Pre-Calculus
Semester 1 Final Exam Review
Name: _
Period: _
UNIT 1: FUNCTIONS
1.
Identify the following characteristics given the graph below.
Domain:
Range:
Increasing:
Decreasing:
Maximum:
Minimum:
AP English IV Literature and Composition
Semester 1
Final Exam Study Guide
Format of final exam:
Reading Comprehension - 40%
38 multiple choice critical thinking
questions for 2 poems and 1 prose pass
/*
* @purpose: To satisfy the requirements of the 16.01 assignment.
*
* @author Jairaj Singh
* @version 12/19/17
*/
public class TestCandidateV3
cfw_
private static Candidate[] election = new Candidat
/*
* @purpose: To satisfy the requirements of the 16.01 assignment.
*
* @author Jairaj Singh
* @version 12/19/17
*/
public class TestCandidateV3
cfw_
private static Candidate[] election = new Candidat
6.5.1 APPLICATIONS oF EXPoNENTIhL Funo'rlons
Perhaps the most well-known application of exponential functions comes from the nancial world.
Suppose you have $100 to invest at your local bank and they
6.2 Paoeserrss oF LDGARITHMS
In Section .l, we introduced the logarithmic flmctions as inverses of exponential functions and
discussed a few of their mctional properties from that perspective. In this
6.4 LDGARITHMIG Eouarrross AND INEQUALITIES
In Section 3.3 we solved equations and inequalities involving exponential flmctions using one of
two basic strategies. We now turn our attention to equation
Theoan 8.4. Properties of Scalar Multiplication
I Associative Property: For every :11. x :1. matrix A and scalars is and r, [krlA 2 nd.
Identity Property: For all m. x :1. matrices A,1A = A.
Additive
Theorem 5.1. Properties of Emotion Composition: Suppose f, g, and h. are functions.
- horigof]=cfw_liog]of,prmridedthecompositefunctionaaredened.
l [fIisdenedasI[z]=nforallrealnumhersz,thcnl'of=fol'
Theorem 8.3. Properties of Matrix Addition
l Cnnrmutative Prnperrtjr: Fur all m x n matriemI A +3 = 3 +11
I Associative Prnperty: Ferallm.><1rtmatrievsI [A+B]+C=A+[B+C
- Identity Prnperty: If Elm is t
Theorem 8.2. How Operations: Given an augmented matrix for a system of linear equations,
the following row operations produce an augmented matrix which corresponds to an equivalent
system of linear eq
8.2 SvsTEMS 0F LINEAR. EQUATIoI-Js: AUGMENTED MATRICES
In Section 3.1 we introduced Gaussian Elimination as a means of transforming a system of linear
equations into triangular form with the ultimate
Roughly speaking, an integral
is improper if:
1.
One of the limits is infinite.
2.
The integrand "blows up" somewhere on the interval of integration.
For example,
are improper because they have infini
Partial fractions is the opposite of adding fractions over a common denominator. It
applies to integrals of the form
The idea is to break
(A function of the form
a rational function.)
into a sum of sm
Trig substitution reduces certain integrals to integrals of trig functions. The idea is to
match the given integral against one of the following trig identities:
If the integral contains an expression
How do you find the area of a region bounded by two curves? I'll consider two cases.
Suppose the region is bounded above and below by the two curves
and on the sides by
and
and
,
.
I divide the region
If u and v are functions of x, the Product Rule says that
Integrate both sides:
This is the integration by parts formula. The integral on the left corresponds to the
integral you're trying to do. Part
The work required to raise a weight of P pounds a distance of y feet is
footpounds. (In m-k-s units, one would say that a force of k newtons exerted over a
distance of y feet does
newton-meters, or jo
Start with an area - a planar region - which you can imagine as a piece of
cardboard. The cardboard is attached by one edge to a stick (the axis of revolution).
As you spin the stick, the area revolve
L'Hopital's Rule is a method for computing a limit of the form
c can be a number,
, or
. The conditions for applying it are:
1.
The functions f and g are differentiable in an open interval containing
For trig integrals involving powers of sines and cosines, there are two important cases:
1.
The integral contains an odd power of sine or cosine.
2.
The integral contains only even powers of sines and
When an integral contains a quadratic expression
, you can sometimes
simplify the integrand by completing the square. This eliminates the middle term of
the quadratic; the resulting integral can then
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Section 2.1 Rates of Change and Limits
59
Chapter 2 Overview
The concept of limit is one of the ideas that distinguish calculus from algebra and
trigonometr