# Placement and Review for Precalculus & Calculus

Undergrad Majors & Programs Math & Computer Science Math Placement Exams

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- Math Placement Exams

- Process and Overview
- Placement Test Results and Recommendations
- Placement Exam Preparation
- Placement Exam Testing
- Registration Clearance and Viewing Results

## Process and Overview

Students come to Bethel with a variety of backgrounds and histories in their math course work, that may have included previous work in algebra, precalculus, or calculus. Success in Bethel’s Precalculus and Calculus 1 courses will be important for students intending to major in mathematics, or other disciplines such as computer science, physics, engineering, chemistry, biology, and biokinetics.

Keeping up in these college-level courses depends on at least three factors: enrollment in the appropriate course, a strong work ethic and good study skills, and a solid foundation in the appropriate algebra, trigonometry, and/or precalculus skills. The Precalculus/Calculus Placement Exam is a tool designed to help students determine if they are ready to take these courses and to identify any skills that should be reviewed before entering the course.

### Placement Exam Timing and Testing Periods

The placement exam can be taken at any time through an online format in a "self-enrollment" Moodle course. **Students can take the exam only one time per testing period** (see below) and the exam must be taken in the appropriate test period associated with the upcoming term.

Test periods for enrollment in the fall semester:

**Test Period 1:** April through July**Test Period 2:** August and September

*Students enrolling in summer courses will use Test Period 1.*

Test periods for enrollment in the spring semester:

**Test Period 3:** October through December**Test Period 4:** January through February 15

This testing policy allows students to take the placement exam up to two times (once per testing period) before each term. The timing allows students who take advantage of testing periods 1 & 3, and who do not place at the appropriate level, to review and retake the exam. We will use the best score from the two possible testing attempts in one registration period.

### Course Prerequisites & Registration

Before registering for Precalculus (MAT121M) or Calculus 1 (MAT124M), all students must take the online Bethel Precalculus and Calculus 1 Placement Exam no later than 24 hours before their registration. New students should take this exam at least 24 hours before their registration can be processed. The placement exam score must be “current,” which means it must be taken during one of the two testing periods immediately preceding the term during which the course is intended to be taken (see testing periods definition above).

## Placement Test Results and Recommendations

The placement test measures skills needed for both courses. Those seeking to enter Precalculus will find that they do not know some of the information on the exam; that’s OK, and this is not expected. After students complete the online placement test, they will receive a *level* score, accompanied by one of the following registration *clearances* and enrollment recommendations:

**Level 4:** *Clearance for MAT124M or below.*

We recommend that you enroll in Calculus 1. With the effort that is appropriate for a college-level mathematics course, you should be able to do well in Calculus 1.

**Level 3:** *Clearance for MAT124M or below with recommendation to review.*

Calculus 1 is probably the right course for you, but a review before starting the course is strongly recommended (see review resources). You may optionally enroll in MAT122 (Calculus 1 Corequisite) for additional support.

**Level 2:** *Clearance for MAT122 or below.*

You may choose to enroll in MAT121M (Precalculus) or MAT124M (Calculus 1). To enroll in MAT124M, a concurrent enrollment in MAT122 (Calculus 1 Corequisite) is required, for a total of 6 credits. With the effort that is appropriate for a college-level mathematics course, you should be able to do well with either option.

**Level 1:** *Clearance for MAT121M with recommendation to review.*

We recommend that you enroll in Precalculus. Review before starting the course is strongly recommended (see review resources).

## Placement Exam Preparation

Before taking the placement exam, students are strongly encouraged to review the Placement Exam Objectives and take advantage of the review information, practice test, and online instructional support. Students may also need to review after taking the placement exam, simply to brush up on selected skills. If you find that you are rusty on some skills, that’s okay. You can review on your own, or Bethel has excellent ALEKS Preparation Courses designed to help you review needed skills.

### Precalculus and Calculus 1 Placement Exam Objectives

Students registering for Precalculus are responsible for part 1, "Algebra Basics," and part 2, "Functions - Basics," objectives 1 and 2. Students enrolling in Calculus 1 are responsible for all objectives.

#### Part 1: Algebra basics

- Apply properties of percents.
- Factor simple polynomials.
- Simplify and evaluate algebraic expressions (including rational expressions and complex fractions), including the use of the:
- Distributive, Associative, and Commutative Properties
- Laws of Exponents (including negative and fractional exponents)

- Solve equations or systems of equations (linear, quadratic, exponential).
- Solve linear inequalities.
- Apply order of operations.
- Multiply polynomials.
- Compute distances in the plane.
- Apply the Pythagorean Theorem.
- Graph linear equations.
- Determine linear equations (slope-intercept, point-slope, point-point)

#### Part 2: Functions - basics

*(Precalculus students are only responsible for objectives 1 and 2 from this section.)*

