You need an 80% or higher in Pre-algebra to advance to Beginning Algebra.

Exit Skills

1. Add, subtract, multiply and divide integers, fractions and decimals.
2. Evaluate algebraic expressions and formulas.
3. Simplify numeric and algebraic expressions using the order of operations.
4. Solve multiple step linear equations in one variable with integers, fractions and decimals.
5. Solve applications using linear equations in one variable.
6. Solve applications using ratios and proportions.
7. Convert among percent, fraction and decimal notations.
8. Solve applications using percent equations.
9. Solve right triangles using the Pythagorean Theorem.
10. Determine the area and perimeter of basic geometric shapes.
11. Convert within and between the English and Metric systems.
12. Graph linear equations by plotting points.

Objectives

1. Review fractions, order of operations, simplifying expressions, real numbers and the number line, real number operations and real number properties.
2. Solve linear equations and inequalities including applications.
3. Graph linear equations and write the equation of a line.
4. Simplify expressions using rules for integer exponents. Solve applications using scientific notation.
5. Add, subtract, multiply and divide polynomials.
6. Factor polynomials, including all special product forms.
7. Solve quadratic equations and applications using the factoring method.
8. Add, subtract, multiply, divide and simplify rational expressions including complex fractions.
9. Solve equations with rational expressions including applications.

Exit Skills

1. Construct truth tables and use them to determine the validity of an argument.
2. Use estimation to determine whether an answer is reasonable.
3. Solve financial applications of compound interest, loans and investments.
4. Develop a strong number sense by putting numbers in perspective, by making comparisons and by identifying misleading information.
5. Critically evaluate statistical studies and graphs.
6. Describe statistical data using measures of center and spread.
7. Solve basic probability applications using multiplication and addition.
8. Use mathematical models to solve linear and exponential applications.
9. Solve basic right triangle applications using trigonometric functions.
10. Recognize the connections between mathematics and other disciplines such as art, politics, nature or business.

Objectives

1. Demonstrate critical and logical thinking skills by analyzing mathematical arguments.
2. Demonstrate the ability to make basic financial decisions.
3. Analyze statistical studies and demonstrate knowledge of the basic concepts of probability.
4. Demonstrate the ability to synthesize quantitative data by putting numbers in perspective, by making reasonable estimates, by using mathematical models to solve applications and by solving right triangle applications.
5. Develop an understanding that mathematics is meaningful and recognize the connections between mathematics and other disciplines.

Exit Skills

Students who successfully complete Math 108 will meet the following objectives:

1. Number and Operations
   1. Recognize and convert among equivalent representations of the same number.
   2. Justify and calculate using non-standard algorithms.
   3. Explain and apply the meaning of the = sign.
   4. Calculate reasonable estimates of complex calculations.
   5. Use properties of real number operations to rearrange and/or simplify indicated operation(s) for mental calculation.
   6. Compare and contrast estimation and mental math and discuss when each is appropriate.
2. Algebraic Relationships
   1. Recognize a linear function from its graph, table of values, equation or description.
   2. Model and solve problems that yield linear, inverse or exponential functions.
   3. Distinguish between linear and non-linear relationships.
   4. Compare, contrast and generalize patterns represented graphically or numerically using both explicit and recursive definitions.
   5. Use Bar modeling to solve word problems.
3. Geometric and Spatial Relationships
   1. Solve problems using the Pythagorean Theorem.
   2. Reposition shapes under formal transformations.
   3. Recognize, categorize and describe symmetry with respect to a line, point or angle of rotation.
4. Measurement
   1. Analyze precision and accuracy in measurement situations by determining the number of significant digits.
5. Data and Probability
   1. Formulate questions, design studies and examine data about a characteristic.
   2. Compare and contrast different representations of the same data, including graphs and measures of center.
   3. Determine measures of Center and spread (Mean, median, mode, outliers, range, interquartile range) of data.
   4. Create stem and leaf plots of data.
   5. Create box and whisker plots from the five-number summary of data.
   6. Conjecture about possible relationships between two characteristics of a sample and/or the results of experiments.

