Mathematics

Students who successfully complete this course might be able to: 1. Demonstrate study skills and habits necessary to succeed in a college math class. 2. Perform all arithmetic operations on whole numbers, integers, fractions and decimals (rational numbers), including order of operations, exponential notation, and comparing numbers. 3. Use the properties of real numbers (commutative, associative, and distributive) to manipulate and evaluate arithmetic expressions. 4. Convert between fraction notation, decimal notation, and percent notation and solve applications. 5. Use the concept of perimeter, area, and volume in real world applications. 6. Find mean, median, and modes of data set. 7. Read pictographs, bar graphs, histograms, circle graphs, and line graphs. 8. Convert between standard notation and scientific notation. 9. Apply ratios and proportions to real world applications. 10. Use the metric and American measurement systems to solve real-world applications, including unit conversions. 11. Evaluate formulas and solve formulas for a given variable. 12. Graph linear equations and inequalities, find the slope and intercepts of lines, and solve related real-world applications. 13. Write an equation of a line in slope-intercept from, point-slope form, and standard from and solve related real-world applications. 14. Solve systems of linear equations graphically, by substitutions, by elimination, including real-world applications. 15. Solve linear inequalities algebraically and systems of linear inequalities in two variables graphically, including real-world problem applications. 16. Evaluate exponential expressions, use rules of exponents with integer exponents. 17. Evaluate, add, subtract, multiply, and divide polynomials. 18. Determine and factor greatest common and factor an expression by grouping. 19. Factor trinomial of the form x^2+bx+c, perfect square trinomial, the difference of two squares, sum and differences of two cubes. 20. Solve quadratic equations by factoring, including real-world applications. 21. Simplify and perform arithmetic operations on rational expressions. 22. Simplify and perform arithmetic operations on radical expressions and expressions with rational exponents. 23. Solve rational and radical equations.

Upon successful completion of this course students should be able to: 1. Scale a recipe, including any unit conversions and other scaling considerations. 2. Calculate costs-as purchased, edible portion, etc., menu pricing using perceived value pricing and contribution margin pricing. 3. Calculate revenue and expenses including sales tax, guest check totals, gratuities, discounts, and calculate payroll expenses. 4. Analyze profit and loss including percent increase and decrease, gross and net profit, and break-even point.

1. Create and interpret distributions of data using various types of charts and graphs.
2. Determine the appropriate measures of center and dispersion for different types of distributions and use them to describe the properties of the distributions, and

use the Empirical Rule.

1. Perform least squares regression and use the results to describe and make inferences about data.
2. Determine and use simple probability to construct a discrete probability distribution and determine the expected value and use to solve applications.
3. Solve problems using the normal distribution and sampling distribution of the mean and proportion (with sigma known and unknown) including finding probabilities

and constructing confidence intervals.

1. Set up and perform hypothesis tests.

1. Create and interpret distributions of data using various types of charts and graphs.
2. Determine the appropriate measures of center and dispersion for different types of distributions and use them to describe the properties of the distributions, and

use the Empirical Rule.

1. Perform least squares regression and use the results to describe and make inferences about data.
2. Determine and use simple probability to construct a discrete probability distribution and determine the expected value and use to solve applications.
3. Solve problems using the normal distribution and sampling distribution of the mean and proportion (with sigma known and unknown) including finding probabilities

and constructing confidence intervals.

1. Set up and perform hypothesis tests.

1. Use inductive and deductive reasoning to solve several types of problems.
2. Use the properties and tools of sets to solve applications and determine if an infinite set is countable.
3. Perform arithmetic operations in additive, multiplicative, ciphered, and positional-valued number systems and in other bases, and discuss early computational

methods and tools.

1. Use the properties of the real number system to solve applications; recognize if a series is arithmetic or geometric, determine the nth term, and find the sum of

the first n numbers and use to solve applications and determine the golden ration of Fibonacci sequences in applications.

1. Determine if a finite mathematical system is an algebraic group and/or a commutative group and explain their conclusion; perform group operations and

modular arithmetic.

1. Use the formulas and concepts of simple and compound interest, installment purchases, APR, mortgages, annuities, sinking funds, and retirement investments

to solve applications.

1. Solve applications with probability, odds, expected value, counting, tree diagrams and conditional probability.
2. Determine measures of center and dispersion of data and create frequency distributions and graphs; determine the linear correlation coefficient and line of best

fit and use in applications.

1. Apply the properties of closure, commutativity, associativity, and identity to addition and multiplication of whole numbers.
2. Represent subtraction of whole numbers using the take-away and missing addend approaches.
3. Construct the addition and multiplication facts table for any base from 2 through 10 and read it “backwards” to find subtraction and division facts respectively.
4. Perform all arithmetic operations in bases 2 through 12.
5. Describe “less than” and “greater than” with whole numbers using the operation of addition.
6. Describe multiplication of whole numbers using repeated addition and rectangular array approaches.
7. Represent division of whole numbers using the missing factors and repeated subtraction.
8. Explain division problems involving zero.
9. Explain whole number exponents using repeated multiplication.

