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Welcome to Math 1, the first course in the Mathematics series for the PreHealth Sciences Training Certificate. This course and the Certificate are designed primarily for learners interested in preparing for and gaining entry for healthrelated programs, and to help address the prerequisites for the Medical College Admission Test (MCAT). This Math 1 course provides indepth learning related to general mathematical concepts and techniques used in the bachelor’slevel study of natural, physical, behavioral, and social sciences. Participants will have the opportunity to review and gain mathematical knowledge on how to analyze and manipulate scientific data. The course will go on to explore important areas of mathematics such as Arithmetic, Algebra, Geometry, Trigonometry, and Vector Algebra that can be applied in the fields of scientific inquiry.
The Math 1 course is sponsored in part by the International Development Research Center and by the University of the Incarnate Word School of Osteopathic Medicine. Like all NextGenU.org courses, it is competencybased, using competencies based on the Association of American Medical Colleges’ Medical College Admission Test. It uses learning resources from accredited, academic, professional, and worldclass organizations and universities such as Rice University. Volunteer designers for this course include Shaunik Sharma BSc, Tristan Aaron Wild, BMSc (Hons); and the late Mohammad AsadiLari a former MDPHD Candidate at the University of Toronto. The course was created by Marco Aurelio Hernandez, Ph.D.; Ma.Genikka Camille Gabral, BEd, MSc; Margaret Niles, Ph.D.; and reviewed by Prof. Sally Keely, MS, COI.
For publications on NextGenU.org’s courses’ efficacy, see NextGenU.org’s publication page.
The completion time for this course is estimated at 132 hours, comprising 35 hours of learning resources, 69 hours of studying and assimilation of the content, and 28 hours of participating in learning activities and quizzes to assist the learners in synthesizing learning materials. This course is equivalent to 3 credit hours in the U.S. undergraduate/bachelor’s degree system.
The course requires the completion of all quizzes, discussion forums, and practical activities to receive a course certificate. Practice quizzes are available throughout the course, composed of multiplechoice questions. After you’ve completed each module, quiz, and learning activity, at the end of the course, you’ll have access to a final exam consisting of 25 multiplechoice questions, a final lab activity, and a chance to evaluate this course. Participants have up to three opportunities to take the final exam and achieve the required passing score of >=70%. Once you’ve passed the final exam and completed the evaluations, you will be able to download a certificate of completion from NextGenU.org and our course’s cosponsoring organizations.
We keep all of your personal information confidential, never sell any of your information, and only use anonymized data for research purposes. Also, we are happy to report your testing information and share your work with anyone (your school, employer, etc.) at your request.
Engaging with this Course:
This free course is aimed at students who have graduated from high school and want to prepare to become a health professional, and/or pass the MCAT exam. You may also browse this course for free to learn for your personal enrichment; there are no requirements.
To obtain a certificate, a learner must first register for the course and then successfully complete:
 Pretest
 All the reading requirements,
 All quizzes and pass with 70% with unlimited attempts,
 All practical activities,
 All discussion forums,
 The final lab activity,
 The final exam with a minimum of 70% and a maximum of 3 attempts, and
 The self and course evaluation forms.
To obtain credit:
 Complete all requirements listed above for the certificate, and
 Your learning institution or workplace should approve the partneruniversitysponsored NextGenU.org course for educational credit, as they usually would for their learner taking a course anywhere.
NextGenU.org is happy to provide your institution with:
 A link to and description of the course training, so they can see all of its components, including the cosponsoring institutions;
 Your grade on the final exam;
 Your work products (e.g., discussion forum responses) and any other required or optional shared materials that you produce and authorize to share with them;
 Your evaluations  course, and selfassessments;
 A copy of your certificate of completion, with the cosponsoring organizations listed.
To obtain a degree, NextGenU.org cosponsors degree programs with institutional partners. To obtain a full degree cosponsored with NextGenU.org, registrants must be enrolled in a degree program as a student of a NextGenU.org institutional partner. If you think your institution might be interested in offering a degree with NextGenU.org, contact us.
We hope you will find this a rewarding learning experience, and we count on your assessment and feedback to help us improve this training for future students.
Here are the next steps to take the course and earn a certificate:
 Complete the registration form.
 Take the pretest.
 Begin the course with Module 1: Real Numbers. In each lesson, read the description, complete all required readings and any required activity, as well as take the corresponding quizzes.

Module 1: Real Numbers
Competencies covered in this module:
 Basic Arithmetic; Prerequisite for Basic Algebra  Real Numbers, Fractions, Significant Digits.
 Conversion Convert Metric to Metric, Metric to English, and perform dimensional analysis.
 Basic Arithmetic  Proportions, Ratios, Percentages.
 Exponents.
 Basic Arithmetic; Prerequisite for Basic Algebra  Real Numbers, Fractions, Significant Digits.