Exit Skills

1. Write equations of lines, graph linear functions, solve applications using linear models and graph a linear inequality in two variables.
2. Determine whether an equation is a function, identify the domain and range of a function, perform the operations of addition, subtraction, multiplication and division of functions, and find the composition of functions.
3. Solve linear systems (2 x 2’s) using the graphing, substitution and elimination methods. Solve linear systems (3 x 3’s) using the elimination method. Solve applications of linear systems.
4. Perform set operations.
5. Solve compound inequalities, absolute value equations and absolute value inequalities.  Write solutions in interval notation and graph solutions on a number line.
6. Evaluate radicals, simplify expressions containing radicals and rational exponents, and perform operations with radical expressions including addition, subtraction, multiplication and division. Solve equations containing radicals. (Radical expressions and equations to be simplified and solved include indices of both 2 and greater.)
7. Recognize nonreal complex numbers, perform operations with nonreal complex numbers including addition, subtraction, multiplication and division, and find powers of i.
8. Solve quadratic equations and their applications using the square root property, factoring method, completing the square and the quadratic formula. Solve equations of quadratic form. Graph and analyze quadratic functions and solve applications using quadratic models.
9. Determine the inverse of a basic function and identify its domain and range. Recognize and graph basic exponential and logarithmic functions. Solve basic exponential and logarithmic equations. Use properties of logarithms to write alternative forms of logarithmic expressions.
10. Use the method of completing the square to find the center-radius form of a circle and sketch its graph.

Exit Skills

1. Use definitions, postulates and previously proven theorems to prove basic geometric relationships deductively, using a two-column “statements and reasons” format.
2. Prove the congruence of two triangles by using sss, sas, asa or aas as appropriate.
3. Prove the congruence of two line segments or angles by locating them in various triangles and then establishing the congruence of those triangles.
4. Use the method of indirect proof to establish the truth of a proposition by demonstrating that the assumption of the truth of its negation results in a contradiction.
5. Prove various geometric propositions that involve quadrilaterals, parallel lines, circles and parts of circles by using their definitions and properties.
6. Prove the similarity of two triangles by using aa.
7. Recognize and use appropriately the various proportions that are valid when two polygons are known to be similar.
8. State the Pythagorean theorem and use it to solve right triangles.
9. State and use the relationship that exists between the lengths of the sides of any 30-60 right triangle.
10. State and use the relationship that exists between the lengths of the sides of any 45-45 right triangle.
11. Define the three primary trigonometric functions of an acute angle of a right triangle and use these trigonometric functions to solve word problems.
12. Find the areas of the common shapes of plane geometry, including being able to find the area of a triangle by using Heron’s formula.
13. Find the slope of a line and use it to write an equation of the line.
14. Graph linear equations.
15. Find the distance between two points in a rectangular coordinate system and find the coordinates of the point that is midway between the two points.
16. Use a compass and a straightedge to perform the fundamental geometric constructions.

Exit Skills

NC = no calculator suggested
WC = with calculator suggested

1. (NC) Convert angles between radian and degree measure.
2. (NC) Define the six trig functions of an angle within a right triangle.
3. (NC) Know the six trig functions of 30, 45, 60, 90 degrees (where defined) and be able to find the trig functions of other angles that have these as the reference angle.
4. (WC) Solve applications using trig functions and the Pythagorean Theorem.
5. (WC) Solve right triangles using trig functions, inverse trig functions and the angle sum in any triangle being 180 degrees.
6. (NC) Given one trig function value in a particular quadrant, find the remaining five trig functions.
7. (NC) Know the circular definition of the trig functions.
8. (WC) Graph the six trig functions over one complete period, including the following information where appropriate: amplitude, period, phase shift, intercepts, any maximum or minimum points and domain and range.
9. (NC) Know the domain and range restrictions for the inverse trig functions and find inverse trig function values of “special” values.
10. (NC) Know the following identities (or be able to derive quickly): six reciprocal identities, three Pythagorean identities, six opposite angle identities, trig functions of a sum or difference of angles, trig functions of a double and half angle. Use these to prove identities using a variety of methods such as substitution, factoring, common denominators and rationalizing using conjugates.
11. (NC) Solve computation problems using identities.
12. (WC) Solve trig equations by using identities, factoring and the quadratic formula.
13. (WC) Know the Law of Sines (including the ambiguous case) and use to solve appropriate triangles.
14. (WC) Know the Law of Cosines, to solve appropriate triangles.
15. (WC) Solve applications using Laws of Sines and Cosines.
16. (WC) Find the area of sectors and triangles.
17. (WC) Graph, add and subtract vectors and solve associated applications.
18. (NC) Convert between rectangular and polar coordinates and graph polar equations.
19. (WC) Use DeMoivre’s Theorem and the Nth-Root Theorem when working with complex numbers.

Exit Skills

The following exit skills were developed with the assumption that the student has a good grasp of all intermediate algebra skills and that word problems and applications are an integral part of any algebra course.