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1. Use the sieve of Eratosthenes to find prime numbers.

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1. State and apply the fundamental theorem of arithmetic.

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1. Apply tests for divisibility by 2, 3, 4, 5, 6, 8, 9, 10, 11, and 12.

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1. Find the prime factorization of a number to find all of its factors.

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1. Find the Greatest Common Factor and Least Common Multiple of any given pair of numbers using the prime factorization method.

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1. Determine equality of fractions.

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1. Express a fraction in the simplest form.

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1. Perform any arithmetic operation on rational numbers and integers, providing rationale for your computations.

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1. Solve applied problems involving ratios, proportions, and percents.

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1. Change any fraction to its decimal form and vice versa.

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1. Define and apply the distributive property of multiplication over addition.

1. Apply the properties of closure, commutativity, associativity, and identity to addition and multiplication of whole numbers.
2. Represent subtraction of whole numbers using the take-away and missing addend approaches.
3. Construct the addition and multiplication facts table for any base from 2 through 10 and read it “backwards” to find subtraction and division facts respectively.
4. Perform all arithmetic operations in bases 2 through 12.
5. Describe “less than” and “greater than” with whole numbers using the operation of addition.
6. Describe multiplication of whole numbers using repeated addition and rectangular array approaches.
7. Represent division of whole numbers using the missing factors and repeated subtraction.
8. Explain division problems involving zero.
9. Explain whole number exponents using repeated multiplication.

1

1. Use the sieve of Eratosthenes to find prime numbers.

1

1. State and apply the fundamental theorem of arithmetic.

1

1. Apply tests for divisibility by 2, 3, 4, 5, 6, 8, 9, 10, 11, and 12.

1

1. Find the prime factorization of a number to find all of its factors.

1

1. Find the Greatest Common Factor and Least Common Multiple of any given pair of numbers using the prime factorization method.

1

1. Determine equality of fractions.

1

1. Express a fraction in the simplest form.

1

1. Perform any arithmetic operation on rational numbers and integers, providing rationale for your computations.

1

1. Solve applied problems involving ratios, proportions, and percents.

1

1. Change any fraction to its decimal form and vice versa.

2

1. Define and apply the distributive property of multiplication over addition.

Students who complete this course will: 1. Construct and work with algebraic expressions, functions, and equations and understand their connection with geometry 2. Illustrate and manipulate planar and spatial objects 3. Perform conversions using both the “English” and metric systems 4. Determine various measurements of geometric objects, such as area, perimeter and volume 5. Apply the concept of congruence to geometric figures, including triangles 6. Understand the basics of descriptive statistics, in both visual and numerical formats 7. Define probability and how it relates to both statistics and geometry 8. Solve counting problems involving the multiplication principle, permutations and combinations

1. Solve application problems for linear equations, specifically Supply and Demand and Break Even Analysis.
2. Solve systems of Linear Equations using matrices.
3. Determine the solution of a linear programming problem using both graphical method and the simplex method.
4. Demonstrate knowledge of financial mathematics that includes determining which formula to use, using the formula correctly, and understanding the answer.

5. Demonstrate knowledge of linear, polynomial, rational, exponential, and logarithmic functions.

1. Solve application problems for linear equations, specifically Supply and Demand and Break Even Analysis.
2. Solve systems of Linear Equations using matrices.
3. Determine the solution of a linear programming problem using both graphical method and the simplex method.
4. Demonstrate knowledge of financial mathematics that includes determining which formula to use, using the formula correctly, and understanding the answer.

5. Demonstrate knowledge of linear, polynomial, rational, exponential, and logarithmic functions.

Students who complete this course successfully will: 1. Demonstrate study skills and habits necessary to succeed in a college math class. 2. Find the domain and range of a function graphically and, where appropriate, algebraically. 3. Determine if a function is even, odd, or neither graphically based on symmetry and algebraically. 4. Identify relations and functions, use the vertical line test to determine if a relation represents a function. 5. Graph elementary functions, piece-wise defined functions, and transformations (translation, stretch/shrink, reflection) of basic functions. 6. Analyze and graph different types of functions including linear function, quadratic function, polynomial functions, and rational functions. 7. Solve real world problems modeled by linear, quadratic, and polynomial functions.

