Number operation review 5 ppsx

Broken-Line Graphs
Broken-line graphs illustrate a measurable change over time. If a line is slanted up, it represents an increase whereas
a line sloping down represents a decrease. A flat line indicates no change as time elapses.
Scatterplots illustrate the relationship between two quantitative variables. Typically, the values of the inde-
pendent variables are the x-coordinates, and the values of the dependent variables are the y-coordinates. When
presented with a scatterplot, look for a trend. Is there a line that the points seem to cluster around? For example:
HS GPA
College GPA
Increase
Decrease
No Change
Increase
Decrease
Change in Time
Unit of Measure
Comparison of Road Work Funds
of New York and California
1990–1995
New York
California
KEY
0
10
20
30
40
50
60
70
80
90

1991 1992 1993 1994 1995
Money Spent on New Road Work
in Millions of Dollars
Year
–NUMBERS AND OPERATIONS REVIEW–
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In the previous scatterplot, notice that a “line of best fit” can be created:
Practice Question
Based on the graph above, which of the following statements are true?
I. In the first hour, Vanessa sold the most lemonade.
II. In the second hour, Lupe didn’t sell any lemonade.
III. In the third hour, James sold twice as much lemonade as Vanessa.
a. I only
b. II only
c. I and II
d. I and III
e. I, II, and III
Answer
d. Let’s evaluate the three statements:
Statement I: In the first hour, Vanessa sold the most lemonade.
In the graph, Vanessa’s bar for the first hour is highest, which means she sold the most lemonade in the
first hour. Therefore, statement I is TRUE.
Statement II: In the second hour, Lupe didn’t sell any lemonade.
Lemonade Sold
Vanessa
James
Lupe
0
2
4

6
8
10
12
14
16
Hour 1 Hour 2 Hour 3
Cups of Lemonade Sold
HS GPA
College GPA
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In the second hour, there is no bar for James, which means he sold no lemonade. However, the bar for
Lupe is at 2, so Lupe sold 2 cups of lemonade. Therefore, statement II is FALSE.
Statement III: In the third hour, James sold twice as much lemonade as Vanessa.
In the third hour, James’s bar is at 8 and Vanessa’s bar is at 4, which means James sold twice as much
lemonade as Vanessa. Therefore, statement III is TRUE.
Answer: Only statements I and III are true.

Matrices
Matrices are rectangular arrays of numbers. Below is an example of a 2 by 2 matrix:
Review the following basic rules for performing operations on 2 by 2 matrices.
Addition
Subtraction
Multiplication
Scalar Multiplication
k

a
1

a
2
a
3
a
4

=

ka
1
ka
2
ka
3
ka
4


a
1
a
2
a
3
a
4

×


b
1
b
2
b
3
b
4

=

a
1
b
1
+ a
2
b
3
a
1
b
2
+ a
2
b
4
a
3
b

1
+ a
4
b
3
a
3
b
2
+ a
4
b
4


a
1
a
2
a
3
a
4

−

b
1
b
2

b
3
b
4

=

a
1
− b
1
a
2
− b
2
a
3
− b
3
a
4
− b
4


a
1
a
2
a

3
a
4

+

b
1
b
2
b
3
b
4

=

a
1
+ b
1
a
2
+ b
2
a
3
+ b
3
a

4
+ b
4


a
1
a
2
a
3
a
4

–NUMBERS AND OPERATIONS REVIEW–
66
Practice Question
Which of the following shows the correct solution to the problem above?
a.
b.
c.
d.
e.
Answer
e.

43
71

+


62
52

=

4 + 63+ 2
7 + 51+ 2

=

10 5
12 3


10 5
12 3


24 6
35 2


−21
2 −1


11 11
4 4



7 8
8 7


43
71

+

62
52

=
–NUMBERS AND OPERATIONS REVIEW–
67

Equations
To solve an algebraic equation with one variable, find the value of the unknown variable.
Rules for Working with Equations
1. The equal sign separates an equation into two sides.
2. Whenever an operation is performed on one side, the same operation must be performed on the
other side.
3. To solve an equation, first move all of the variables to one side and all of the numbers to the other. Then
simplify until only one variable (with a coefficient of 1) remains on one side and one number remains on
the other side.
CHAPTER
Algebra Review
This chapter reviews key skills and concepts of algebra that you need

to know for the SAT. Throughout the chapter are sample questions in
the style of SAT questions. Each sample SAT question is followed by
an explanation of the correct answer.
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