1. Solve quadratic equations, equations of quadratic form and miscellaneous equations.
2. Solve quadratic, rational, compound and absolute value inequalities writing solutions in interval notation.
3. Graph families of functions using transformations and state domain and range in interval notation.
4. Solve higher-degree polynomial equations using the Remainder, Factor, Rational Root, Conjugate Root, and Bounds Theorems and graph polynomial functions.
5. Graph rational functions identifying vertical and horizontal asymptotes.
6. Find the rule for the inverse of a function and graph the inverse.
7. Graph exponential and logarithmic functions.
8. Solve exponential and logarithmic equations.
9. Solve systems of non-linear equations and inequalities.
10. Solve 3 x 3 systems of linear equations using Gaussian elimination.
11. Perform matrix algebra operations including addition, subtraction, and multiplication.
12. Find terms of a sequence using recursion and explicit formulas, and find the nth term formula for arithmetic and geometric sequences.
13. Use summation notation, find the sum of a finite arithmetic series and find the sum of finite and infinite geometric series.

Objectives

1. Identify and graph families of functions, find their inverses and zeros and solve related equations.
2. Solve systems of equations, linear and non-linear, using an appropriate method including matrix methods.
3. Distinguish between general varieties and special types of sequences and series and use appropriate formulas for finding summations and nth terms.

Exit Skills

The following exit skills were developed with the assumption that the student has a good grasp of all intermediate algebra skills and that word problems and applications are an integral part of any algebra course.

1. Solve quadratic equations, equations of quadratic form and miscellaneous equations.
2. Solve quadratic, rational, compound and absolute value inequalities writing solutions in interval notation.
3. Solve higher-order polynomial equations using the Remainder, Factor, Rational Root and Conjugate Root Theorems.
4. Graph rational functions identifying vertical and horizontal asymptotes.
5. Find the rule for the inverse of a function and graph the inverse.
6. Graph exponential and logarithmic functions.
7. Solve exponential and logarithmic equations.
8. Solve systems of non-linear equations and inequalities.
9. Solve 3 x 3 systems of linear equations using Gaussian elimination, inverse of a matrix and Cramer’s Rule.
10. Perform matrix algebra operations including addition, subtraction, products and the evaluation of determinants by the minor-cofactor method.
11. Graph conic sections including circles, parabolas, ellipses and hyperbolas.
12. Find terms of a sequence using recursion and explicit formulas, and find the nth term formula for arithmetic and geometric sequences.
13. Use summation notation, find the sum of a finite arithmetic series and find the sum of finite and infinite geometric series.

Objectives

1. Identify and graph families of functions, find their inverses and zeros and solve related equations.
2. Solve systems of equations, linear and non-linear, using an appropriate method including matrix methods.
3. Recognize equations of and sketch a graph of the conic sections.
4. Distinguish between general varieties and special types of sequences and series and use appropriate formulas for finding summations and nth terms.

Exit Skills

The following exit skills were developed with the assumption that the student has a good grasp of all intermediate algebra skills and that word problems and applications are an integral part of any algebra course.

1. Solve quadratic equations, equations of quadratic form and miscellaneous equations.
2. Solve quadratic, rational, compound and absolute value inequalities writing solutions in interval notation.
3. Graph families of functions using transformations and state domain and range in interval notation.
4. Solve higher-degree polynomial equations using the Remainder, Factor, Rational Root, Conjugate Root Theorems, Bounds Theorem, and the Intermediate Value Theorem.
5. Simplify difference quotients including polynomial, rational and radical functions.
6. Graph rational functions identifying vertical and horizontal asymptotes, including use of limits.
7. Find the rule for the inverse of a function and graph the inverse.
8. Graph exponential and logarithmic functions.
9. Solve exponential and logarithmic equations.
10. Solve systems of non-linear equations and inequalities.
11. Solve 3 x 3 systems of linear equations using Gaussian elimination, inverse of a matrix and Cramer’s Rule.
12. Perform matrix algebra operations including addition, subtraction, products and the evaluation of determinants by the minor-cofactor method.
13. Graph conic sections including circles, parabolas, ellipses and hyperbolas.
14. Find terms of a sequence using recursion and explicit formulas, and find the nth term formula for arithmetic and geometric sequences.
15. Use summation notation, find the sum of a finite arithmetic series and find the sum of finite and infinite geometric series.
16. Use the binomial theorem to expand a binomial.

