_/64
Calculus AP
Name_
Quiz 2.1-2.2
Date_
SHOW ALL WORK TO RECEIVE CREDIT FOR ANSWERS.
1. Use the definition of the derivative to find the derivative of
() =
1
2 + 1
2. Find the equation of the tangent line to the graph at the indicated point. Show all wo
2.1 The Derivative and the Tangent Line Problem
As we have already discussed, Calculus grew out of certain problem mathematicians that
previously could not solve. An example of this is finding the slope of a tangent line
8
8
6
6
k
4
4
C
B
A
2
2
5
is a se
2.2 Basic Differentiation Rules and Rates of Change
Rules to make finding derivatives easier. You still need to remember the limit definition!
Theorem 2.2 The Constant Rule
The derivative of a constant function is 0. That is, if is a real number then
( )
Answers
MULTIPLE CHOICE
1. (C) The given limit represents the alternative form of the definition of a
derivative:
chl = limm
X4! X ._. C
If the function is dened as x) = ln(X+1), then substituting in c = 1
gives rm = lim H1(X + 1) " In 2
Xhl X _ 1
pages
2.3 Product and Quotient Rules and Higher-Order Derivatives
Differentiation Rules
Product Rule: The product of two differentiable functions
and
is differentiable and
Example 1:
Find the derivative of
. First, multiply the factors and use the
sum/differenc
Calculus
Rates of Change
`
Name_
Date_
Equations 1-7 give the position function of a body, s is in meters, and t is in seconds.
a. Find the bodys displacement and average velocity from t = 0 to t = 2
b. Find the bodys velocity at time t = 2.
1. s(t) = .8t
Measurement Equivalent
1 Tbsp = 3 tsp
1 C. =16 tbsp
1 C. = 48 tsp
1 gal. = 4 qts
1 qt. = 2 pt.
1 pt. = 2 c.
Boiling= 212F
Freezing= 32F
Lab Duties
- Executive chef duties: Main cook, get equipment,
get ingredients, clean the stovetop(Everday), put
dishes
Variables in Algebra(1.1)
Define:
variable-
value-
variable expression-
numerical expression-
evaluate-
Variable Expressions
8y, 8*y,(8)(y)
16 , 16 y,
y
Meaning
8 times y
16 divided by 8
Operation
Multiplication
Division
3+x
3 plus x
Addition
7t
7 minus t
1.4 Equations and Inequalities
Define:
Equation:
Inequality:
Solution:
Example 1:
Check to see if 2 and 3 are solutions of the equation 4x + 1 = 9.
Example 2: Solve equations with mental math
To solve equations with mental math, think of the equation as
1.5 Translating Words into Mathematical Symbols
Example 1 Translate Addition Phrases
Phrase
Translation
The sum of six and a number
_
8 more than a number
_
A number plus five
_
A number increased by seven
_
Example 2 Translate Subtraction Phrases
Phrase
1.6 A Problem Solving Plan Using Models
Example 1 Write an Algebraic Model
You and some friends are at a Chinese restaurant. You order several $2
plates of wontons, egg rolls, and dumplings. Your bill is $25.20, which
includes tax of $1.20. Use modeling t
1.8 An Introduction to Functions
A _ is a rule that establishes a relationship between
two quantities, called the _ and the _.
For each input value there is exactly one output value.
One way to describe a function is to make an_.
Example 1 - Make an input
1.3 Order of Operations
Definitions:
1) Order of Operations
2) Left to Right Rule -
Example 1: Evaluate without grouping symbols.
Evaluate the expression 3x2 + 1 when x = 4. Use the order of operations.
Example 2: Use the left to right rule.
Evaluate eac
2.1 The Real Number Line
Real numbers can be pictured as points on a line. Every real number is
either _, _, or _.
