Transcript Document

Lesson 3-1 Square Roots
Lesson 3-2 Estimating Square Roots
Lesson 3-3 Problem Solving Investigation: Use a
Venn Diagram
Lesson 3-4 The Real Number System
Lesson 3-5 The Pythagorean Theorem
Lesson 3-6 Using the Pythagorean Theorem
Lesson 3-7 Distance on the Coordinate Plane
Five-Minute Check (over Chapter 2)
Main Idea and Vocabulary
Targeted TEKS
Example 1: Find Square Roots
Example 2: Find Square Roots
Example 3: Find Square Roots
Example 4: Use Square Roots to Solve
an Equation
Example 5: Use Square Roots to Solve a Problem
• Find square roots of perfect squares.
• Perfect square
– Squares of integers
• square root
– OPPOSITE of squaring a number
– Means “what number times itself”
• radical sign
– The square root symbol
Square Roots
 √X means “What number times itself = X”
 Every POSITIVE number has TWO square roots!!
 EX: √64 = +8 and – 8
 EX: √100 = +10 and –10
 To find the square roots of fractions, find the square
root of the numerator and denominator.
 EXAMPLE: √(16/64)
 = √16 / √64 = 4/8 = ½ and – ½
 Remember: Whatever I do to one side of an equation
 I MUST DO THE SAME THING TO THE OTHER SIDE!
 If they ask me to solve an algebra equation with a squared
term, THEY WANT BOTH THE POSITIVE AND NEGATIVE
SOLUTIONS!!
Find Square Roots
Find
indicates the positive square root of 81.
Answer:
Interactive Lab: Square Roots
Find
A. A.
A 4
B. B.
B 6
C. C.
C 8
0%
D
0%
C
0%
B
D. D.
D 16
A
0%
Find Square Roots
Find
indicates the negative square root of
Answer:
Find
A. A
A.
B.
B
C.
C
B.
D.
0%
0%
D.
D
0%
C
A
0%
B
C.
D
Find Square Roots
Find
indicates both the positive and negative square
roots of 1.44.
Answer: Since (1.2)2 = 1.44 and (–1.2)2 = 1.44,
= ±1.2, or 1.2 and –1.2.
Find
A. A.
A ±1.2
B. B.
B ±1.25
C. C.
C ±1.5
0%
D
0%
C
0%
B
D. D.
D ±1.75
A
0%
Use Square Roots to Solve an Equation
ALGEBRA Solve x2 = 225.
x2 = 225
Write the equation.
x =
Definition of square root
x = 15 and x = –15
Check 15  15 = 225 and
(–15)  (–15) = 225
Answer: The equation has two solutions, 15 and –15.
ALGEBRA Solve x2 = 81.
A. –9
A. A
B. 9
D.
D
0%
0%
0%
0%
D
C
D. –8 and 8
C
C.
B
B
C. –9 and 9
A
B.
Use Square Roots to Solve
a Problem
MUSIC The art work on the square picture in a
compact disc case is approximately 14,161 mm2 in
area. Find the length of each side of the square.
Words
Area is equal to the square of the length of a side.
Variable
Let s represent the length of a side.
Equation
14,161 = s2
Use Square Roots to Solve
a Problem
14,161 = s2
=s
2nd
c
14161
ENTER
=
Write the equation.
Definition of square root
Use a calculator.
119 = s
Answer: The length of a side of a compact disc case is
about 119 millimeters since distance cannot be
negative.
ART A piece of art is a square picture that is
approximately 11,025 square inches in area. Find
the length of each side of the square picture.
A. A.
A 85 inches
B. B.
B 93 inches
D. D.
D 105 inches
0%
0%
D
0%
C
A
0%
B
C. C.
C 95 inches
Five-Minute Check (over Lesson 3-1)
Main Idea
Targeted TEKS
Example 1: Estimate Square Roots
Example 2: Estimate Square Roots
Example 3: Estimate Square Roots to
Solve a Problem
• Estimate square roots.
 Estimating Square Roots – PART 1
•
To Estimate a NON-PERFECT square root:
1. Find the nearest perfect square LOWER
2. Find the nearest perfect square HIGHER
3. Graph them on a number line
4. “Guesstimate” the square root.
 When estimating square roots, IT IS VERY
USEFUL TO PLOT NUMBERS ON A NUMBER
LINE.
Estimate Square Roots
Estimate
to the nearest whole number.
The first perfect square less than 54 is 49.
The first perfect square greater than 54 is 64.
