Download 8TH GRADE COMPREHENSIVE REVIEW

• Purpose: PSSA Review for 8th Grade Mathematics
(Can be used as enrichment or remediation for middle school levels)
• Contents: Concept vocabulary & practice exercises/ solutions.
Fill-in-the-blank, Multiple Choice, Short & Extended Response
• Sources:
PA Assessment Anchors & Eligible Content for 8th Grade Mathematics
PA Assessment Anchor Glossary for 7th & 8th Grade Mathematics
PDE Standard Aligned Systems Online Resources
McGraw Hill Pre-Algebra & Algebra I 2012 Series
Holt McDougal 8th Grade Mathematics 2012 Series
• Reinforcement: www.studyisland.com
http://www.ixl.com/math/grades
www.mathmaster.org
PSSA Coach, Assessment Anchors
Measuring Up to the Pennsylvania Academic Standards
INSTRUCTIONS
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There are five categories tested; Numbers & Operations,
Measurement, Geometry, Algebraic Concepts, Data Analysis &
Probability.
Each category has a two page vocabulary (fill-in-the-blank) review,
followed by multiple choice, short response, and extended response
exercises that are aligned with each of the Assessment Anchor
subcategories.
Navigate through the review as you would a regular PowerPoint slide
show.
Fill-in-the-blank answers will appear, in order, at the click of a mouse.
Exercise answers
will also appear at the click of a mouse.
Use the reference symbol
to access the 8th Grade Formula
Sheet if needed.
Use the symbol
found on the Formula Sheet to return to your
previous slide.
PLEASE BEGIN!! 
3
Numbers & Operations
Vocabulary Review
Reciprocal is 1.
1. The product of a number and its __________
Rational
2. Any number that can be written as a fraction is called a _________.
number
Scientific notation is a short-hand way of writing extremely large or
3. ________________
extremely small numbers.
Real numbers is the set of all rational and irrational
4. The set of ____________
numbers.
Perfect square
5. The product of an integer multiplied by itself is called a _____________.
Word Bank:
Rational number
Scientific notation
Order of Operations
Proportion
Reciprocal
Unit price
Perfect square
Real numbers
Square root
Expanded form
4
Numbers & Operations
Vocabulary Review
Expanded
6. A number written as the sum of values of its digits is called _________.
form
7. A number that is multiplied by itself to form a product is called a
Square root of that product.
___________
Unit price is used to compare price per item.
8. A(n) __________
9. Rules describing what sequence to use in evaluating expressions is
Order of Operations
known as __________________.
Proportion is an equation showing that two ratios are equal.
10.A ___________
Word Bank:
Rational number
Scientific notation
Order of Operations
Proportion
Reciprocal
Unit price
Perfect square
Real numbers
Square root
Expanded form
5
Numbers & Operations
Practice…
Representing Numbers in equivalent forms.
Scientific Notation
Exponential Form
 The Earth is approximately
93,000,000 miles from the
sun. What is the distance
written in scientific
notation?
 Which number represents
4.5 x 104 written in
standard notation?
A.
B.
C.
D.
9.3 x 106
93 x 106
93 x 107
9.3 x 107
A.
B.
C.
D.
0.00045
0.000045
45,000
450,000
6
Numbers & Operations
Practice…
Representing Numbers in equivalent forms.
Expanded Notation
 Which expression is equivalent to the number 8,006,425?
A.
B.
C.
D.
(8x107)+(6x106)+(4x103)+(2x102)+(5x101)
(8x10)+(6x10)+(4x10)+(2x10)+(5x10)
(8x106)+(6x105)+(4x104)+(2x103)+(5x102)
(8x106)+(6x103)+(4x102)+(2x101)+(5x100)
7
Numbers & Operations
Practice…
Representing Numbers in equivalent forms.
Square Root