Objectives

1. Identify and graph families of functions, find their inverses and zeros and solve related equations.
2. Solve systems of equations, linear and non-linear, using an appropriate method including matrix methods.
3. Recognize equations of and sketch a graph of the conic sections.
4. Distinguish between general varieties and special types of sequences and series and use appropriate formulas for finding summations and nth terms.

Exit Skills

1. Use a variety of problem solving techniques, including inductive and deductive reasoning.
2. Make investigations of mathematical ideas and be able to use patterns and observations to make conjectures.
3. Question the reasonableness of a solution in relation to the original problem.
4. Approximate mental calculations and develop estimation skills.
5. Demonstrate a basic understanding about the nature of numbers used in mathematics and have an appreciation of our numeration system in terms of some historical numeration systems. Demonstrate a facility in using the operations of the real numbers and an understanding of the properties of real numbers.
6. Use variables to represent mathematical quantities and expressions; represent mathematical functions and relationships using tables, graphs and equations.
7. Demonstrate an understanding of basic geometric concepts such as parallelism, perpendicularity, congruence, similarity and symmetry.

Objectives

1. Recognize and use a variety of problem solving techniques that include inductive and deductive reasoning.
2. Demonstrate problem-solving techniques with a variety of problems including financial management, probability and statistics.
3. Demonstrate an understanding of the nature of numbers and develop an appreciation of our numeration system including its properties and operations.
4. Demonstrate an understanding of basic geometric and trigonometric concepts and apply those concepts to solve problems.

Exit Skills

The following exit skills were developed with the assumption that the student has a good grasp of all intermediate algebra skills and that word problems and applications are an integral part of any algebra course.

1. Solve quadratic equations, equations of quadratic form and miscellaneous equations.
2. Solve quadratic, rational, compound and absolute value inequalities writing solutions in interval notation.
3. Graph families of functions using transformations and state domain and range in interval notation.
4. Solve higher-degree polynomial equations using the Remainder, Factor, Rational Root, Conjugate Root Theorems, Bounds Theorem, and the Intermediate Value Theorem.
5. Simplify difference quotients including polynomial, rational and radical functions.
6. Graph rational functions identifying vertical and horizontal asymptotes, including use of limits.
7. Find the rule for the inverse of a function and graph the inverse.
8. Graph exponential and logarithmic functions.
9. Solve exponential and logarithmic equations.
10. Solve systems of non-linear equations and inequalities. 
11. Solve 3 x 3 systems of linear equations using Gaussian elimination, inverse of a matrix and Cramer’s Rule.
12. Perform matrix algebra operations including addition, subtraction, products and the evaluation of determinants by the minor-cofactor method.
13. Graph conic sections including circles, parabolas, ellipses and hyperbolas.
14. Find terms of a sequence using recursion and explicit formulas, and find the nth term formula for arithmetic and geometric sequences.
15. Use summation notation, find the sum of a finite arithmetic series and find the sum of finite and infinite geometric series.
16. Use the binomial theorem to expand a binomial.
17. Define the trigonometric functions using the circular and triangular definitions.
18. Convert between degree and radian measure. 
19. Locate and find trigonometric functions of special angles and angles corresponding by reference.
20. Use amplitude, period, phase shift and vertical shift to graph trigonometric equations.
21. Identify the range restrictions for the inverse trigonometric functions and find inverses.
22. Prove and use basic, Pythagorean, angle sum and difference, double angle and half angle identities to simplify expressions, verify identities and solve conditional equations.
23. Graph, add and subtract vectors and solve associated applications.
24. Prove and use the Law of Sines and the Law of Cosines, and solve associated applications.
25. Convert between rectangular and trigonometric form of complex numbers.
26. Multiply and divide complex numbers in trigonometric form, and use DeMoivre’s theorem and the N^th-Root theorem to find integer powers and roots of complex numbers.
27. Convert between rectangular and polar coordinates and equations and graph common polar equations.

Exit Skills

1. Understand the difference between inferential and descriptive statistics. Use the various sampling techniques including random sampling, stratified, random, cluster, and systematic sampling.
2. Use graphs to describe and interpret data sets including frequency histogram, frequency polygon, ogive, and pie charts.
3. Calculate measures of central tendency (mean, median and mode), measures of variation (range, variance, standard deviation), and measures of position (quartiles and percentiles).
4. Use the Fundamental Counting Rule, combinations and permutations to calculate probabilities.
5. Understand basic terminology and concepts of probability including sample spaces, complementary events, independent events and mutually exclusive events.
6. Calculate probabilities and expected values using the addition rule, multiplication rule and conditional probability.
7. Know properties of the Binomial Distribution and be able to calculate binomial probabilities.
8. Know properties of the Normal Distribution including the Empirical Rule. Calculate probabilities using the Normal Distribution. Use the central limit theorem and approximate the Binomial Distribution using the Normal Distribution.
9. Calculate confidence interval estimates for the mean of a population, for proportions and for variance. Determine sample size needed to obtain confidence levels.
10. Perform hypothesis tests for mean, proportion, variance, difference between two means and difference between proportions.
11. Test differences in three or more means using one-way analysis of variance (ANOVA).
12. Use correlation and perform a simple linear regression.
13. Use a scientific calculator and/or computer software to perform statistical analyses and assist in decision-making.