Plot each square root on a number line. Then plot
.
Estimate Square Roots
49 < 54 < 64
Write an inequality.
72 < 54 < 82
49 = 72 and 64 = 82
Find the square root of
each number.
7<
<8
Simplify.
Answer: So,
is between 7 and 8. Since 54 is closer
to 49 than 64, the best whole number estimate
for
is 7.
Estimate
to the nearest whole number.
A. A.
A 5
B. B.
B 6
C. C.
C 7
0%
D
0%
C
0%
B
D. D.
D 8
A
0%
Estimate Square Roots
Estimate
to the nearest whole number.
The first perfect square less than 41.3 is 36.
The first perfect square greater than 41.3 is 49.
Plot each square root on a number line. Then plot
Estimate Square Roots
36 < 41.3 < 49
Write an inequality.
62 < 41.3 < 72
36 = 62 and 49 = 72
Find the square root of
each number.
6<
<7
Simplify.
Answer: So,
is between 6 and 7. Since 41.3 is
closer to 36 than 49, the best whole number
estimate for
is 6.
Estimate
to the nearest whole number.
A. A.
A 3
B. B.
B 4
C. C.
C 5
0%
D
0%
C
0%
B
D. D.
D 6
A
0%
Estimate Square Roots to
Solve a Problem
FINANCE If you were to invest $100 in a bank
account for two years, your investment would earn
interest daily and be worth more when you withdrew
it. If you had $120 after two years, the interest rate,
written as a decimal, would be found using the
expression
. Estimate this value.
Estimate Square Roots to
Solve a Problem
First estimate the value of
100 < 120 < 121
100 and 121 are the
closest perfect squares.
102 < 120 < 112
100 = 102 and 121 = 112
10 <
Find the square root of
each number.
< 11
Estimate Square Roots to
Solve a Problem
Since 120 is closer to 121 than 100, the best
whole number estimate for
is 11. Use this to
evaluate the expression.
Answer: The approximate interest rate is 0.10 or 10%.
FINANCE If you were to invest $100 in a bank
account for two years, your investment would earn
interest daily and be worth more when you withdrew
it. If you had $150 after two years, the interest rate,
written as a decimal, would be found using the
expression
Estimate this value.
.
FINANCE Estimate the value of
.
A. 0.10
A. A
B. 0.15
D.
D
0%
0%
0%
0%
D
C
D. 0.25
C
C.
B
B
C. 0.20
A
B.
Five-Minute Check (over Lesson 3-2)
Main Idea
Targeted TEKS
Example 1: Use a Venn Diagram
• Use a Venn diagram to solve problems.
 A Venn Diagram usually consists of 2 or 3 circles
that intersect each other.
 Area that intersects represents number of
people involved in BOTH circles!
 To create Venn Diagrams do the following:
1) Figure out how many people go in the
intersecting areas. – START IN THE MIDDLE!
2) Subtract to find out how many
ppl are in the non-intersecting areas.
 REMEMBER: THE TOTAL
NUMBER OF PEOPLE IN EACH
CATEGORY IS THE TOTAL NUMBER
IN THE CIRCLE!!!
Use a Venn Diagram
LANGUAGES Of the 40 foreign exchange students
attending a middle school, 20 speak French, 23
speak Spanish, and 22 speak Italian. Nine students
speak French and Spanish, but not Italian. Six
students speak French and Italian, but not Spanish.
Ten students speak Spanish and Italian, but not
French. Only 4 students speak all three languages.
Use a Venn diagram to find how many exchange
students do not speak any of these languages.
Use a Venn Diagram
Explore
You know how many students speak each of
the different languages. You want to organize
the information.
Plan
Make a Venn diagram to organize the
information.
Solve
Draw three overlapping circles to represent
the three different languages. Since 4
students speak all 4 languages, place a 4 in
the section that represents all three
languages. Use the other information given in
the problem to fill in the other sections as
appropriate.
Use a Venn Diagram
Solve
Add the numbers in each region of the diagram:
1 + 9 + 6 + 4 + 10 + 2 = 32
Since there are 40 exchange students altogether,
40 – 32 = 8 of them do not speak French, Spanish,
or Italian.
Use a Venn Diagram
Check
Check each circle to see if the appropriate
number of students is represented.
Answer: Eight of the exchange students do not speak
French, Spanish, or Italian.
