This page might be updated as the course progresses, including both review materials and lectures and sources to help with new material.
Here are some handouts:
- A handout on exponents, radicals, and factoring, to help you catch up on some topics we will not cover in class. If you need more help on these topics, please visit the Khan Academy website for short helpful videos on these topics.
- A trig circle, with all of the values of sine and cosine which we expect you to know.
- A handout on trig identities, with all of the trig identities which we expect you to know.
- The trig addition song, so you never wonder what sin(u+v) is equal to again.
- A handout on logarithm rules, with all of the log rules which we expect you to know.
- A blank copy of Exam 1 and solutions
- These are the limit laws from the book. You will be given an exact replica of this on Exam 2 and on the Final Exam.
- A blank copy of Exam 2 and solutions
Your first resource for help in the class should be the instructors and course assistants. You are welcome to office hours for any kind of question, we are here to help you and ready to explain the same thing as many times as necessary. You can also email us if you have any concerns, or if you would like to make an appointment to speak to one of us in private.
Stanford offers free drop in tutoring for Math 19 through the Center for Teaching and Learning (CTL). All of the information is on the Undergraduate tutoring website.
Some graduate students also offer their services to tutor for Math 19, you can find their names and email address on the list of private tutors maintained by the math department. Beware, private tutors tend to be expensive.
The most representative exams for us are those from Fall 2012. Material covered for a given midterm in the past does not necessarily correspond to the material covered in Math 19 this quarter (even in Fall 2012), so bear this in mind when using these to study for exams.
We will not provide solutions other than the ones already available here, but you are welcome to ask any instructor or course assistant to show you correct solutions to any problem.
The Stanford Math Department has introduced an online learning tool to help you acquire the precalculus skills you will need for the Math 20 series. We cannot emphasize enough how important a strong foundation in precalculus skills is to succeed in calculus. If there is any doubt in your mind that you are ready for calculus, or if any of the precalculus problems we are presenting in class seem difficult or foreign to you, do yourself a favor and sign up for ALEKS. If you need, financial aid is available to help you pay for the cost of the software ($34 for 6 weeks of help, $82 for 18 weeks of help).
During Weeks 1 and 2 of the quarter, you have the option of completing topics in the software ALEKS instead of turning in the assigned problems:
- To receive 10/10 on Homework 1, you must be placed into Module 8 (or higher) and have completed 117 topics (or more) by Thursday, October 3 at 5pm.
- To receive 10/10 on Homework 2, you must be placed into Module 13 (or higher) and have completed 210 topics (or more) by Thursday, October 10 at 5pm.
Once you have completed Module 12, you might want to work on the topics of Modules 15 and 16 as they will be important for us this year.
Another interesting resource for this class is Khan Academy, a website which hosts short, very helpful lectures. We highly recommend you spend some time looking through their Algebra lectures. We also expect their Calculus lectures will be very helpful throughout the course. They have a very popular sequence hosted at iTunesU. Some sample sessions are given below. You may not need all (or any) of these or you may need more. Try some out and don't hesitate to contact any member of the teaching staff if you have any questions. If you are feeling either bold or highly confused, you can start from the beginning with a very thorough set of diagnostic exercises that can help pinpoint where you should be focusing. To do the diagnostic exercises, start at the exercise dashboard (and be patient, it starts with arithmetic and finishes at calculus).
The following is a list of video topics we think will be particularly helpful to Math 19-20-21 students. This list may or may not be updated as the course progresses.
Trigonometry: For all trig videos, you can see the Basic Trigonometry Homepage and the Trig identities and examples Homepage. For maximum success, work out the exercises.
Rational inequalities: For all videos having to do with rational expressions, you can see the Rational Expressions Homepage. For maximum success, work out the exercises.
- quadratic inequalities (2 parts)
- functions (4 parts/)
- domain of a function
- rational inequalities (2 parts)
- function inverses (4 parts)
- algebraic long division
- limits: introduction, examples (5 parts)
- squeeze theorem
- proof:lim (sin x)/x
- exponential growth
- parametric equations
- logarithmic scale
- function inverses
- Work through all of the videos, including sequences and series! There is not so much here and getting these short, concise summaries will help your overall comprehension.