LeAnn got an answer of about 3.87 when she entered 15 on her
calculator and pressed the (√) key. Which of the following
statements is the most likely explanation for her to believe that her
calculator’s answer is or not reasonable?
A.
It is not reasonable, because the answer should be a whole
number.
It is reasonable because 3 squared is 9 while 4 squared is 16.
It is not reasonable, because the answer should be only slightly
more than 3.
It is reasonable, because 15 is and odd number.
B.
C.
D.
8
Numbers & Operations
Practice…
Completing calculations by applying the order of operations.
Order of Operations
 3³ + 4(8-5) ÷ 6 =
A.
B.
C.
D.
6.5
11
29
27.5
 Evaluate
7 + 5[(3 + 2)² - (2³ + 1)]
A.
B.
C.
D.
97
87
36
22
9
Numbers & Operations
Practice…
Completing calculations by applying the order of operations.
Order of Operations
 Karen is solving this
problem.
(3² + 4²)² = ?
Which step is correct in the
process of solving this
problem?
 Which statement is
correct?
A.
B.
C.
D.
(2 x 3) + 5 ÷ 8 = 2
(2 x 3 + 5) ÷ 8 = 2
2 x (3 + 5) ÷ 8 = 2
(2 x 3) + 5 ÷ 8 = 2
A. (3² + 4⁴)
B. (9² + 16²)
C. (7²)²
D. (9 + 16)²
10
Numbers & Operations
Practice…
Represent or solve problems using rates, ratios, proportions
and/or percents.
Rates

A.
B.
C.
D.
A secretary can type 56
words per minute. How much
time will she need to type a
4200-word report?
7 hours 30 minutes
1 hour 4 minutes
1 hour 28 minutes
1 hour 15 minutes
Ratios

In 1991, and American, Ann
Trason, set a world record by
running 100km in
Hours
Minutes
Seconds
7
50
09
Which is the best estimate of her
average speed?
A.
B.
C.
D.
12 km per hr
14 km per hr
16 km per hr
18 km per hr
11
Numbers & Operations
Practice…
Represent or solve problems using rates, ratios, proportions
and/or percents.
Proportions
(Short Response)

Julio’s wages vary directly as the number of hours that he works. If
his wages for 5 hours are $29.75, how much will he earn for 30
hours?
Scoring Rubric:
**[2 points] $178.50, and appropriate work is shown, such as solving a
proportion, using a table, or trial and error with at least three trials and
appropriate checks.
*[1 point] An incorrect proportion is set up, but no solution or an incorrect
solution is found.
*[1 point] $178.50, but no work is shown or fewer than three trials with
appropriate checks are shown.
[0 points] A zero response is completely incorrect, irrelevant, or incoherent or is
a correct response that was obtained by an obviously incorrect procedure.
13
Numbers & Operations
Practice…
Represent or solve problems using rates, ratios, proportions
and/or percents.
Distance & Rates

(Short Response)
Bob and Rebecca both drove to a baseball game at a college stadium.
Bob lives 70 miles from the stadium and Rebecca lives 60 miles from it,
as shown in the accompanying diagram. Bob drove at a rate of 50 miles
per hour, and Rebecca drove at a rate of 40 miles per hour. If they both
left home at the same time, who got to the stadium first?
70 miles
Bob’s House
60 miles
Scoring Rubric:
Rebecca’s House
**[2 points] Bob, and appropriate work is shown, such as using the distance formula to
calculate the two travel times or setting up a proportion.
*[1 point] Appropriate work is shown, but one computational or conceptual error is made but
an appropriate answer is found.
*[1 point] Appropriate work is shown, but no answer or an incorrect answer is found.
[0 points] Bob, but no work or inappropriate work is shown.
[0 points] A zero response is completely incorrect, irrelevant, or incoherent or is a correct
14
response that was obtained by an obviously incorrect procedure.
Numbers & Operations
Practice…
Using estimation strategies in problem-solving situations.
Estimation

A.
B.
C.
D.
Ken bought a used car for
$5,375. He had to pay an
additional 15 percent of the
purchase price to cover both
sales tax and extra fees. Of
the following, which is the
closest to the total amount
Ken paid?
$806
$5,510
$5,760
$6,180

A.
B.
C.
D.
The state law requires that
students attend school 180
days out of the 365 days in a
year. Approximately what
percent of a year must
students attend school?
2%
50%
75%
200%
15
Numbers & Operations
Practice…
Computing and/ or explaining operations with integers,
fractions and/ or decimals.
Fractions

A grocery store sells brown sugar by the pound. The table below
shows how many cups of sugar a customer will get for the number
of pounds purchased.
Number of Pounds
Number of Cups
3
7
4
9 1/3
5
11 2/3
6
14
The pattern continues. What is the total number of cups of brown
sugar in a 7-pound package?
A.
B.
C.
D.
15 2/3
16 1/3
16 2/3
17 1/3
16
Numbers & Operations
Practice…
Computing and/ or explaining operations with integers,
fractions and/ or decimals.
Fractions
Decimals

Subtract (-)
14 5/8
- 6 3/8

Divide (÷)
3
0.24
A.
B.
C.
D.
8 3/8
7 2/8
8 1/4
9
A.
B.
C.
D.
0.08
8.0
0.72
12.5
17
Numbers & Operations
Practice…
Computing and/ or explaining operations with integers,
fractions and/ or decimals.
Subtracting Negatives
Adding Negatives