SPORTS Of the 30 students in Mr. Hall’s gym class,
14 students play basketball, 9 students play soccer,
and 11 students play volleyball. Three students play
basketball and soccer, but not volleyball. One
student plays soccer and volleyball, but not
basketball. Six students play basketball and
volleyball, but not soccer. Only 2 students play all
three sports. Use a Venn diagram to organize this
information and then answer the question on the
next slide.
How many students in Mr. Hall’s gym class do not
play basketball, soccer, or volleyball?
A. A
A. 6 students
D.
D
D. 10 students
0%
0%
0%
0%
D
C
C. 9 students
C
C.
B
B
B. 8 students
A
B.
Five-Minute Check (over Lesson 3-3)
Main Idea and Vocabulary
Targeted TEKS
Key Concept: Irrational Numbers
Example 1: Classify Numbers
Example 2: Classify Numbers
Example 3: Classify Numbers
Concept Summary: Real Number Properties
Example 4: Graph Real Numbers
Example 5: Compare Real Numbers
Example 6: Compare Real Numbers
Example 7: Compare Real Numbers to Solve a Problem
• Identify and classify numbers in the real number
system.
• Rational Numbers
– Numbers that can be written as a fraction
– Includes all WHOLE numbers and INTEGERS
– Whole numbers = 0, 1, 2, 3 …
– Integers = …, -3, -2, -1, 0, 1, 2, 3 …
• Irrational Number
– Any number that CAN NOT be written as a fraction
– IT NEVER REPEATS AND NEVER ENDS!
• Real Numbers
– All rational and irrational numbers
 CLASSIFYING NUMBERS
 There are two kinds of Irrational Numbers
A. Constants like PI
B. Square Roots of NON-PERFECT squares (and other
roots of non-perfect numbers, but that’s for Algebra 2!)
 EVERYTHING ELSE IS A RATIONAL NUMBER!!
NOTES – CONT.
ESTIMATING NON-PERFECT SQUARE ROOTS – Part 2
 To Estimate a NON-PERFECT square root:
1. Find the nearest perfect square LOWER
2. Find the nearest perfect square HIGHER
3. Graph them on a number line
4. “Guesstimate” the square root.
 COMPARING REAL NUMBERS – I can only
compare things in math that ????
 To compare a rational and irrational number,
SQUARE BOTH OF THEM!
Classify Numbers
Name all sets of numbers to which 0.090909…
belongs.
The decimal ends in a repeating pattern.
Answer: It is a rational number because it is
equivalent to
Name all sets of numbers to which 0.1010101010…
belongs.
A. A
A. rational
D.
D
D. integer, rational
0%
0%
0%
0%
D
C
C. whole, rational
C
C.
B
B
B. irrational
A
B.
Classify Numbers
Name all sets of numbers to which
belongs.
Answer: Since
, it is a whole number, an
integer, and a rational number.
Name all sets of numbers to which
belongs.
A. A.
A integer
B. B.
B integer, rational
C. C.
C integer, whole
0%
D
0%
C
0%
B
D. D.
D integer, rational, whole
A
0%
Classify Numbers
Name all sets of numbers to which
belongs.
Answer: Since the decimal does not repeat or
terminate, it is an irrational number.
Name all sets of numbers to which
belongs.
A. rational
A. A
B. irrational
D.
D
0%
0%
0%
0%
D
C
D. integer, irrational
C
C.
B
B
C. integer
A
B.
Graph Real Numbers
Estimate
and
graph
and
to the nearest tenth. Then
on a number line.
or about 2.8
or about –1.4
Answer:
Estimate
and
Answer:
and
to the nearest tenth. Then graph
on a number line.
Compare Real Numbers
Replace  with <, >, or = to make
a true sentence.
Write each number as a decimal.
Answer: Since 3.875 is greater than 3.872983346…,
Replace  with <, >, or = to make
a true sentence.
A. <
B. >
C. =
1. A
2. B
3. C
0%
1
0%
2
0%
3
Compare Real Numbers
Replace  with <, >, or = to make
a true sentence.
Write
as a decimal.
Answer: Since
is less than 3.224903099…,
Replace  with <, >, or = to make
a true sentence.
A. <
B. >
C. =
1. A
2. B
3. C
0%
1
0%
2
0%
3
Compare Real Numbers to
Solve a Problem
BASEBALL The time in seconds that it takes an
object to fall d feet is
How many seconds
would it take for a baseball that is hit 250 feet
straight up in the air to fall from its highest point to
the ground?
Replace d with
≈ 0.25  15.81
Use a calculator.
≈ 15.81
≈ 3.95 or about 4 Simplify.
