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Fall 2021

Math/Science Preparatory Courses:

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MSP161 - Math/Science Prep

Credits: 2

Catalog Description: This course is the first semester of a four (4) semester preparatory curriculum designed to provide the knowledge and skills necessary for participating in the STEM enrichment program including readiness for MAT 136, CHE 101, and PHY 131. Students will begin an exploration of science and math topics typically covered in first half of PHY 100 – How things Work and the first half of MAT 102 – Algebra 2. Students will explore the physical world and its impact on human life, including the basic principles of mechanics, thermodynamics, electricity, magnetism, waves, optics, and atomic physics as well as the solving of first degree inequalities, introduction to functions, linear equations in two variables and graphing, solving systems of two or three linear equations and inequalities, a brief review of polynomial operations and factoring.

Lecture: 2 hrs.

Course Learning Outcomes (CLOs):
Content from PHY 100 - Upon successful completion of the MSP161 and MSP162 series of courses as documented through writing, objective testing, case studies, laboratory practice, and/or classroom discussion, students will be able to demonstrate:

*1. The ability to explore natural phenomena using scientific methods, in the course's laboratory. (Natural phenomena mean actual physical processes taking place live, as opposed to videos or simulations. Laboratory means an appropriate facility containing necessary equipment, as defined by the list included in the Course Outline. For a minimum of ten of the three-hour labs, students must measure something real, in the presence of the instructor.) This includes the ability to:
a. use laboratory equipment when given written instructions.
b. use methods covered in class to determine desired quantities from measurements.
c. draw valid conclusions on whether their results are in agreement with generally accepted values or principles.
Students must earn at least two thirds of the possible lab points to receive credit for the course.

*2. The ability to apply data, concepts, and models in the field of physics, as documented by performance on quizzes, exams and the comprehensive departmental final. These tests contain both questions requiring a verbal response, and questions requiring brief calculations at the level of basic arithmetic, with the emphasis on verbal questions. The following will be demonstrated:
a. the ability to use and respond to terminology.
b. the ability to interpret graphs.
c. the ability to apply basic physical principles verbally.
d. the ability to select the correct formula for a situation, fill in numbers and do the arithmetic.
e. the ability to interpret formulas verbally (eg, at twice the speed, there is four times the kinetic energy.)
f. the ability to do the above in the context of a variety of topics. Since this is not intended to serve as a prerequisite for any other course, there is some flexibility in the instructor's choice of specific topics; however, there will be some coverage of all the general areas listed in the catalog description.

3. Critical thinking (reasoning) ability. At least 25% of the questions on the final and other exams will require the application of what has been taught to arrive at a conclusion, as opposed to simply reciting memorized material or dropping numbers into a formula.

Content from MAT 102 - Upon successful completion of the MSP 161, 162, 163, and 164 series of courses as documented through writing, objective testing, case studies, laboratory practice, and/or classroom discussion, the student will be able to:

1. Correctly translate and solve first-degree equations and inequalities.

*2. Given a relation, identify if it is a function. If so, find its domain and range, and then correctly evaluate the function given a value in its domain.

3. Given a linear equation, correctly graph it on a rectangular coordinate system.

4. Find the equation of a line given one of the following:
a.A point on the line and the slope of the line
b.Two points on the line
c.A point on the line and the equation of a line parallel or perpendicular to it

5. Given a system of linear equations, correctly solve the system by graphing, substitution or the addition method.

6. Given a system of inequalities, solve the system by the graphing method.

7. Given two or more polynomials, correctly add, subtract, multiply or divide the expressions.

8. Given two or more rational expressions, correctly add, subtract, multiply or divide the expressions.

9. Given an equation involving rational expressions, correctly solve the equation.

10. Given two or more radical expressions, add, subtract, multiply and divide the expressions and write the answer in simplest form.

11. Given two complex numbers, add, subtract, multiply or divide the numbers and write the answer in the form a + bi.

12. Given a quadratic equation, solve it by factoring, taking square roots, completing the square or using the quadratic formula.

* This course objective has been identified as a student learning outcome that must be formally assessed as part of the Comprehensive Assessment Plan of the college. All faculty teaching this course must collect the required data and submit the required analysis and documentation at the conclusion of the semester to the Office of Institutional Research and Assessment.



Content Outline:
Content from PHY 100 (selection of 7 of the following concepts)
1. Motion, force, and Newton's Laws.

2. Circular motion, gravitation and orbital motion.

3. Fluid mechanics and The Gas Law.

4. Work, energy and power; temperature and heat.

5. Heat engines and the laws of thermodynamics.

6. Vibration and waves.

7. Resonance, sound, and musical instruments.

8. Electric potential, current, and power.

9. Electrical safety; magnetism.

10. Electromagnetic induction (generators, transformers, etc.).

11. Electromagnetic waves. Interference.

12. Reflection, refraction, and optics.

13. Atomic structure and spectra. The nucleus.

14. Radioactivity and nuclear energy.

Content from MAT 102 (selection of approximately ½ the following concepts)
1. REVIEW OF REAL NUMBERS (optional)