- Understand the definition of a function
- Evaluate functions

----------- - Identify domain and range
- Compose functions
- Evaluate piecewise defined functions
- Determine the inverse of a function

#### Part 3: Families of functions

For each of the following functions, students should be able to (1) understand and apply basic properties, (2) solve equations and inequalities, (3) recognize graphical representations, and (4) identify simple transformations (i.e. shifts, reflections, and stretches/compressions):

- Linear functions
- Quadratic functions
- Polynomial functions (degree> 2)
- (especially roots and behavior)

- Rational functions
- (especially domain, range and asymptotes)

- Exponential functions
- (especially definition and properties of roots/exponents)

- Logarithmic functions
- (especially definition and laws of logarithms)

- Trigonometric functions
- (especially basic definitions, special values of unit circle, degrees to and from radians, and Pythagorean Identities)

### Review Resources

The following four resources are available for student’s preparation and review:

#### 1. Sample Precalculus and Calculus 1 Placement Exam

- Sample exam for Precalc ⁄ Calc (pdf)
- Answers to sample exam for Precalc ⁄ Calc (pdf)
- Grading interpretation for Practice Exam (pdf)

#### 2. Sample Problems

- Basic Algebra (Precalculus and Calculus) (pdf)
- Exponential and Logarithmic Functions (Precalculus and Calculus) (pdf)
- Trigonometry (Calculus) (pdf)

#### 3. Online Review

The following links give free online resources for reviewing prealgebra, algebra and precalculus skills:

#### 4. ALEKS® Course Review

If you would like to approach your review for Precalculus or Calculus more thoroughly, or if you know you have significant deficiencies in your background that you would like to correct, you may choose to use Bethel's ALEKS "Prep. for Precalculus" or "Prep. for Calculus 1" courses. These courses are online and self-paced. A 6-week access code for each course can be purchased for less than $30. Each course begins with a diagnostic test, and then creates a personalized plan for working through various topics that need attention. To enroll in one of these courses please see: ALEKS enrollment instructions for Prep. for Precalculus (pdf) or the ALEKS enrollment instructions for Prep. for Calculus (pdf).

*ALEKS is a registered trademark of ALEKS Corporation.*

## Placement Exam Testing

When you are ready to take the test, use the directions below, to go to the Precalculus and Calculus 1 Placement Exam Moodle course. You will “self-enroll” in this Moodle course to take the exam. The exam should be taken on your own (we want to see if YOU are ready for the course). You will not benefit by cheating or using resources other than your own mind, because you need an accurate assessment of your skill level in order to be placed in the appropriate course-a course in which you can most likely succeed.

No calculators are allowed on the placement exam, and you should set aside 30-60 minutes for the exam. After you have finished taking the exam, you will receive an email with your level score and further instruction on how to retrieve more detailed results. Your score will also be placed into Banner (Bethel’s student information system) within 24 hours of taking the test, and you will be cleared for the courses as outlined above.

To get the most accurate assessment for yourself:

- Do not use a calculator, another person, online searches, books, or any other resources. We want to see the skills you have in your own head.
- If you plan to take Calculus 1, and are currently in Precalculus, wait to take the placement exam until you have completed at least 90% of the course.

### Directions for taking the Precalculus and Calculus 1 Math Placement Exam

Make sure you are ready to take the exam (see policies above). **You may take the placement test only once per testing period.**

- Use Firefox or Chrome to enroll in the “self-enrollment” Moodle course for testing. A page like the one below will appear.
- Click the “Enroll me” button and then follow the directions in the course.

## Registration Clearance and Viewing Results

After you take the placement exam, your score will be sent to the registrar’s office within 24 hours.

You will also receive two emails with results information:

(New students: note that this email may come to your personal or Bethel email address - check both! To access Bethel email, log in to MyBethel with your Bethel login. On the page that appears, click on the mail icon in the upper right hand corner to get your email)**Email 1:**Within one hour after taking the placement exam, you will receive an email with your**level**score. Please pay attention to the details in the email, especially for the choices of Level 2.**Email 2:**Within the next 24 hours after taking the exam, you will receive an email detailing all question topics and your results. This email will tell you which topics you had right or wrong, so that you can brush up on any skills that need review before your course. More information about review will be included in the email. You may also generate the Detailed Results Report (requires your Bethel login AND allow pop-ups to view).**No emails?**If you do not receive either of these emails, check your spam filter and/or spam mail box, your Bethel and/or non-Bethel email boxes, and if you don't find the email, contact the Director of Math Testing at: mathcs-testing-manager@bethel.edu. In your correspondence, include the date you took the exam and which email(s) you are missing (the first level email and/or the second detailed results email).

Congratulations on completing this step in the placement and review process. Don't forget to complete the process by following up with review: you will thank yourself when you start your course.

For additional questions, contact the Director of Math Testing at: mathcs-testing-manager@bethel.edu.