Answer: It will take about 4 seconds for the baseball to
fall to the ground.
BASEBALL The time in seconds that it takes an
object to fall d feet is
How many seconds
would it take for a baseball that is hit 450 feet straight
up in the air to fall from its highest point to the
A. ground?
A
D. about 6.2 seconds
D
0%
0%
0%
D
D.
0%
C
C
C. about 5.6 seconds
B
C.
A
B.
A. about 4.9 seconds
B
B. about 5.3 seconds
Five-Minute Check (over Lesson 3-4)
Main Idea and Vocabulary
Targeted TEKS
Key Concept: Pythagorean Theorem
Example 1: Find the Length of a Side
Example 2: Find the Length of a Side
Key Concept: Converse of Pythagorean Theorem
Example 3: Identify a Right Triangle
• Use the Pythagorean Theorem.
• Legs
– The shorter sides of a RIGHT triangle
– The sides that form the RIGHT angle
• Hypotenuse
– The LONGEST side of a RIGHT triangle
• Pythagorean Theorem
– Describes the relationship between the legs and
hypotenuse of RIGHT triangles!
– ONLY APPLIES TO RIGHT TRIANGLES!!
• Converse
– “The opposite of”
 In a Right triangle:
 A2 + B2 = C2
 Can be used to find the third side of any right
triangle if I know the other two sides.
Find the Length of a Side
Write an equation to find the
length of the missing side of
the right triangle. Then find the
missing length. Round to the
nearest tenth, if necessary.
Find the Length of a Side
c2 = a2 + b2
Pythagorean Theorem
c2 = 122 + 162
Replace a with 12 and b with 16.
c2 = 144 + 256
Evaluate 122 and 162.
c2 = 400
Add 144 and 256.
c=
Definition of square root
c = 20 or –20
Simplify.
Answer: The equation has two solutions, 20 and –20.
However, the length of a side must be positive.
So, the hypotenuse is 20 inches long.
Write an equation to find the
length of the missing side of the
right triangle. Then find the
missing length. Round to the
nearest tenth, if necessary.
A. A.
A 17 in.
B. 19 in.
B. B
D.
D
0%
D
0%
C
0%
B
0%
A
C. 20 in.
C. C
D. 21 in.
Find the Length of a Side
The hypotenuse of a right triangle is 33 centimeters
long and one of its legs is 28 centimeters. What is
a, the length of the other leg?
c2 = a2 + b2
332 = a2 + 282
1,089 = a2 + 784
1,089 – 784 = a2 + 784 – 784
305 = a2
=a
17.5 ≈ a
Pythagorean Theorem
Replace c with 33 and b
with 28.
Evaluate 332 and 282.
Subtract 784 from each
side.
Simplify.
Definition of square root
Use a calculator.
Find the Length of a Side
Answer: The length of the other leg is about
17.5 centimeters.
The hypotenuse of a right triangle is 26 centimeters
long and one of its legs is 17 centimeters. What is a,
the length of the other leg?
A. A.
A about 16.2 cm
B. about 18.5 cm
B. B
C. about 19.7 cm
C. C
D. about 21.4 cm
0%
D
0%
C
D
0%
B
D.
A
0%
Identify a Right Triangle
The measures of three sides of a triangle are 24
inches, 7 inches, and 25 inches. Determine whether
the triangle is a right triangle.
c2 = a2 + b2
?
2
25 =
72 + 242
?
Pythagorean Theorem
Replace a with 7, b
with 24, and c with 25.
625 = 49 + 576
Evaluate 252, 72, and 242.
625 = 625
Simplify.
Answer: The triangle is a right triangle.
The measures of three sides of a triangle are 13
inches, 5 inches, and 12 inches. Determine whether
the triangle is a right triangle.
A. It is a right triangle.
B. It is not a right triangle.
C. Not enough information 1. A
to determine.
2. B
3. C
0%
1
0%
2
0%
3
Five-Minute Check (over Lesson 3-5)
Main Idea
Targeted TEKS
Example 1: Use the Pythagorean Theorem to
Solve a Problem
Example 2: Test Example
• Solve problems using the Pythagorean Theorem.
 To Solve problems with the Pythagorean
Theorem:
1. Draw and Label a picture
2. Write down the Pythagorean Theorem
3. “Plug in what you know, and solve for what you
don’t!”