2. FIRST-DEGREE EQUATIONS AND INEQUALITIES
2.1 Solving First-degree Equations
A. Solve equations using the addition or multiplication property of equations
B. Solve equations using both the addition and multiplication properties
C. Solve equations containing parentheses
D. Solve literal equations for one of the variables
2.2 Applications: Puzzle Problems
A. Solve integer problems
B. Solve coin and stamp problems
2.3 Applications: Mixture and Uniform Motion Problems
A. Solve value mixture problems
B. Solve percent mixture problems (optional)
C. Solve uniform motion problems
2.4 First-degree Inequalities
A. Solve an inequality in one variable
B. Solve a compound inequality
C. Solve application problems

3. LINEAR FUNCTIONS AND EQUATIONS IN TWO VARIABLES
3.1 The Rectangular Coordinate System
A. Graph points in a rectangular coordinate system
B. Find the length and midpoint of a line segment
C. Graph a scatter diagram (optional)
3.2 Introduction to Functions
A. Evaluate a function
3.3 Linear Functions
A. Graph a linear function by using the t-table method
B. Graph an equation of the form Ax + By = C by using the t-table method
C. Find x- and y-intercepts of a straight line
D. Application problems
3.4 Slope of a Straight Line
A. Find the slope of a line given two points
B. Graph a line given a point and a slope
3.5 Finding Equations of Lines
A. Find the equation of a line given a point and the slope
B. Find the equation of a line given two points
C. Application problems (optional)
3.6 Parallel and Perpendicular Lines
A. Find parallel and perpendicular lines
3.7 Inequalities in Two Variables
A. Graph the solution set of an inequality in two variables

4. SYSTEMS OF LINEAR EQUATIONS AND INEQUALITIES
4.1 Solving Systems of Linear Equations by Graphing and by the Substitution
Method
A. Solve a system of linear equations by graphing
B. Solve a system of linear equations by substitution
C. Solve investment problems (optional)
4.2 Solving Systems of Linear Equations by the Addition Method
A. Solve a system of two linear equations in two variables by the addition
method
B. Solve a system of three linear equations in three variables by addition method
4.3 Solving Systems of Equations by Using Determinants (optional)
4.4 Application Problems
A. Solve rate-of-wind or rate-of-current problems
B. Solve application problems
4.5 Solving Systems of Linear Inequalities
A. Graph the solution set of a system of linear inequalities

5. POLYNOMIALS
5.1 Exponential Expressions
A. Multiply monomials
B. Divide monomials and simplify expressions with negative exponents
C. Write a number using scientific notation
D. Solve application problems (optional)
5.2 Introduction to Polynomials
A. Evaluate polynomial functions
B. Add or subtract polynomials
5.3 Multiplication of Polynomials
A. Multiply a polynomial by a monomial
B. Multiply two polynomials
C. Multiply polynomials that have special products
D. Solve application problems
5.4 Division of Polynomials
A. Divide polynomials using long division
B. Divide polynomials using synthetic division
C. Evaluate a polynomial using synthetic division (optional)
5.5 Factoring Polynomials
A. Factor a monomial from a polynomial
B. Factor by grouping
C. Factor a trinomial of the form x2 + bx + c
D. Factor ax2 + bx + c
5.6 Special Factoring
A. Factor the difference of two perfect squares or a perfect-square trinomial
B. Factor the sum or difference of two perfect cubes
C. Factor a trinomial that is quadratic in form
D. Factor completely
5.7 Solving Equations by Factoring
A. Solve an equation by factoring
B. Solve application problems

6. RATIONAL EXPRESSIONS
6.1 Multiplication and Division of Rational Expressions
A. Find the domain of a rational function
B. Simplify a rational function
C. Multiply rational expressions
D. Divide rational expressions
6.2 Addition and Subtraction of Rational Expressions
A. Rewrite rational expressions in terms of a common denominator
B. Add or subtract rational expressions
6.3 Complex Fractions
A. Simplify a complex fraction
6.4 Ratio and Proportion
A. Solve a proportion
B. Solve application problems
6.5 Rational Equations
A. Solve a fractional equation
B. Solve work problems
C. Solve uniform motion problems (optional)
6.6 Variation
A. Solve variation problems

7. RADICAL EXPRESSIONS
7.1 Rational Exponents and Radical Expressions
A. Simplify expressions with rational exponents
B. Write exponential expressions as radical expressions and vice versa
C. Simplify radical expressions that are roots of perfect powers
7.2 Operations on Radical Expressions
A. Simplify radical expressions
B. Add or subtract radical expressions
C. Multiply radical expressions
D. Divide radical expressions
7.3 Solving Equations Containing Radical Expressions
A. Solve a radical equation
B. Solve application problems
7.4 Complex Numbers
A. Simplify a complex number
B. Add or subtract complex numbers
C. Multiply complex numbers
D. Divide complex numbers

8. QUADRATIC EQUATIONS
8.1 Solving Quadratic Equations by Factoring or by Taking Square Roots
A. Solve a quadratic equation by factoring
B. Write a quadratic equation given its solutions
C. Solve a quadratic equation by taking square roots
8.2 Solving Quadratic Equations by Completing the Square
A. Solve a quadratic equation by completing the square (Limit examples to those with a Lead Coefficient of One.)
8.3 Solving Quadratic Equations by Using the Quadratic Formula
A. Solve quadratic equations by using the quadratic formula
8.4 Solving Equations that are Reducible to Quadratic Equations (optional)
8.5 Quadratic Inequalities and Rational Inequalities (optional)
8.6 Applications of Quadratic Equations
A. Solve application problems

Effective Term: Fall 2012