Objectives

1. Employ sampling techniques to collect data and summarize data using graphs and descriptive statistics.
2. Solve counting and probability applications.
3. Determine whether or not a variable conforms to a particular probability distribution including the binomial distribution, normal distribution, F-distribution or t-distribution.
4. Compute confidence interval estimates and perform hypothesis tests pertaining to one and two samples. Test multiple samples via analysis of variance.
5. Perform a linear regression analysis. 

Exit Skills

1. Perform the various algebraic and trigonometric computations encountered in calculus.
2. Demonstrate understanding of the concept of the limit of a function – from both a graphical perspective and an algebraic perspective – and the role of the limit concept in defining continuity.
3. Find derivatives by using the basic definition involving a limit.
4. Find derivatives of polynomial, rational, radical, and trigonometric functions, as well as composites of such functions, by using the power rule, the product rule, the quotient rule, the chain rule, and implicit differentiation, as appropriate.
5. Use both the prime notation and the Leibniz notation for derivatives.
6. Use first and second derivatives, together with algebraic analysis, to produce an accurate graph of a given function, identifying all asymptotes, symmetry, relative maximums and minimums, stationary and inflection points, and intervals on which the function is increasing, decreasing, concave up, and concave down.
7. Use derivatives to solve problems that involve related rates.
8. Use differentials, when appropriate, in problem-solving.
9. Evaluate definite integrals by using the basic definition involving the limit of a Riemann sum.
10. Evaluate integrals, using substitution where appropriate.
11. Use integration to solve simple differential equations.
12. Use integration to find areas of plane regions, lengths of plane curves, surface areas of solids of revolution, and volumes of such solids by disk, washer, and shell methods.
13. Use calculus in applications involving rectilinear motion, moments and centroids of plane regions, fluid force, and work.

Exit Skills

1. Articulate and implement problem-solving strategies, including
1. Look for a pattern.
2. Examine a related problem.
3. Examine a simpler case.
4. Make a table.
5. Make a diagram, including bar modeling.
6. Guess and check.
2. Examine and articulate the logic of the base 10 number system by comparing/contrasting it with various number systems.
3. Describe and complete operations on sets.
4. Examine the properties of operations on real numbers and their subsets of whole numbers, integers, and rational numbers.
5. Model situations that involve numerical operations.
6. Examine standard and non-standard algorithms for calculating operations on real numbers.
7. Compute in bases other than 10, including 2, 5, and 12, and translate numbers from and to base 10 and other bases.
8. Develop strategies for calculating numerical operations mentally.
9. Describe the difference between terms/factors and constants/variables.
10. Explore relationships between symbolic notations and graphs of lines with special attention to the meaning of slope.
11. Explore the divisibility rules and explain why the rules work for divisibility by 2,3,4,5,6,8,10 with 7 and 11 optional.
12. Examine the concepts of greatest common divisor/least common multiple with manipulatives (e.g., rod lengths), Venn diagrams, prime factors, and Euclid’s method.
13. Solve and explain problems that require proportional reasoning using vocabulary and concepts elementary students would understand.
14. Review a K-8 curriculum in light of the grade level standards mandated by the Missouri Department of Elementary and Secondary Education.
15. Use Boolean logic to evaluate truth tables and inverse, converse, and contrapositive statements.
16. Calculate using clock and modular arithmetic.

Objectives

1. Problem solve using truth tables and other logic rules, patterns (arithmetic, algebraic and geometric) and sets along with Venn diagrams.
2. Identify and use properties of real numbers; perform operations using rules of exponents including radicals and their relationship to rational exponents.
3. Find least common multiples and greatest common divisors using factorization and find greatest common denominators using the Euclidean Algorithm.
4. Perform operations in modular and clock arithmetic and bases others than base ten.