1. Be CAREFUL to plug the hypotenuse in for C!!!!
Use the Pythagorean Theorem
to Solve a Problem
RAMPS A ramp to a newly constructed building
must be built according to the guidelines stated in
the Americans with Disabilities Act. If the ramp is
24.1 feet long and the top of the ramp is 2 feet off the
ground, how far is the bottom of the ramp from the
base of the building?
Notice the problem
involves a right triangle.
Use the Pythagorean
Theorem.
Use the Pythagorean Theorem
to Solve a Problem
24.12 = a2 + 22
580.81 = a2 + 4
580.81 – 4 = a2 + 4 – 4
576.81 = a2
=a
24.0 ≈ a
Replace c with 24.1 and b
with 2.
Evaluate 24.12 and 22.
Subtract 4 from each side.
Simplify.
Definition of square root
Simplify.
Answer: The end of the ramp is about 24 feet from the
base of the building.
RAMPS If a truck ramp is 32 feet long and the top of
the ramp is 10 feet off the ground, how far is the end
A. of
A the ramp from the truck?
A. about 30.4 feet
B. B
B. about 31.5 feet
C. C.
C about 33.8 feet
0%
D
0%
C
0%
B
D. D.
D about 35.1 feet
A
0%
Use the Pythagorean Theorem
The cross-section of a camping tent is shown below.
Find the width of the base of the tent.
A. 6 ft
B. 8 ft
C. 10 ft
D. 12 ft
Use the Pythagorean Theorem
Read the Test Item
From the diagram, you know that the tent forms two
congruent right triangles. Let a represent half the base of
the tent. Then w = 2a.
Use the Pythagorean Theorem
Solve the Test Item
Use the Pythagorean Theorem.
c2 = a2 + b2
Write the relationship.
102 = a2 + 82
c = 10 and b = 8
100 = a2 + 64
Evaluate 102 and 82.
100 – 64 = a2 + 64 – 64
36 = a2
=a
6=a
Subtract 64 from each side.
Simplify.
Definition of square root
Simplify.
Use the Pythagorean Theorem
The cross-section of a camping tent is shown below.
Find the width of the base of the tent.
A. 6 ft
B. 8 ft
C. 10 ft
D. 12 ft
Answer: The width of the base of the tent is 2a or
(2)6 = 12 feet. Therefore, choice D is correct.
This picture shows the
cross-section of a roof.
long is each rafter, r?
A. How
A
D.
D 22 ft
0%
0%
0%
0%
D
D.
C
C
C. 20 ft
B
C.
A
B.
A. 15 ft
B
B. 18 ft
Five-Minute Check (over Lesson 3-6)
Main Ideas and Vocabulary
Targeted TEKS
Example 1: Name an Ordered Pair
Example 2: Name an Ordered Pair
Example 3: Graphing Ordered Pairs
Example 4: Graphing Ordered Pairs
Example 5: Find Distance on the Coordinate Plane
Example 6: Use a Coordinate Plane to Solve a
Problem
• Graph rational numbers on the coordinate plane.
• Find the distance between two points on the
coordinate plane.
• coordinate plane – TURN TO PAGE 173 AND DRAW A
COORDINATE PLANE
• ordered pair
• origin
• x-coordinate
• y-axis
• abscissa
• x-axis
• y-coordinate
• quadrants
• ordinate

To graph a point on a coordinate

Move LEFT or RIGHT on the X axis FIRST

Move UP or DOWN on the Y axis SECOND

Remember “RUN BEFORE YOU JUMP!”
 To Find the Distance between two points do the
following:
1. DRAW a right triangle connecting the dots using
the gridlines on the graph
2. FIND the lengths of the legs (count or subtract)
3. USE the Pythagorean Theorem to find the
distance.
Name an Ordered Pair
Name the ordered pair for point A.
• Start at the origin.
• Move right to find the
x-coordinate of point A,
which is 2.
• Move up to find the
y-coordinate, which is
Answer: So, the ordered pair for point A is
Name the ordered pair for point A.
A. A.
A
B. B.
B
C. C.
C
0%
D
0%
C
A
D. D.
D
0%
B
0%
Name an Ordered Pair
Name the ordered pair for point B.
• Start at the origin.
• Move left to find the
x-coordinate of point B,
which is
• Move down to find the
y-coordinate, which is –2.
Answer: So, the ordered pair for point B is
Name the ordered pair for point B.
A. A.
A
B. B.
B
C. C.
C
0%
D
0%
C
A
D. D.
D
0%
B
0%
Graphing Ordered Pairs
Graph and label point J(–3, 2.75).