Real Number Line
The scale numbers on a real number line are equally spaced and
represent _. An integer is either positive, negative or
zero
Addition Problem
5 + (-3)
-2 + (-6)
2.3 Subtracting Real Numbers
Equivalent Subtraction Problem
5-3
-2 6
Subtraction Rule
To subtract two real numbers, change the subtraction sign to a plus sign and change
the number behind the sign to its opposite.
Examp
2.2 Adding Real Numbers
You add a _ number by moving to the _ on
a number line.
You add a _ number by moving to the _ on
a number line.
Example 1 Add Using a Number Line
Use a number line to find the sum.
a. -2 + 5
b. 2 + (-6)
c. -3 + (-2)
_
Use the numbe
Section 2.4: Adding and Subtracting Matrices
A _ is a rectangular arrangement of numbers into horizontal rows
and vertical columns.
Each number in the matrix is called an _ or an _.
The size of a matrix is described as follows:
(the number of rows) X (the
2.6 The Distributive Property
The Distributive Property
The product of a and (b + c):
a(b + c) = ab + ac
Ex: 3(x + 7) = _
(b + c)a = ba + ca
Ex: (x + 5)6 = _
The product of a and (b c):
a(b c) = ab ac
Ex: 3(x 2) = _
(b c)a = ba bc
Ex: (x 4)8 = _
Example
3.1 Solving Equations Using Addition and Subtraction
Equivalent Equations
Original Equation
Equation
X3=5
_
X + 6 = 10
_
X=83
_
Action
Equivalent
_
_
_
Two operations that will undo each other, such as addition and
subtraction, are called _.
Example 1 Sol
3.2 Solving Equations Using Multiplication and Division
Multiplication and division are _ that can
help you to isolate the variable on one side of the equation. You can
use _ to undo division and use
_ to undo multiplication.
Example 1 Solve
-4x = 1
Examp
4.3 Graphing Lines Using Intercepts
The _ is where the graph of a line crosses over the xaxis. The y-coordinate will be zero and the x-coordinate will be the
point where it crosses the x-axis.
The _ is where the graph of a line crosses over the yaxis. The
3.6 Solving Decimal Equations
Example 1 Round for the final answer.
Solve and round to the nearest hundredth.
-38x 39 = 118
Solve the equation. Round to the nearest hundredth.
1. 24x + 43 = 66
2. -42x + 28 = 87
3. 22x 39x
= 19
Example 2 Solving equations
4.1 The Coordinate Plane and Scatter Plots
A _ is formed by two real number
lines that intersect at a right angle at the _.
The horizontal axis is the _ and the vertical axis is
the _.
Each point in a coordinate plane corresponds to an
_ of real numbers.
4.4 Slope of a Line
Example 1 The Slope Ratio
Find the slope of a hill that has a vertical rise of 40 feet and a horizontal
run of 200 feet. Let m represent the slope.
The slope(m) of a line that passes through points () and (, ) is
m=
=
Example 2 Positiv
4.6 Graphing Lines Using Slope-Intercept Form
Slope Intercept Form:
y = mx + b
m = _, b = _
Example 1:
Find the slope and the y-intercept of 2x + y = -3.
*First, make sure the y is by itself
Find the slope and the y-intercept of each equation.
1) y x = 5
Chapter 5:
Writing Linear Equations
Mr. Baker
5.1 Writing Linear Equations in
Slope-Intercept Form
The slope-intercept form of an equation of a line with
slope _ and y-intercept _ is:
y = mx + b
Example 1
Write an equation for a line whose slope is 3 and
Chapter 6:
Solving and Graphing Linear
Inequalities
Mr. Baker
6.1: Solving One-Step Linear Inequalities
The graph of a linear inequality in one variable is the set of points on a number
line that represent all solutions of the inequality:
Verbal Phrase
In
4.5 Direct Variation
Model for Direct Variation: _ where k 0.
K is called the_.
Example 1 Write a Direct Variation Model.
The variables x and y vary directly. One pair of values is x = 5 and y =
20.
a. Write an equation that relates x and y.
b.
Find the v