Exit Skills

1. Compute simple probabilities using sample spaces. Calculate probabilities involving multistage experiments, conditional probability and independent events. Calculate odds and mathematical expectation. Solve problems involving permutations and combinations.
2. Plot statistical graphs using frequency tables including bar and line graphs.
3. Calculate measures of central tendency and variation including mean, median, mode, range, standard deviation and variance. Solve simple problems involving the normal distribution. Understand the concepts of percentiles and quartiles.
4. Understand basic geometric concepts of points, lines, angles, perpendicularity of lines and planes, and polygons, including triangles, trapezoids, parallelograms, rectangles, squares and rhombi.
5. Understand definitions and theorems involving the following types of angles: supplementary, complementary, adjacent, vertical, alternate interior and exterior and corresponding angles. Know properties involving angles in polygons.
6. Solve problems in 3-dimensional geometry involving prisms, pyramids, polyhedrals, cylinders and cones.
7. Perform simple geometric construction problems including angle bisectors and perpendicular bisectors.
8. Know different forms of triangle congruence including SSS, SAS and ASA and triangle similarity.
9. Know properties of circles and spheres.
10. Know rudiments of translations, reflections, line symmetries, rotations, turn symmetries, point symmetries and tessellations of the plane.
11. Use and convert the metric system.
12. Calculate areas of polygons and circles.
13. Understand and use the Pythagorean Relationship.
14. Calculate surface areas and volumes of 3-dimensional figures.
15. Know the Cartesian coordinate system, equations of lines, graphing linear inequalities, distance and midpoint formulas and equations of circles. Be able to Solve 2 X 2 systems of linear equations.

Objectives

1. Know the basic geometric concepts of points, lines, angles, and polygons, use theorems involving angles and know the properties of circles and spheres.
2. In 2-space, perform geometric constructions, calculate areas of polygons and circles, use the Pythagorean Relationship and identify triangle congruencies. In 3-space, calculate surface areas and volumes of solids.
3. Use and convert the metric system.
4. Compute simple probabilities using permutations and combinations, calculate measures of central tendencies, variations and normal distribution, and plot statistical data using bar and line graphs.
5. Work in the Cartesian coordinate system, graph linear equations and inequalities, and solve 2 X 2 linear systems of equations.

Exit Skills

1. Perform the various algebra computations encountered in Survey Calculus.
2. Find the derivative of a function using the basic limit definition.
3. Find derivatives using the following: power rule, product rule, quotient rule, chain rule, implicit differentiation, higher order derivatives, and derivatives of exponential and logarithmic functions.
4. Apply derivatives to solve problems of  marginal analysis in business and economics.
5. Analyze a function using derivatives to locate maxima, minima, and inflection points, and sketch the graph.
6. Solve problems involving increments and differentials.
7. Solve related rates problems.
8. Evaluate both indefinite and definite integrals.
9. Solve simple differential equations involving growth and decay.
10. Evaluate integrals using substitution and integration by parts.
11. Evaluate functions of two or more variables and find partial derivatives.
12. Use Second Partial Derivatives Test to find maxima/minima/saddle points for functions of two variables.
13. Use Lagrange Multipliers to maximize/minimize, subject to constraints, a function of two or more variables.
14. Evaluate double integrals over rectangular regions.

Objectives

1. Demonstrate mastery of algebraic skills involving expressions (factoring, rational, exponential, logarithms, and radical) and solving equations (linear, quadratic, exponential, and logarithmic).
2. Find derivatives using all rules including implicit differentiation for algebraic, exponential, and logarithmic functions.
3. Use derivatives for graphing, marginal analysis, increments and differentials applications, and rated rates problems.
4. Evaluate single integrals, both indefinite and definite, by methods of substitution and integration by parts; use single integrals to solve application problems.
5. Evaluate double integrals over rectangular regions.
6. Find partial derivatives of multiple variable functions and solve optimization problems using the Second Partial Derivatives Test and Lagrange Multipliers.

Exit Skills

1. Understand the integral definition of the natural logarithm function and its use in defining both the natural exponential function and the meaning of irrational exponents.
2. Use calculus to produce accurate graphs of functions containing exponential and/or logarithmic expressions
3. Define and use the hyperbolic and inverse hyperbolic functions.
4. Differentiate, and integrate transcendental functions, including exponential, logarithmic, hyperbolic, and inverse trigonometric functions, and evaluate limits of functions that contain these transcendentals
5. Evaluate indeterminate forms, using L’Hôpital’s Rule and logarithmic differentiation when appropriate.
6. Integrate a wide variety of functions by using appropriate techniques including parts, partial fraction decomposition, trigonometric substitution, and numerical methods such as Simpson’s Rule
7. Evaluate improper integrals.
8. Use appropriate tests to determine whether an infinite series converges or diverges and to determine whether or not an alternating series converges absolutely.
9. Produce a Maclaurin or Taylor series, as appropriate, to represent a function and determine the interval of convergence of the series.
10. Perform operations, including differentiation and integration, on power series.
11. Graph conic sections, including those with translated and/or rotated axes.
12. Graph parametric and polar curves and find areas of polar regions.
13. Calculate the arc length of parametric and polar curves and find the equations of tangents to such curves.