Solve:
27 – (-9)

Solve:
-4 + 23
A.
B.
C.
D.
-3
-18
18
36
A.
B.
C.
D.
-19
19
20
-27
18
Numbers & Operations
Practice…
Calculating mean.
Average
(Short Response)

TOP Electronics is a small business with five employees. The mean
(average) weekly salary for the five employees is $360. If the
weekly salaries of four of the employees are $340, $340, $345, and
$425, what is the salary of the fifth employee?
Scoring Rubric:
**[2 points] $350, and appropriate work is shown, such as (1450 +x) ÷ 5 = 360,
or trial and error with at least trials and appropriate checks.
*[1 point] Appropriate work is shown, but one computational error is made
*[1 point] The total of the five salaries is shown to be 5 · 360 = 1800, but no
further correct work is shown.
*[1 point] $350, but no work is shown or fewer than three trials with appropriate
checks are shown.
[0 points] A zero response is completely incorrect, irrelevant, or incoherent or is
a correct response that was obtained by an obviously incorrect procedure.
19
Measurement
Vocabulary Review
Surface area is the sum of the areas of all the faces of a 3-D figure.
1. ____________
angles is equal to 180°.
2. The sum of Supplementary
___________________
Net
3. A _______
is a 2-D shape that can be folded to create a 3-D figure.
4. A 3-D solid that has two congruent and parallel faces is known as a
Prism
_______.
Complementary angles is equal to 90°.
5. The sum of ____________________
Word Bank:
Net
Circumference
Prism
Supplementary angles
Complementary angles
Formula
Interior angle
Polygon
Surface area
Volume
20
Measurement
Vocabulary Review
Interior angle is an angle inside of a shape.
6. A(n) _____________
Polygon is a closed plane figure formed by three or more line
7. A (n) _________
segments that intersect only at their endpoints (vertices).
8. The number of cubic units needed to fill a given space is known as
Volume
________.
Circumference is the measured distance around a circle.
9. ______________
Formula is a rule showing relationships among quantities.
10.A ________
Word Bank:
Net
Circumference
Prism
Supplementary angles
Complementary angles
Formula
Interior angle
Polygon
Surface area
Volume
21
Measurement
Practice…
Converting measurements.
Customary measurements
Metric measurements

How many feet are in 15
miles?

Greg is 150 centimeters tall.
How many meters is that?
A.
B.
C.
D.
352
35,200
79,200
89,760
A.
B.
C.
D.
0.500
1.5
15
15,000
22
Measurement
Practice…
Determining the measurement of a missing side(s) or angle(s)
in a polygon.
Missing Angles

A.
B.
C.
D.
In a quadrilateral, each of two
angles has a measure of
115°. If the measure of a third
angle is 70°, what is the
measure of the remaining
angle?
60°
70°
130°
140°

Find the measure in degrees,
of the smallest angle in this
triangle:
3x
A.
B.
C.
D.
20
40
60
80
2x
4x
24
Measurement
Practice…
Determining the measurement of a missing side(s) or angle(s)
in a polygon.
Missing Angles

(Short Response)
In the accompanying diagram of ∆BCD, m<C=70, m<CDE=130, and
side BD is extended to A and to E. Find m<CBA.
C
70°
Scoring Rubric:
A
B
130°
D E
**[2 points] 120, and appropriate work is shown, such as m<CDB= 180 – 130 = 50
and m<CBA = 70 + 50 = 120 or correctly labeled angles in a diagram.
*[1 point] Appropriate work is show, but one computational error is made.
*[1 point] Appropriate work is show, but one conceptual error is made.
*[1 point] m<CBD = 60 is found, but no further correct work is shown.
*[1 point] 120, but no work is shown
[0 points] A zero response is completely incorrect, irrelevant, or incoherent or is a
correct response that was obtained by an obviously incorrect procedure.
26
Measurement
Practice…
Determining the measurement of a missing side(s) or angle(s)
in a polygon.
Missing Sides

The length of each side of a
figure below is 4 inches (in.).
4 in.
What is the perimeter of the figure?
A.
B.
C.
D.

