# Thread: Required Pre-Calc knowledge for a Calculus course?

1. ## Required Pre-Calc knowledge for a Calculus course?

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.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
3.2 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

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

2. It's a little easier to tell you what you can leave out. You should skip the following sections:

P.6 Exploring Data: Representing Data Graphically
1.5 Shifting, Reflecting, and Stretching Graphs
2.3 Complex Numbers
2.5 Solving Inequalities Algebraically and Graphically
2.6 Exploring Data: Linear Models and Scatter Plots
3.2 Polynomial Functions of Higher Degree
3.3 Real Zeros of Polynomial Functions
3.4 The Fundamental Theorem of Algebra
4.5 Exponential and Logarithmic Models
4.6 Exploring Data: Nonlinear
5.7 Applications and Models
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
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
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
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

Study the following sections only if you have time:
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

3. Thank you for you help. You have no idea how much I appreciate it.

There is one other class that I have to take with a mathematical background:

CSCI 150: Discrete Structures
Mathematical background required for computer science. Sets, relations, cardinality, propositional calculus, discrete functions, truth tables, induction, combinatorics.

Are there any sections you would remove from the "omitted" list because of that class?

4. I would say that the list of things that your skipping should not include anything from chapter 9 apart from 9.7 apart from that I think that list looks good.

5. I personally think that Discrete Structures is generally a pretty self-contained course, and you shouldn't have to review anything specific for that course. It may however require a bit more mathematical maturity than a Calculus course, so be prepared to work a bit harder.

6. yeah I would say that 9.1,9.2 and 9.3 will help with a calculus course and 9.4,9.5 and 9.6 would be a good a good thing to go over for a discrete course (they probably won't be too well covered in a discrete course as they will have been covered by most students in a pre-calc course for example) so I would look at those (especially induction)