• Start at the origin and move
3 units to the left. Then
move up 2.75 units.
• Draw a dot and label it
J(–3, 2.75).
Answer:
Graph and label point J(–2.5, 3.5).
B.
C
D.
D
D.
0%
0%
0%
0%
D
C.
C
B
A
B.
C.
B
A.
A. A
Graphing Ordered Pairs
Graph and label point K
• Start at the origin and move 4 units to the right.
Then move down
units.
Answer:
• Draw a dot and label it
K
Graph and label point K
C
B.
D.
D
D.
0%
0%
0%
0%
D
C.
C
B
A
B.
C.
B
A. A.
A
Find Distance in the Coordinate Plane
Graph the ordered pairs (0, –6) and (5, –1). Then find
the distance between the points.
Let c = the distance between the
two points, a = 5, and b = 5.
Find Distance in the Coordinate Plane
c2 = a2 + b2
Pythagorean Theorem
c2 = 52 + 52
Replace a with 5 and
b with 5.
c2 = 50
52 + 52 = 50
=
c ≈ 7.1
Definition of square root
Simplify.
Answer: The points are about 7.1 units apart.
Graph the ordered pairs (0, –3) and (2, –6). Then find
the distance between the points.
A. A.
A about 3.1 units
B. B.
B about 3.6 units
C. C.
C about 3.9 units
0%
D
0%
C
0%
B
D. D.
D about 4.2 units
A
0%
Use a Coordinate Plane to
Solve a Problem
TRAVEL Melissa lives in
Chicago, Illinois. A unit on
the grid of her map
shown below is 0.08 mile.
Find the distance
between McCormickville
at (–2, –1) and Lake Shore
Park at (2, 2).
Let c = the distance between McCormickville and Lake
Shore Park. Then a = 3 and b = 4.
Use a Coordinate Plane to
Solve a Problem
c2 = a2 + b2
Pythagorean Theorem
c2 = 32 + 42
Replace a with 3 and
b with 4.
c2 = 25
32 + 42 = 25
=
c=5
Definition of square root
Simplify.
The distance between McCormickville and Lake Shore
Park is 5 units on the map.
Answer: Since each unit equals 0.08 mile, the distance
is 0.08  5 or 0.4 mile.
TRAVEL Sato lives in Chicago. A
unit on the grid of his map
below is 0.08 mile. Find
A. shown
A
the distance between
Shantytown at (2, –1) and the
B. intersection
B
of N. Wabash Ave.
and E. Superior St. at (–3, 1).
C. A.
C about 0.1 mile
0%
0%
D
0%
C
A
D. about 0.4 mile
0%
B
B. about 0.2 mile
D. D
C. about 0.3 mile
Five-Minute Checks
Image Bank
Math Tools
Square Roots
The Pythagorean Theorem
Lesson 3-1 (over Chapter 2)
Lesson 3-2 (over Lesson 3-1)
Lesson 3-3 (over Lesson 3-2)
Lesson 3-4 (over Lesson 3-3)
Lesson 3-5 (over Lesson 3-4)
Lesson 3-6 (over Lesson 3-5)
Lesson 3-7 (over Lesson 3-6)
To use the images that are on the
following three slides in your own
presentation:
1. Exit this presentation.
2. Open a chapter presentation using a
full installation of Microsoft® PowerPoint®
in editing mode and scroll to the Image
Bank slides.
3. Select an image, copy it, and paste it
into your presentation.
(over Chapter 2)
Write the fraction
as a decimal.
A. 1.2...
A. A
B. 0.911
B. B
C. 0.8181...
C. C
0%
D
0%
C
0%
B
D. 0.11
D. D
A
0%
(over Chapter 2)
Write the mixed number
as a decimal.
A. 7.6
A. A
B. 6.625
B. B
C. 5.375
C. C
0%
D
0%
C
0%
B
D. 3.75
D. D
A
0%
(over Chapter 2)
Multiply. Write in simplest form.
A.
A. A
B.
B. B
C.
C. C
0%
D
0%
C
0%
B
D.
D. D
A
0%
(over Chapter 2)
Divide. Write in simplest form. –9 ÷
A. –27
A. A
B. –18
B. B
C. –16
C. C
0%
D
0%
C
0%
B
D. –4.5
D. D
A
0%
(over Chapter 2)
Mercury is the closest planet to the Sun. Mercury is
3.6 × 107 miles away from the Sun. Write the distance
from Mercury to the Sun in standard form.
A. A
A. 360,000 miles
0%
D.
