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Required Pre-Calc knowledge for a Calculus course?

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  • Thread starter eindoofus
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  • #1

Main Question or Discussion Point

I’m planning on going back to college and I need to take the following math course in a month and a half when the new Spring semester begins:

MATH 150 Calculus with Analytic Geometry I
Limits, continuity, differentiation and integration of elementary functions and trigonometric functions, applications.

However, I haven’t done math in about 7 years and most of my Pre-Calc knowledge is either rusty or gone. I don’t have the option of taking a preparation course since the ladder of classes I need to take all begin with Calculus, and I don’t have the time or money to prolong the process.

Below is the table of contents from a used Pre-Calc book I bought. I’m hoping to go through it as quickly as possible try to relearn what I forgot. From these listed chapters and sections what should I study in order to prepare for my MATH 150 course? What sections can I omit and what sections do I have to pay special attention too? Thanks for any help you can give.

Chapter P - Prerequisites
P.1 Real Numbers
P.2 Exponents and Radicals
P.3 Polynomials and Factoring
P.4 Rational Expressions
P.5 The Cartesian Plane
P.6 Exploring Data: Representing Data Graphically

Chapter 1 – Functions and Their Graphs
1.1 Graphs of Equations
1.2 Lines in the Plane
1.3 Functions
1.4 Graphs of Functions
1.5 Shifting, Reflecting, and Stretching Graphs
1.6 Combinations of Functions
1.7 Inverse Functions

Chapter 2 – Solving Equation and Inequalities
2.1 Linear Equations and Problem Solving
2.2 Solving Equations Graphically
2.3 Complex Numbers
2.4 Solving Equations Algebraically
2.5 Solving Inequalities Algebraically and Graphically
2.6 Exploring Data: Linear Models and Scatter Plots

Chapter 3 – Polynomial and Rational Functions
3.1 Quadratic Functions
3.2 Polynomial Functions of Higher Degree
3.3 Real Zeros of Polynomial Functions
3.4 The Fundamental Theorem of Algebra
3.5 Rational Functions and Asymptotes
3.6 Graphs of Rational Functions
3.7 Exploring Data: Quadratic Models

Chapter 4 – Exponential and Logarithmic Functions
4.1 Exponential Functions and Their Graphs
4.2 Logarithmic Functions and Their Graphs
4.3 Properties of Logarithms
4.4 Solving Exponential and Logarithmic Equations
4.5 Exponential and Logarithmic Models
4.6 Exploring Data: Nonlinear

Chapter 5 – Trigonometric Functions
5.1 Angles and Their Measure
5.2 Right Triangle Trigonometry
5.3 Trigonometric Functions of Any Angle
5.4 Graphs of Sine and Cosine Functions
5.5 Graphs of Other Trigonometric Functions
5.6 Inverse Trigonometric Functions
5.7 Applications and Models

Chapter 6 – Analytic Trigonometry
6.1 Using Fundamental Identities
6.2 Verifying Trigonometric Identities
6.3 Solving Trigonometric Equations
6.4 Sum and Difference Formulas
6.5 Multiple-Angle and Product-to-Sum Formulas

Chapter 7 – Additional Topics in Trigonometry
7.1 Law of Sines
7.2 Law of Cosines
7.3 Vectors in the Plane
7.4 Vectors and Dot Products
7.5 Trigonometric Form of a Complex Number

Chapter 8
8.1 Solving System of Equations
8.2 Systems of Linear Equations in Two Variables
8.3 Multivariable Linear Systems
8.4 Matrices and Systems of Equations
8.5 Operations and Matrices
8.6 The Inverse of a Square Matrix
8.7 The Determinant of a Square Matrix
8.8 Applications of Matrices and Determinants

Chapter 9 – Sequences, Series, and Probability
9.1 Sequences and Series
9.2 Arithmetic Sequences and Partial Sums
9.3 Geometric Sequences and Series
9.4 Mathematical Induction
9.5 The Binomial Theorem
9.6 Counting Principles
9.7 Probability

Chapter 10 – Topics In Analytic Geometry
10.1 Conics
10.2 Translations of Conics
10.3 Parametric Equations
10.4 Polar Coordinates
10.5 Graphs of Polar Equations
10.6 Polar Equations of Conics

Answers and Replies

  • #2
I forgot to include one other course with a mathematical background that I will taking next semester along with Calculus that might affect what I need to study:

CSCI 150: Discrete Structures
Mathematical background required for computer science. Sets, relations, cardinality, propositional calculus, discrete functions, truth tables, induction, combinatorics.
  • #3
Probably Chapters 1,2,3,10.
For the second semester (or maybe later in the first semester) Chapters 4,6,7 ...
  • #4
I did pretty much the same thing... right into Calc. without ever taking precalc and it had been ~6 years since I had taken trig.

I'd recommend Ch. 1, 3 and 4 to begin with... logs pop up almost right away(in my book anyway).

Another thing you can't escape is Trig... take the time and make sure you know the unit circle.
  • #5
chapters 4 and 5 are pretty important

chapter 1 can be useful as a general refresher/practice

7.3-5 are pretty cool topics and could be fun
  • #6
Hi eindoofus :)

I'm finishing up calc I w/analytic geom now, and I did exactly what you are doing before I took this course. I would recommend 1 and 3-6 strongly. The others are beneficial also, and you should study them as you are able, but I think 1 and 3-6 cannot wait. Number two is very important, but if you are already familiar with solving equations, I would say it is safe to come back to it later. Numbers 7 and 10 can probably be reviewed while on those topics in calculus. I found it useful to also know formulas for volumes, areas, etc... of spheres, cones, etc...you do not have to memorize them, but have tools accessible.
Another user noted that you cannot escape trig, and that is terribly true. It is good to be familiar with some trig identities or to have them accessible, logarithms and log identities are important, and factoring and polynomials are WAAAAY important.
Also when it comes to trig, radians are most used in calculus...I don't think we ever had an exercise with degrees in my class.

6 is used more with integrals, which I think is usually covered later in the semester, but I think it is better to study it before the semester begins.
also i don't know how comfortable with algebra stuff, but make sure you're comfortable with radicals and exponents
  • #7
Brush up on your Algebra skills if you already haven't. Plenty of people in my Cal. IV class know the Calculus but they lack Algebra skills.

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