# 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, or biokinetics.

Keeping up in these college-level courses depends on at least three factors, enrolling in the appropriate course, having a strong work ethic and good study skills, and possessing 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:** March 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 and February

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.

### Course Prerequisites & Registration

#### Prerequisite Policy for Precalculus and Calculus 1

Before registering for Precalculus (MAT123M) 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).

#### Registration

Students scoring level 1 and 2 will be cleared to register for Calculus 1, students scoring at a level 1 - 4 will be cleared to register for Precalculus. Level 4 students intending to take Precalculus, must also sign a course contract.

## 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 okay and 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 1:** Clearance for Calculus 1 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 2:** Clearance for Calculus 1 or below with recommendation to review

Calculus 1 is probably the right course for you, but review before starting the course is strongly recommended (see review section below).

**Level 3:** Clearance for Precalculus

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

**Level 4:** Clearance for Precalculus with recommendation to review

You will tentatively be placed in Precalculus. Review before starting the course is strongly recommended, and a contract is required to maintain your registration.

### Course Contracts for Precalculus and Calculus 1

Placement levels have been associated with success in these courses, so students are strongly urged to enroll in the course for which they place. The following plots and statistics give average grades in courses for students enrolling in Precalculus and Calculus 1 from Fall 2011 - Fall 2014.

For **Precalculus**,

- if you score at the appropriate level (level 1 - 3), you have an 83% chance of getting a "C" or better, and an 8% chance of getting an “F” or “W”
- if you score a level 4 , you only have a 63% chance of getting a C or better, and a 23% chance of getting an “F” or “W” (based on statistics for Precalculus students between Fall 2011 - Fall 2014, with 175 students).

For **Calculus**,

- if you score at the appropriate level (level 1 - 2), you have a 93% chance of getting a "C" or better, with a 5% chance of getting an “F” or “W.”
- if you score a level 3-4, you only have a 68% chance of getting a "C" or better, and a 21 % chance of getting an “F” or “W”

(based on statistics for Calculus students between Fall 2011 - Fall 2014, with 296 students).

#### Process for Level 3 & 4 Students who want to take Calculus & Level 4 Students who want to take Precalculus

Students who score at a level below that which they anticipated should take time to review and retest in the next testing period, if available. Those students who do not have time to retest and who fall in the following two categories must sign a course contract:

**level 3-4 students who want to take Calculus:**these students must sign a Calculus course contract (pdf), have the professor clear the student for enrollment, and start a review regimen (see review section below).**level 4 students who want to take Precalculus:**these students must sign a Precalculus course contract (pdf) to maintain registration status. The course contract must be signed by the end of the first week of classes. However, these students should start a review regimen, if possible, before the course begins (see review section below).

Generally, contracts will be signed with the professor of the intended course. Current students should email the professor to set up a time to discuss enrollment. New students can discuss enrollment options with math faculty during Welcome Week advisor hours (typically Friday of Welcome Week; see the schedule). If it is determined that the student should take a course that doesn’t coincide with the recommendation, the student must sign a contract. After signing the contract and discussing a review plan, the professor can clear the student to register for the course.

### Registration and Course Preparation

Placement scores are given to the Registrar’s office and placed in the student record on Banner (Bethel’s Student Information System). Registration holds (restrictions) are removed as follows: level 1 and 2 students may register for Calculus 1 or Precalculus, level 3 and 4 students may register for Precalculus only.

After completing the placement exam, it’s worthwhile to carefully review your results and make a personal skill review plan. Review plans can include one of Bethel’s Aleks preparation courses. Acting on this critical final step of the Placement and Review Process will help students be ready for success in Precalculus and Calculus 1.

Since course readiness is key to success in these courses, each student’s skill level and readiness for Precalculus and Calculus 1 will be tested on the second or third day of classes using a Skills Test. This test is similar to the Placement test and serves as the final step in the review and preparation process-giving students one final moment to assess their skills and change courses before the final add/drop day at the beginning of the semester.

#### Skills Test

As mentioned in the Process and Overview section, course readiness is key to success in these courses. Each student’s skill level and readiness for Precalculus and Calculus 1 will be tested on the second or third day of classes using a “Skills Test.” This test is similar to the Placement Test and serves as the final step in the review and preparation process-giving students one final moment to assess their skills and change courses before the final add/drop day at the beginning of the semester. In each course, the Skills Test will be scored and will count as half a course exam grade.

## 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. Keep in mind that you will face accountability measures during the first week of classes in the form of the Skills Test. In addition, since the Skills Test is very similar to the placement exam, you should use the placement exam as a fair “practice” and assessment for review for this in-class, graded exam.

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, search online, use 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.
- Choose 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, and you will be cleared as follows:

- Level 1 & 2: cleared to register for Calculus 1 and Precalculus
- Level 3 & 4: cleared to register for Precalculus.

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, as extra conditions exist for students who score Level 3 & 4 who want to take Calculus 1 and Level 4 students who want to take Precalculus. These students must see their prospective course professor to discuss enrollment, review, and sign the required contract for these situations. Here is the email 1 general text if you lose your personal results email 1.**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 and/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. If you lose this email, here is the email 2 general text. 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 2nd 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.