D
D. 360,000,000 miles
0%
0%
0%
D
C
C. 36,000,000 miles
C
C.
B
B
B. 3,600,000 miles
A
B.
(over Chapter 2)
Samuel used 1/4 cup of regular sugar and 2/3 cup of
brown sugar to make molasses cookies. How much
did Samuel use to make the molasses cookies?
A. sugar
A
A. 3/12 cup
B. B
B. 2/7 cup
C. C.C 3/7 cup
0%
D
0%
C
0%
B
D. D.D 11/12 cup
A
0%
(over Lesson 3-1)
Find
A. 81
A. A
B. 18
B. B
C. 9
C. C
0%
D
0%
C
0%
B
D. 3
D. D
A
0%
(over Lesson 3-1)
Find –
A. –14
A. A
B. –12
B. B
C. 12
C. C
0%
D
0%
C
0%
B
D. 14
D. D
A
0%
(over Lesson 3-1)
Solve the equation q2 = 16.
A. ±
A. A
B. ±
B. B
C. ± 4
C. C
0%
D
0%
C
0%
B
D. ± 8
D. D
A
0%
(over Lesson 3-1)
Solve the equation
.
A.
A. A
B.
B. B
C.
C. C
0%
D
0%
C
0%
B
D.
D. D
A
0%
(over Lesson 3-1)
Find the positive square root of 36.
A. 6
A. A
B. 9
B. B
C. 12
C. C
0%
D
0%
C
0%
B
D. 18
D. D
A
0%
(over Lesson 3-1)
The chairs in the multi-purpose room of a school
need to be arranged in a square. If there are 225
how many should be in each row?
A. chairs,
A
A. 13
B. B
B. 14
0%
0%
D
0%
C
A
D. D.
D 25
0%
B
C. C.
C 15
(over Lesson 3-2)
Estimate
to the nearest whole number.
A. 5
A. A
B. 6
B. B
C. 7
C. C
0%
D
0%
C
0%
B
D. 8
D. D
A
0%
(over Lesson 3-2)
Estimate
to the nearest whole number.
A. 6
A. A
B. 7
B. B
C. 8
C. C
0%
D
0%
C
0%
B
D. 9
D. D
A
0%
(over Lesson 3-2)
Estimate the solution of x2 = 102 to the nearest
integer.
A. A.
A±4
B. B.
B±5
D. D.
D ± 11
0%
0%
D
0%
C
A
0%
B
C. C.
C ± 10
(over Lesson 3-2)
Estimate the solution of p2 = 62 to the nearest integer.
A. ± 3
A. A
B. ± 4
B. B
C. ± 7
C. C
0%
D
0%
C
0%
B
D. ± 8
D. D
A
0%
(over Lesson 3-2)
Choose the two numbers that have square roots
between 9 and 10.
A. A.
A 82, 87
B. B.
B 80, 87
D. D.
D 82, 101
0%
0%
D
0%
C
A
0%
B
C. C.
C 79, 101
(over Lesson 3-2)
Which of the following is in order from least to
greatest?
A. A.
A
B. B.
B
D. D.
D
0%
0%
D
0%
C
A
0%
B
C. C.
C
(over Lesson 3-3)
PETS The table shows the
pets of students in the 8th
grade. How many students
A. have
A a dog?
A. 7
B. B
B. 11
C. C.
C 18
0%
0%
D
0%
C
A
0%
B
D. D.
D 29
(over Lesson 3-3)
CONCESSIONS One evening at a movie concession stand, 80
customers bought popcorn, 55 customers bought a soft drink,
and 35 bought a box of candy. Of those who bought exactly two
items, 35 bought popcorn and a soft drink, 10 bought a soft
A. drink
A and candy, and 5 bought popcorn and candy. Three
customers bought all three. How many customers bought only
popcorn?
B.
B
A. 20
C. B.C 37
C. 42
0%
0%
D
0%
C
A
0%
B
D. D.D 50
(over Lesson 3-3)
Mrs. Jenkins conducted a survey of her student’s favorite type
of book. Of the 28 students in her class, 14 said fiction was
their favorite, and 7 said nonfiction was their favorite. Of her
A. students,
A
3 said that both types of books were their favorite.
How many students said that neither fiction nor nonfiction was
their favorite?
B.
B
A. 3
C. B.C 10
C. 6
0%
0%
D
0%
C
A
0%
B
D. D.D 4
(over Lesson 3-4)
Name all sets of numbers to which the real number
286 belongs.
