Generally, I do not advise students to take full summer courses in the summer, especially precalculus. Precalculus is extremely important for calculus. Many times, my calculus students have trouble with the precalculus portion of a calculus problem. I did not advance my own 5 children at school. They followed the school path for honors math. My kids scored 5s on the AP Calculus exam, A+, A, B grades in math. They went onto Yale, Rice University, UCLA, University of Michigan, UC Davis and were accepted into Harvard, Stanford, Columbia, UC Berkeley. The point is that my kids were very capable in math and I did not advance them.

Some disadvantages of skipping precalculus at school:

  • Many precalculus concepts are very important for calculus. Too often, the precalculus portion of a problem stumps calculus students.
  • Taking precalculus early in high school offsets students for the SAT/ACT exams. Generally, these exams are taken in the junior year. If you are a junior taking calculus, you may not remember your precalculus and algebra 2 as well as needed for the SAT/ACT exams. My youngest children, Jessica and Scott, took calculus as juniors at James Logan High School. This is the Logan honors path. They both took the ACT in the spring of their sophomore year. The ACT is an algebra 2 based exam – only about 60% of the precalculus book is needed for the ACT exam. Usually, sophomores do not take the ACT. The ACT is critical reading, English and an essay. Taking the ACT as a junior and senior will give you more time to prepare for these 3 portions of the ACT. The SAT has evidence-based reading/writing and an essay.
  • Learning precalculus in a summer is very difficult. Precalculus is hard with 9 months to learn it. It is extremely difficult to learn in 6 weeks. If you are lost at any point, it will compound very quickly. If you are sick for a few days, you may miss an entire chapter. I have not taught precalculus to any of my kids in 6 weeks. It can be done if a teacher knows what chapters are unimportant for calculus and teaches only those concepts. Generally, teachers just follow the book.
  • Some universities will require or recommend SAT Subject Math level 2 test for students applying to college in certain majors. The SAT Subject Math exam is precalculus based and some geometry. Poor scores on this exam may reduce your chances of getting into some universities. Download the SAT Subject Tests Student Guide for more information on the topics.
  • Taking Calculus AB in the sophomore year and then Calculus BC in the junior year, may not be desirable for several reasons. Calculus BC is much harder than Calculus AB. All grades from your sophomore and junior years will be reported on your UC and CSU college applications. Grades from the senior year are not a part of the application since applications are due on November 30th.
  • You may need more math in college beyond calculus BC. By taking calculus BC in your junior year, you may forget necessary skills for the next math class needed in college. A UC student shared with me that she did poorly in her college calculus class. She must retake the course. There were 400 students in her class and the graduate student instructor taught once a week. Without good math grades, she could not continue with her course work in her major.
  • Exceptional calculus skills may be necessary for some college classes. My son was a biochemistry major at BYU. In his 300 level physics classes, calculus was required for this class. Even though Allen received a 5 on the AP Calculus BC exam and was the top calculus student at American High School, by the time he took physics 300 level classes, he could not remember his calculus. He called home and asked me to fly him home for me to tutor him. I told him to find a calculus tutor at school.
  • I have also tutored college chemistry majors in calculus for their chemistry class. Calculus was necessary for the chemistry problems (integration and instantaneous rate of change). Some other college sciences courses require calculus. Calculus is often a stumbling block for science majors and even business majors at college. I have worked with various college students teaching calculus for a non-math class.
  • If you are taking a summer college math course, it is best to earn an A or B grade. Even a B may not be good enough depending on your future path. This college transcript may follow you as you apply for college and be a part of your college GPA.

Take precalculus in the summer only if:

  • You are highly motivated.
  • Math comes easily to you.
  • Have a great teacher.
  • Do not need to take the SAT Subject Math exam.

I have had very few students succeed in skipping precalculus at school. I am the only one in my family that skipped precalculus and went straight to calculus. I loved math as a child. I do could it easily and studied it for pleasure. I won many math awards starting in elementary school. I placed 9th in math contest at my high school as a freshman. I won 2 more awards in math in high school. My son Allen also won math awards for being the top student in math each year at American High School. Even while serving a mission for our church, he would do math problems.

Most students should not skip a math class. Geometry is the only math class that a student might successfully skip. Some Fremont Unified high schools are offering a 1 semester geometry class starting 2016. This could work if the curriculum includes the geometry necessary for:

  • SAT/PSAT
  • ACT – The ACT test contains about 20-25% geometry
  • Calculus – Geometry is needed for optimization and related rates calculus problems.
    These are both word problems based on geometry.

New Haven Unified honors students can skip 6th grade math. Honors students go straight to prealgebra in the 6th grade. 6th grade math can be a good math class to skip. Unfortunately, most schools do not give students the choice to skip elementary math classes.