Objectives

1. Perform limits, derivatives and integrals of transcendental functions including logarithmic, exponential, hyperbolic and inverse trigonometric functions.
2. Integrate functions using appropriate methods including integration by parts, decomposition, trigonometric substitution and Simpson’s rule.
3. Perform Calculus of polar curves and parametric curves including slope, arc length and area.
4. Determine whether infinite series converge or diverge using appropriate tests.
5. Calculate a Taylor series and its interval of convergence, and perform operations on power series for use in computations.

Exit Skills

1. Perform the basic operations of vector algebra including the calculation of dot products and projections, cross products, and scalar triple products.
2. Write a vector equation, parametric equations, and symmetric equations of a line in space.
3. Write an equation of a plane in space using vector form, point-normal form, and general form.
4. Differentiate and integrate vector-valued functions.
5. Find the arc length of a vector-valued function.
6. Analyze the motion of a particle along a curve (position, velocity, speed, and acceleration).
7. Calculate the curvature of a curve at a point.
8. Find a unit vector that is normal to a surface.
9. Graph various quadric surfaces and write the equation of the plane tangent to a surface at a point.
10. Convert between rectangular, cylindrical, and spherical coordinates.
11. Evaluate the limits and explore the continuity of functions of two or more vari-ables.
12. Calculate the first and second partial derivatives of functions of two or more variables, using the multivariable chain rule as necessary.
13. Calculate directional derivatives and the gradient of a function.
14. Use LaGrange multipliers to maximize or minimize, subject to constraints, a function of two or more variables.
15. Use the two-variable Second Partial Derivative Test to find maxima, minima, and saddle points for functions of two variables.
16. Evaluate double integrals to calculate the area of a non-rectangular region, or of a region defined by polar curves, and to calculate the area of a surface defined in rectangular or cylindrical coordinates.
17. Use triple integrals to find the volume and centroid of a solid, whether defined in rectangular, cylindrical, or spherical coordinates.
18. Use the Jacobian for transformations in two- and three- spaces to evaluate multiple integrals by an appropriate change of variables.
19. Evaluate line integrals and know when the result is independent of the path.
20. Evaluate surface integrals.
21. Use and apply the theorems of Green, Gauss, and Stokes.

Objectives

1. Study vector algebra and introductory vector analysis.
2. Find the equations of planes and lines in space.
3. Graph surfaces, including quadric surfaces, and find the equation of the tangent plane.
4. Study multivariable functions by using partial derivatives to find relative maximum(s)/minimum(s), including those with constraints and using multiple integrals to find volume and surface area.
5. Generalize the concepts of functions, derivatives and integrals.

Exit Skills

Assumes use of a scientific calculator.

1. Add, subtract, and multiply matrices if possible. Calculate determinants by cofactor expansion and row reduction and use appropriate properties.
2. Solve linear systems by Gaussian Elimination, Cramer’s Rule, and the inverse matrix method, if possible. If the system has infinitely many solutions, find the general solution.
3. Factor a square matrix to a product of elementary matrices.
4. Define a vector space and determine if a set forms a vector space.
5. Determine whether subsets of vector spaces are subspaces.
6. Determine whether a set of vectors in a vector space is linearly independent or linearly dependent.
7. Determine whether a given vector is in the span of a set of vectors. If so, write the given vector as a linear combination of the vectors in the set.
8. Define basis and dimension of a vector space.  Find a basis (and dimension) for a vector space, including the row space, column space and null space of a matrix.
9. Find the transition matrix from one basis of a vector space to another basis.
10. Find real and complex eigenvalues and eigenvectors of a square matrix.  Find bases for eigenspace.
11. Define diagonalizable matrix and determine whether a square matrix A is diagonalizable. If so, find a matrix which diagonalizes A.
12. Define an inner product space and determine whether a set of vectors forms an inner product space.
13. Show whether a set of vectors is orthogonal, orthonormal or neither. Use the Gram-Schmidt orthonormalization process to transform a basis into an orthonormal basis.
14. Find an orthogonal matrix which diagonalizes a symmetric matrix.
15. Define and recognize Hermitian, Unitary, and Normal matrices.
16. Define a linear transformation and determine whether a transformation is linear.
17. Find a basis for the kernel and range of a linear transformation.
18. Determine whether a linear transformation is invertible.  If so, find the rule for the inverse transformation.
19. Find the matrix of a linear transformation.