A. A.
A rational, integer, whole
number, real
B. B.B integer, irrational, rational,
real
0%
0%
D
0%
C
D. D.D irrational, real
0%
B
C
C. integer, irrational, real
A
C.
(over Lesson 3-4)
Name all sets of numbers to which the real number
belongs.
A. A.
A rational, real
B. B.
B integer, real
D. D.
D irrational, real
0%
0%
D
0%
C
A
0%
B
C. C.
C whole number, real
(over Lesson 3-4)
Estimate
to the nearest tenth.
A. 6
A. A
B. 5.8
B. B
C. 5
C. C
0%
D
0%
C
0%
B
D. 2.9
D. D
A
0%
(over Lesson 3-4)
Estimate
to the nearest tenth.
A. 16.6
A. A
B. 17
B. B
C. 17.9
C. C
0%
D
0%
C
0%
B
D. 18
D. D
A
0%
(over Lesson 3-4)
Are irrational numbers sometimes, always, or never
rational numbers?
A. always
B. sometimes
C. never
0%
C
0%
B
0%
A
1. A
2. B
3. C
(over Lesson 3-4)
To which set does
not belong?
A. A.
A real
B. rational
B
0%
0%
0%
D
D
A
D.
0%
C
C. fractions
C. C
D. negative integers
B
B.
(over Lesson 3-5)
Write an equation you could use to
find the length of the missing side
of the right triangle in the figure.
A. Then
A find the missing length.
Round to the nearest tenth if
necessary.
B. B
A. x2 + 42 = 32; 5 cm
C. B.C x2 + 32 = 42; 3.6 cm
C. 32 + 42 = x2; 5 cm
D. D
D. 32 + 42 = x2; 25 cm
cm
cm
(over Lesson 3-5)
Write an equation you could use
to find the length of the missing
side of the right triangle in the
Then find the missing
A. figure.
A
length. Round to the nearest
tenth if necessary.
B. B
A. 152 + x2 = 252; 20
C. B.C 252 + x2 = 152; 24.7
0%
0%
D
0%
C
A
D. 152 + 252 = x2; 29.2
0%
B
2 + 252 = x2; 25.3
C.
15
D. D
(over Lesson 3-5)
Write an equation you could use to
find the length of the missing side
of the right triangle in the figure.
A. Then
A find the missing length. Round
to the nearest tenth if necessary.
B.
B
A. 122 + 132 = x2; 17.7
C. B.
C 122 + 132 = x2; 13.5
0%
0%
D
0%
C
A
D. x2 + 122 = 132; 5
0%
B
C. x2 + 122 = 132; 12.5
D. D
(over Lesson 3-5)
Is a triangle with side lengths of 18, 25, and 33 a right
triangle?
A. yes
B. no
1. A
2. B
0%
B
A
0%
(over Lesson 3-5)
A man drives 33 miles east and 12 miles south.
Approximately how many miles is the man from his
point?
A. starting
A
A. 33
B. B
B. 50
C. C.
C 35
0%
0%
D
0%
C
A
0%
B
D. D.
D 12
(over Lesson 3-6)
In the figure, a plane is traveling from
point A to point B. How far will the
plane have flown when it reaches its
destination? Write an equation that
A. can
A be used to answer the question
and solve. Round to the nearest tenth
if necessary.
B.
B
A.
km
km
3002 – 2002 = p2; 223.6 km
C. B.C 300 – 200 = p; 100 km
300 + 200 = p; 500 km
0%
0%
0%
D
A
0%
C
D. D.D 3002 + 2002 = p2; 360.3 km
B
C.
(over Lesson 3-6)
Refer to the figure. A girl is pinning
ribbon to a 3’ × 4’ bulletin board. How
long will the ribbon have to be to
stretch from corner to corner
A. diagonally?
A
Write an equation that
can be used to answer the question
and solve. Round to the nearest tenth
necessary.
B. ifB
A.
42 + 32 = r2; 5 ft
C. B.C 4 + 3 = r; 7 ft
0%
0%
D
r2 – 32 = 42; 2.6 ft
0%
C
D.
0%
B
D
42 – 32 = r2; 3.6 ft
A
D.
C.
(over Lesson 3-6)
In the figure, triangle ABC
is a right triangle. What is
A. the
A perimeter of the
triangle?
B. A.
B 42 in.
B. 58 in.
C. C
0%
D
0%
C
0%
B
0%
A
C. 72 in.
D. D
D. 84 in.
This slide is intentionally blank.