Where Precalculus fits.
The usual US order:
- Algebra 1
- Geometry
- Algebra 2
- Precalculus
- Calculus
The order is not the same in every school, and the names change too. Some schools teach “Algebra 2/Trig”. Palo Alto lists courses like “Analysis H” next to Precalculus (Palo Alto Unified). Ask the school which class prepares students for calculus.
Two other versions:
- Honors Precalculus: ask the school how the topics, pace and homework differ from the regular class.
- AP Precalculus: a College Board course with an AP exam in May. A good score may earn college credit, if the college accepts it (AP Central). See our guide Is AP Precalculus hard?
What is in Precalculus.
The list changes from school to school. These are the main topics in the CK-12 course and the Texas standards. Khan Academy’s course covers most of them.
- Functions and their graphs. How to combine functions, undo them (inverse functions), and move their graphs. Calculus is the study of how functions change, so this is the base.
- Polynomial and rational functions. Where a graph crosses zero, and what happens near a value where you can’t divide. Calculus asks the same questions with limits.
- Exponential and logarithmic functions. Growth and decay, like money with interest or a population. A log answers “to what power?”. Calculus uses both all the time.
- Trigonometry. Sine, cosine and tangent, the unit circle, radians (a new way to measure angles), and identities (equations that are always true). Trig describes anything that repeats, like a wave or a wheel. Many calculus problems use it.
- Often also: vectors (a size and a direction), matrices (numbers in a grid), conic sections (circles, ellipses, parabolas), sequences and series (number patterns and their sums), and a first look at limits.
Is precalculus hard?
For many students, yes. It is often the hardest math class so far. Here is why:
- It uses all of Algebra 2. Factoring, exponents, fractions with x in them. Precalculus expects these to be fast.
- Trig is a lot of new content. The unit circle, radians and identities are new for most students.
- Each topic uses the last one. A gap in one unit shows up again in the next.
- It asks for a different kind of thinking. Less “follow these steps”, more “what does this function do?”.
Students say it too. “Precalc extends from algebra 2 for the first couple of units. After that you start trig, and its stuff that you have never seen before,” one student wrote on College Confidential. Another, on CollegeVine: “you might be asked to think a bit differently than you did in your high school math classes.”
The useful part for a parent: often the trouble is not the new topic. It is an Algebra 2 skill that is not solid yet. When a trig problem goes wrong, it is often the algebra inside it. Ask the teacher which one it is. Then your child knows what to practice, one skill at a time.
Struggle in precalculus is normal. It does not mean your child is “not a math person” or cannot learn this. Ask where they get stuck, and start there.
Is precalculus harder than Algebra 2? For many students, yes: it uses Algebra 2 and adds trig on top. Whether calculus feels harder after that depends on the student and the class.
Signs your child needs help.
- Grades fall after the first trig unit.
- Homework takes much longer than it did in Algebra 2.
- “I get it in class, but not at home.”
- Your child starts to avoid math, or says “I’m just bad at it”.
- Test mistakes are mostly algebra mistakes, not new topics.
Act early. Each unit uses the one before it. A gap in October is much easier to close than a gap in March.
How to help a student who is stuck.
Free options first:
- The teacher. Ask when the teacher offers extra help. Your child brings a problem they tried and points to the step where they got stuck.
- School tutoring or a math lab, if the school has one.
- Khan Academy. Free precalculus lessons and practice (Khan Academy). Start with the topic your child is on in class.
- A study group. Your child explains each step to a friend, and notes where they get stuck.
Paid options:
- A human tutor. Prices vary a lot. See what a math tutor costs. Ask if the tutor has taught precalculus, and ask them to check the Algebra 2 skills first.
- Sophie, our own tutor. From $8 an hour. About Sophie.
When a human tutor is the better choice: your child needs someone in the room, needs help to get organized, or needs help in many subjects.
A few precalculus practice problems.
- Functions. If f(x) = 2x + 1 and g(x) = x², what is f(g(3))?
Answer: 19. Why: Do the inside first. g(3) = 9, then f(9) = 19. - Polynomials. Where does x² − 5x + 6 equal zero?
Answer: x = 2 and x = 3. Why: It factors as (x − 2)(x − 3), and a product is zero when one factor is zero. - Rational functions. Where does the graph of f(x) = 1/(x − 2) have a vertical asymptote?
Answer: x = 2. Why: Near x = 2 the bottom gets close to zero. From the left, f(x) gets more and more negative. From the right, more and more positive. - Logs. Solve 2ˣ = 32.
Answer: x = 5. Why: A log asks “2 to what power gives 32?”, and 2⁵ = 32. - Trig. What is sin 30°?
Answer: 1/2. Why: In a 30-60-90 triangle, the side across from 30° is half the hypotenuse.
If problem 1 or 2 is confusing, show the work to the teacher and ask which Algebra 2 skill to review.
What comes after Precalculus.
- AP Calculus AB or BC, the usual next step. See AP Calc AB vs BC.
- College calculus, for students who finish high school with Precalculus.
- Statistics, for example AP Statistics, for students who want a math class without calculus.