Objectives

1. Perform operations on matrices when appropriate, including inversion, determinants, factoring to elementary products and finding the basis for the row and column space.
2. Define a vector space and inner product space and determine if sets of vectors form a vector space, inner product space or subspace.
3. Determine whether vectors are linearly independent, orthogonal, and orthonormal and use the Gram-Schmidt process to orthonormalize when appropriate.
4. Determine the eigenvalues and eigenvectors of a matrix when appropriate and find an orthogonal matrix that diagonalized a symmetric matrix.
5. Determine if transformations are linear, find the matrix of a linear transformation and find a basis for the kernel and range.

Exit Skills

1. Solve first order differential equations, which are separable, or can be made separable using a linear substitution or rational substitution or other substitutions.
2. Solve first-order differential equations using an integrating factor.
3. Solve first-order nonhomogeneous differential equations using the two-step method.
4. Solve Bernoulli equations.
5. Find orthogonal trajectories.
6. Solve second-order and higher order homogeneous differential equations using an auxiliary equation.
7. Solve linear and nonlinear applications..
8. Solve the Cauchy-Euler differential equation.
9. Solve second-order and higher order nonhomogeneous differential equations using the methods of reduction of order, variation of parameters, operators and annihilators, and undetermined coefficients.
10. Solve systems of constant coefficient differential equations using matrix methods.
11. Use Laplace transforms to solve differential equations and systems of differential equations with initial conditions.
12. Use power series methods, including the method of Frobenius, to solve differential equations.
13. Use Euler’s method, Improved Euler Method, and Runge-Kutta methods to solve differential equations numerically.

Objectives

1. Solve first-order differential equations including those equations classified as separable, exact, linear, Bernoulli, homogeneous and Cauchy-Euler, using integrating factors where appropriate.
2. Solve higher-order constant coefficient homogeneous and nonhomogeneous differential equations using reduction of order, undetermined coefficients and variation of parameters.
3. Solve differential equations using power series including the method of Frobenius.
4. Solve systems of differential equations, including the method of Laplace transforms and the eigenvalue/eigenvector method.
5. Solve differential equations numerically, including Euler’s methods and Runge-Kutta methods.

Exit Skills

1. Read, understand and state propositions, conjunctions, disjunctions and negations.
2. Read, understand and state conditional and bi-conditional sentences, antecedents and consequents.
3. Use quantifiers correctly in mathematical statements.
4. Use direct and indirect methods to write mathematical proofs.
5. Use mathematical induction, when appropriate, to write mathematical proofs.
6. Define null sets, power sets, subsets and disjoint sets then use these definitions to write mathematical proofs.
7. Define union, intersection, difference and complements then use these definitions to write mathematical proofs.
8. Define and understand the Well Ordering Principle and utilize it, when appropriate, in writing mathematical proofs.
9. Define Cartesian Products and use this definition in writing mathematical proofs.
10. Define domain and range use these definitions in writing mathematical proofs.
11. Define the reflexive, symmetric and transitive properties and use these definitions in writing mathematical proofs.
12. Define equivalence relations and use this definition in writing mathematical proofs.
13. Define a partition and use this definition in writing mathematical proofs.
14. Define functions and composition of functions and use these definitions in writing mathematical proofs.
15. Define injective and surjective functions and use these definitions in writing mathematical proofs.
16. Define finite and infinite sets and use these definitions in writing mathematical proofs.
17. Define the countability of sets and use this definition in writing mathematical proofs.
18. Define the Pigeonhole Principle and use this definition in writing mathematical proofs.
19. Define a general algebraic structure and use this definition in writing mathematical proofs.
20. Define groups and use this definition in writing mathematical proofs.
21. Define sequences and use this definition in writing mathematical proofs.
22. Define the “Limit of a Sequence,” using the delta-epsilon definition, and use this definition in writing mathematical proofs.
23. State and prove the Heine-Borel Theorem and use the results of this theorem to write mathematical proofs.
24. State and prove the Bolzano-Weierstrauss Theorem and use the results of this theorem to write mathematical proofs.