Module 1: Lesson 1: The Real Numbers
Student Learning Outcomes:
Upon completion of this lesson, you will be able to: Describe the systems used to classify numbers.
 Explain, identify and work with mathematical expressions involving rational numbers.
 Explain and identify irrational numbers.
 Demonstrate the order of real numbers using the number line, the opposite of a real number, and the absolute value of a real number.
 Perform calculations using the order of operations.
 Define and use the properties of real numbers.
 Multiply and divide fractions.
 Add and subtract fractions.
 Perform all operations on fractions.
 Write fractions as decimals and decimals as fractions.
 Define and do operations with significant digits considerations.
 Demonstrate how decimals and fractions are used in real life.
10 URLs, 1 Forum 
Module 1: Lesson 2: The Rudiments of Measurement
Student Learning Outcomes:
Upon completion of this lesson, you will be able to: Convert from one unit of length, weight, volume, time, and speed to another in the American (SI) System.
 Convert from one unit of length, weight, volume, and speed to another in the Metric System.
 Convert measures from American System to Metric System and vice versa.
 Use units to balance equations.
 Estimate length, distance, and other quantities.
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Module 1: Lesson 3: Ratio, Proportion, and Percentages
Student Learning Outcomes:
Upon completion of this lesson, you will be able to: Solving ratio and rates problems.
 Examine the use of proportions in solving reallife problems.
 Calculate percentages of given values.
 Calculate a reverse percentage problem.
 Convert between percent, decimals, and fractions.
 Calculate percent increase or decrease.
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Module 1: Lesson 4: Introduction to Exponents
Student Learning Outcomes:
Upon completion of this lesson, you will be able to: Examine the use of powers in mathematical expressions  evaluate powers.
 Use scientific notation to express very large or very small numbers.
 Simplify square roots.
 Rationalize the denominators of square root expressions.
 Estimate square roots.
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Module 1: Lesson 5: Working with Exponents
Student Learning Outcomes:
Upon completion of this lesson, you will be able to: Identify the components of an expression with integer exponents.
 Perform the order of operations with exponents.
 Simplify an expression with exponents using the product and quotient rules.
 Simplify expressions using the negative and zero exponent rules.
 Simplify expressions using all the rules for exponents.
3 URLs, 2 Quizzes 
Module 2: The Fundamentals of Algebra
Competency covered in this module:
 Basic Algebra.
 Graphing  Calculate Slopes from Data Found in Figures, Graphs, and Tables.

Module 2: Lesson 1: Algebra Expressions and Equations
Student Learning Outcomes:
Upon completion of this lesson, you will be able to: Use variables and operators, and translate words into algebraic expressions.
 Evaluate algebraic expressions.
 Simplify algebraic expressions using the associative, commutative, and distributive properties of multiplication.
 Simplify expressions using "grouping" of like terms.
 Solve equations from algebraic expressions or words involving integers.
 Solve equations with fraction or decimal coefficients.
 Solve absolute value equations.
 Represent intervals on the number line.
 Solve linear inequalities.
 Solve linear absolute value inequalities.
Click here to start this lesson10 URLs 
Module 2: Lesson 2: Operations on Polynomials
Student Learning Outcomes:
Upon completion of this lesson, you will be able to: Identify the degree and the leading coefficient of a polynomial.
 Add and subtract polynomials.
 Multiply polynomials.
 Perform operations on polynomials with several variables.
 Divide a polynomial by a monomial.
 Divide a polynomial by a binomial using long division or synthetic division.
 Apply operations on polynomials to reallife situations.
Click here to start this lesson5 URLs, 1 Quiz 
Module 2: Lesson 3: Factoring Polynomials
Student Learning Outcomes:
Upon completion of this lesson, you will be able to: Factor a polynomial using the greatest common factor.
 Factor a polynomial by grouping.
 Factor perfect square trinomials.
 Factor using the difference of squares.
 Apply polynomial factoring to reallife situations.
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Module 2: Lesson 4: Graphing Linear Equations
Student Learning Outcomes:
Upon completion of this lesson, you will be able to: Graph equations on the rectangular coordinate system.
 Find the distance between two points.
 Find the midpoint of a line from its equation.
 Explain what the slope of a line is, and be able to find the slope of a given line.
 Explain the connection between slope and rate of change, and find rates of change in application problems.
 Graph a linear equation.
7 URLs, 1 Forum, 2 Quizzes 
Module 3: Introduction to Functions, and Systems of Linear Equations
Competency covered in this module:
 Introduction to Functions  Foundation for Study of Logarithmic, Exponentials, Trigonometric, and Inverse Trigonometric Functions.
 Simultaneous Equations.

Module 3: Lesson 1: Introduction to Functions
Student Learning Outcomes:
Upon completion of this lesson, you will be able to: Determine whether a relation is a function.
 Evaluate a function given in tabular, algebraic, or word form.
 Find function values from a graph.
 Use the vertical and horizontal line tests to determine whether a function is onetoone.
 Find the domain of a function from its equation.
 Find the range of a function from its equation.
 Use inequality, set builder, and interval notation to specify domain and range.
 Find domain and range from a graph.
 FInd rate of change from a tabular function.
 Work with piecewisedefined functions.
 Determine whether a function is increasing, decreasing, or constant, and find its absolute max and min by its graph.
 Identify the equation of a translated absolute value function.
 Find the inverse of a function from its equation.
Click here to start this lesson7 URLs, 1 Quiz 
Module 3: Lesson 2: Solving Systems of Linear Equations (Simultaneous Equations) in Two Variables
Student Learning Outcomes:
Upon completion of this lesson, you will be able to: Define a system of linear equations.
 Determine whether an ordered pair is a solution to a system of Linear equations.
 Solve a system of linear equations by substitution and elimination.
 Identify an inconsistent system of linear equations.
 Express the solution to a system of dependent equations.
 Choose the most convenient method to solve a system of linear equations.
3 URLs, 1 Forum 
Module 3: Lesson 3: Applications of Systems of Equations
Student Learning Outcomes:
Upon completion of this lesson, you will be able to: Solve Geometry applications using systems of linear equations.
 Solve mixture applications using systems of linear equations.
 Use graphs to solve a system of linear inequalities.
2 URLs, 2 Quizzes 
Module 4: Quadratic, and Rational Expressions and Equations
Competency covered in this module:
 Basic Algebra.

Module 4: Lesson 1: Quadratic Expressions and Quadratic Equations
Student Learning Outcomes:
Upon completion of this lesson, you will be able to: Solve quadratic equations by factoring and using the zero property.
 Solve quadratic equations by the square root property.
 Solve quadratic equations by completing the square.