### Placement and Advanced Placement Credit & Calculus Readiness Test

There is a big difference between calculus study at Lehigh and calculus at most high schools. A solid high–school precalculus course is necessary background for calculus at Lehigh. Students need a strong foundation in functions (forms, graphs, roots) and trigonometry to really thrive in calculus. Most students who take calculus in high school are accustomed to using a graphing calculator. Calculators are not used in Lehigh calculus classes. A firm understanding of the symbolic and algebraic manipulations used in calculus, without relying on calculators, is necessary for more advanced applications of calculus in mathematics and in other fields. Many students find a summer course in calculus at a local community college to be helpful in bridging from high school mathematics to Lehigh calculus.

#### Advanced Placement for Calculus

Students who score 4 or 5 in the AB advanced placement exam may receive 4 credits for Math 21 and those who score 4 or 5 on the BC advanced placement exam may receive 8 credits for Math 21 and 22. Students should preregister for Math 21, 31, or 51 now, and if the AP exam scores warrant credit, the appropriate adjustments can be made later. Advanced placement and course credit is also granted for successful completion ofapproved college coursestaken during high school. Approval is granted on a case–by–case basis and depends on submission of detailed information as to course content.

We recommend that students consider beginning Lehigh calculus a semester below their advanced placement. If you have credit for Math 21 and are eligible for Math 22, consider taking Math 21; if you have credit for Math 21 and Math 22 and are eligible for Math 23, consider taking Math 22. You will relinquish some or all of your AP credit, but experience has shown that many AP courses do not provide adequate preparation for calculus at Lehigh. Depending on demand, the department of mathematics may offer anticipatory exams for Math 51, 21, 22 and 23 during the orientation period.

#### Calculus Placement

There are four different calculus sequences as described below. Students should read the descriptions to determine which courses are appropriate for their interests and possible majors. Once an appropriate course is determined, SAT quantitative scores are suggested as a guideline for determining placement.Students interested in any of the sequences with a quantitative SAT score below 600 should take Math 0, Preparation for Calculus. Students interested in Math 51 or 81 with an SAT score of 600 or above can take math 51 or 81. However, those with scores close to 600 might consider Math 0 depending on high school background. Students interested in Math 21 with an SAT score below 650 and above 600 should consider the Math 75 and 76 as a replacement for Math 21. Department permission is required for placement into Math 31. It is based on motivation, SAT scores, and prior courses.

Further questions regarding placement should be directed to the contacts listed at the bottom on the page.

#### Calculus Courses

With three different calculus sequences, the Mathematics Department is able to tailor its offerings to students with different preparations and needs for studying calculus.

**1. The 20s sequence**

- Math 21, Calculus I (4 credits each) fall and spring
- Math 22, Calculus II (4 credits each) fall and spring
- Math 23, Calculus III (4 credits each) fall and spring
- alsoMath 75 and76, Calculus I, parts A and B, substitute for Math 21

The 20s sequence (12 credits) is required of all engineering students as well as majors in Mathematics, Computer Science, and many natural science programs. The three semesters cover single– and multiple–variable calculus and introduce differential equations.Each week there are 3 lectures and one meeting in a small group with a graduate student. Each of these

courses is offered in both semesters each year

Math 75 and 76 (2 credits each).These are 2 credit courses that together replace MATH 21. These two courses constitute a year long sequence (which must be started in the fall) that substitutes for MATH 21. The slower pace and additional precalculus material is intended to allow students who need more preparation to master the material of MATH 21. Both courses have 2 lectures and one meeting in a small group with a graduate student

Successful completion of Math 21* or*Math 76 is a prerequisite for Math 22. Students who start with Math 21 and find themselves struggling can switch to Math 75 or Math 51 as long as they do so in a timely fashion.

**2. The 30s sequence**

- Math 31, Honors Calculus I (4 credits) fall
- Math 32, Honors Calculus II (4 credits) spring
- Math 33, Honors Calculus III (4 credits) fall

The 30s sequence(12 credits) is the most in–depth and rigorous sequence and requires the most student effort. It covers the same material as the 20s sequence and, therefore, meets any stated requirement for the 20s sequence. Classes are small, and the ‘Honors’ designation in the course title records the student’s high aptitude and motivation for mathematics.

**3. The 50s sequence**

- Math 51, Survey of Calculus I (4 credits) fall and spring
- Math 52, Survey of Calculus II (3 credits) spring

The 50s sequence covers much of the material covered in 21 and 22 but not in as much depth, allowing the material to be completed with fewer credits (totaling 7 credits). This sequence is suited for Architecture and some natural science and social science programs. Math 21 is usually an acceptable substitute for Math 51 but not the reverse, and Math 21 is an acceptable prerequisite for 52 but 51 is not a prerequisite for 22; students with strong mathematics backgrounds might consider starting with the 20s sequence if they have any question about which sequence best suits their curriculum. The 50s sequence is essentially a terminal one, leaving students unprepared for most subsequent mathematics courses, so students who are contemplating further study in mathematics should seriously consider the 20s sequence.

**Math 81, Calculus with Business applications (4 credits) fall and spring**

Math 81 covers much of the material covered in 21 but with greater emphasis on applications in business and economics. Math 81 or Math 21 is required of all students in the College of Business and Economics. Math 81 is an acceptable prerequisite for 52 but it is not a prerequisite for 22; students with strong mathematics backgrounds might consider starting with the 20s sequence if they have any question about which sequence best suits their curriculum. Math 81 is essentially a terminal course, leaving students unprepared for most subsequent mathematics courses, so students who are contemplating further study in mathematics should seriously consider the 20s sequence.

**MATH 0: Preparation for Calculus (2 credits, Fall):**

This course is for students who need more preparation before moving on to calculus, as evidenced by low scores on the readiness exam. The 2 credits do not count toward the total number of credits required for graduation, but the grade does count in the student’s GPA. Students should pass Math 0 with a grade of C– before taking Math 51 or 21.

For more information: contact Professor Terry Napier via email attjn2@lehigh.eduor Mary Ann Dent, Academic Coordinator at (610) 758-3731 or via email atmad8@lehigh.edu.