Students who complete this course successfully will: 1. Demonstrate study skills and habits necessary to succeed in a college math class. 2. Find the domain and range of a function graphically and, where appropriate, algebraically. 3. Determine if a function is even, odd, or neither graphically based on symmetry and algebraically. 4. Identify relations and functions, use the vertical line test to determine if a relation represents a function. 5. Graph elementary functions, piece-wise defined functions, and transformations (translation, stretch/shrink, reflection) of basic functions. 6. Analyze and graph different types of functions including linear function, quadratic function, polynomial functions, and rational functions. 7. Solve real world problems modeled by linear, quadratic, and polynomial functions.

1. Perform accurate calculations related to dosages, fluid administration, and medication preparation. 2. Interpret drug labels, dose intervals, and routes of administration. 3. Convert a patient’s weight from United States customary units to Metric units and vice versa. 4. Determine drug dosages based on animal weight, concentration, and desired therapeutic effect. 5. Prepare mixtures and dilutions to a desired concentration. 6. Determine the volume, flow/drip rate, or stop time for an infusion for a given patient. 7. Determine the calculations needed for anesthesia administration and titrations.

Students who successfully complete this course will: 1. Demonstrate study skills and habits necessary to succeed in a college math class. 2. Determine if a given function is one-to-one and if so, find the inverse function. 3. Evaluate logarithmic expressions. 4. Simplify, graph, and solve exponential and logarithmic functions and equations. 5. Use growth and decay formula to solve application problems. 6. Convert measures of angles between degrees and radians. 7. Find trigonometric function values for any multiple of 30, 45 ,60 and 90 degrees. 8. Use the unit circle and right triangle trigonometry to identify and graph the six trigonometric functions. 9. Prove trigonometric identities using basic, co-function, double angle, half-angle, power reducing, sum/difference, and Pythagorean identities. 10. Use inverse trigonometric functions to simplify expressions and to solve trigonometric equations. 11. Use the Law of Sines and Law of Cosines to solve triangles including real world applications. 12. Analyze the graphs exponential and logarithmic functions, trigonometric functions, inverse trigonometric function, and conic sections.

1. Perform accurate calculations related to dosages, fluid administration, and medication preparation. 2. Interpret drug labels, dose intervals, and routes of administration. 3. Convert a patient’s weight from United States customary units to Metric units and vice versa. 4. Determine drug dosages based on animal weight, concentration, and desired therapeutic effect. 5. Prepare mixtures and dilutions to a desired concentration. 6. Determine the volume, flow/drip rate, or stop time for an infusion for a given patient. 7. Determine the calculations needed for anesthesia administration and titrations.

1. Define the limit of a function and determine its value graphically, numerically and analytically. 2. Determine if a function is continuous at a given point. 3. Compute the derivative of a function. 4. Apply the concept of differentiation to various applications such as extrema, curve sketching and approximation. 5. Define an antiderivative. 6. Develop methods to find both approximate and exact areas under a curve.

1. Compute the area between curves, volumes of solids of revolution, the average value of a function and arc length of a function.
2. Compute antiderivatives of functions using several techniques.
3. Use numerical techniques to approximate definite integrals.
4. Determine whether sequences and series converge or diverge.
5. Approximate functions as Taylor polynomials.

6. Analyze, graph and compute the derivatives of parametric equations and functions in polar coordinates.

1. Gain knowledge in the logical basis of mathematics.
2. Learn how to write proofs and gain insight into various strategies to approach proving a statement.
3. Understand the basic structures in mathematics, including sets, functions, sequences, sums and matrices.
4. Perform modular arithmetic and work with congruences in various applications such as cryptography.
5. Learn the concepts of proof by induction and recursion.
6. Solve basic counting problems, including those using the Pigeonhole Principle.

7. Work with permutations, combinations and manipulate various binomial identities.

1. Solve basic counting problems, including those using the Pigeonhole Principle.
2. Work with permutations, combinations and manipulate various binomial identities.
3. Understand the inclusion-exclusion principle and apply it to real-world problems.
4. Gain knowledge in the basic understanding of relations.
5. Develop an understanding of graph theory including directed and undirected graphs as well as trees and their applications to computer science.

6. Understand the concept of Boolean functions and its application to circuits.

1. Solve problems by applying and interpreting descriptive statistics.
2. Solve problems by applying basic rules of probability.
3. Solve problems by utilizing the Normal Distribution.

4. Construct confidence intervals to solve problems.

1. Find and interpret confidence intervals to estimate population parameters.
2. Perform hypothesis tests on one and two samples.
3. Perform linear regressions and interpret results.
4. Perform ANOVA tests.

5. Develop and analyze statistical control charts.

1. Define the concept of vectors and solve problems using vectors in 2D and 3D applications. 2. Apply the concepts of limits and differentiation to multivariate functions, including applications. 3. Apply the concept of integration to multivariate functions. 4. Develop various methods to solve both double and triple integrals. 5. Bring together the concept of vectors and calculus in terms of a line integral. 6. Use the different types of methods to solve line integrals.