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Math 1: General Course Outline

Catalog Description

1. Precalculus. (4) Lecture, three hours; discussion, one hour. Preparation: three years of high school mathematics. Requisite: successful completion of Mathematics Diagnostic Test at UCLA. Function concept. Linear and polynomial functions and their graphs, applications to optimization. Inverse, exponential, and logarithmic functions. Trigonometric functions. P/NP or letter grading.

The purpose of Math 1 is to give students a strong preparation for taking calculus. Students completing Math 1 are expected to continue in Math 3A or Math 31A. Math 1 does not satisfy the quantitative reasoning requirement for the College of Letters and Science.

Math 1 covers material that is ordinarily addressed in the high school curriculum. However, this material is not required for admission to the University of California, and for this reason the course is offered for credit at UCLA.

In order to enroll in Math 1, students should have a good background in intermediate algebra. Before enrolling in Math 1, students must take and pass the Mathematics Diagnostic Test at the specified minimum performance level.

Students who obtain the grade of C- or better at UCLA in Math 1 may enroll directly in Math 3A or Math 31A without taking the Mathematics Diagnostic Test.

Textbook

D. Lippman & M. Rasmussen. Precalculus. An investigation of functions.
Available online at www.opentextbookstore.com/precalc

Outline update: P. Greene, 8/13

Schedule of Lectures

Lecture Section Topics

1

1.1

Functions and Function Notation

2

1.2

Domain and Range

3

1.3

Rates of Change and Behavior of Graphs

4

1.4, 1.5

Composition of Functions , Transformation of Functions

5

1.5, 1.6

Transformation of Functions , Inverse functions

6

2.1, 2.2

Linear Functions and Graphs of Linear Functions

7

2.2, 2.3

Graphs of Linear Functions , Modeling with Linear Functions *

8

2.5

Absolute Value Functions

9

3.1

Power Functions and Polynomials

10

3.2

Quadratic Functions

11

3.3

Graphs of Polynomial Functions

12

3.4

Rational Functions

13

3.5

Inverse and Radical Functions

14

4.1

Exponential Functions

15

4.2

Graphs of Exponential Functions

16

4.3

Logarithmic Functions

17

4.4

Logarithm Properties

18

4.5

Graphs of Logarithmic Functions

19

5.1 and 5.2

Circles and Angles

20

5.2, 5.3

Angles, Points in Circles using Sine and Cosine

21

5.4

The other Trigonometric Functions

22

6.1, 6.2 (Tangent only)

Sinusoidal Graphs and the Graph of Tangent

23

6.3

Inverse Trig Functions

24

6.4

Solving Trig Equations

25

7.2

Addition and Subtraction Identities ( Omit product to sum---sum to product identities **

26

7.3

Double Angle and Half Angle identities