The interior angles of a sign
total 1080°. What type of
polygon is the sign?
A.
B.
C.
D.
Hexagon
Pentagon
Heptagon
Octagon
12 in.
16 in.
20 in.
24 in.
27
Measurement
Practice…
Determining measures of perimeter, circumference, area,
surface area and/ or volume.
Scaling Area

A farmer has a rectangular field that measures 100 feet by 150 feet. He
plans to increase the area of the field by 20%. He will do this by
increasing the length and width by the same amount, x. Which equation
represents the area of the new field?
A. (100 + 2x)(150 + x) = 18,000
B. 2(100 + x) + 2(150 + x) = 15,000
C. (100 + x)(150 + x) = 18,000
D. (100 + x)(150 + x) = 15,000
29
Measurement
Practice…
Determining measures of perimeter, circumference, area,
surface area and/ or volume.
Surface Area

The box pictured below is open
at the top. Find its outside
surface area.
Volume

The volume of the rectangular
solid below is 1,440 cubic
inches.
20 cm
3 in
15 cm
10 cm
A.
B.
C.
D.
45 cm²
1150 cm²
1300 cm²
3750 cm²
What could be the length and
width of this rectangular solid?
A.
B.
C.
D.
4 inches by 10 inches
8 inches by 20 inches
10 inches by 48 inches
30 inches by 40 inches
30
Measurement
Practice…
Determining measures of perimeter, circumference, area,
surface area and/ or volume.
Perimeter

A.
B.
C.
D.
Delroy’s sailboat has two sails
that are similar triangles. The
larger sail has sides of 10 feet,
24 feet, and 26 feet. If the
shortest side of the smaller sail
measures 6 feet, what is the
perimeter of the smaller sail?
15 ft
36 ft
60 ft
100 ft
Circumference

The circumference of a circle
is 16∏. What is the radius of
the circle?
A.
B.
C.
D.
4
8
16
32
32
Measurement
Practice…
Determining measures of perimeter, circumference, area,
surface area and/ or volume.
Perimeter

How does the perimeter of a
rectangle change when each
side is increased by 2 units
A. The perimeter doubles
B. The perimeter quadruples
C. The perimeter increases by 4
units
D. The perimeter increases by 8
units
Area

If the diameter of a car tire is
30 cm, what is the area of
that circle? Round your
answer.
A.
B.
C.
D.
30.14 cm²
314 cm²
7,070 cm²
707 cm²
34
Geometry
Vocabulary Review
angles are
1. When a transversal intersects two lines, Corresponding
___________________
on the same side of the transversal and on the same side of the given
lines. (Also, similar or congruent figures.)
Isosceles triangle has exactly two congruent sides.
2. A(n) _________________
Pythagorean Theorem is a formula for finding the length of a
3. The ____________________
side of a right triangle when the lengths of two sides are given.
Alternate exterior angles are located outside a set of
4. A pair of ________________
parallel lines and on opposite sides of the transversal.
5. A pair of opposite congruent angles formed when two lines intersect
Vertical angles
are called _____________.
Word Bank:
Isosceles triangle
Adjacent angles
Coordinate plane
Acute triangle
Vertical angles
Corresponding angles Alternate exterior
Pythagorean Theorem Alternate interior
Scalene triangle
36
Geometry
Vocabulary Review
Scalene triangle has no congruent sides.
6. A(n) _______________
Acute triangle has each angle measuring less than 90°.
7. A (n) ____________
Alternate interior angles are located between a set of
8. A pair of _______________
parallel lines and on opposite sides of the transversal.
Coordinate plane is a 2-D system which contains both horizontal
9. A ________________
and vertical axes.
10._______________
Adjacent angles share a common side and common vertex and do
not overlap.
Word Bank:
Isosceles triangle
Adjacent angles
Coordinate plane
Acute triangle
Vertical angles
Corresponding angles Alternate exterior
Pythagorean Theorem Alternate interior
Scalene triangle
37
Practice…
Geometry
Identifying, using, and/or describing properties of angles,
triangles, quadrilaterals, circles, pyramids, cubes, prisms,
spheres, cones and/or cylinders..
Circular Geometry

A duck swims from the edge of a circular pond to a fountain in
the center of the pond. Its path is represented by the dotted line
in the diagram below.
Duck’s Path
What term describes the duck’s path?
A.
B.
C.
D.
Chord
Radius
Diameter
Central angle
38
Practice…
Geometry
Identifying, using, and/or describing properties of angles,
triangles, quadrilaterals, circles, pyramids, cubes, prisms,
spheres, cones and/or cylinders..
Parallelograms

The height of a parallelogram
is 13.5 feet. The base is four
times the height. What is the
area of the parallelogram?
A.
B.
C.
D.
45.5625 ft²
54 ft²
182.25 ft²
729 ft²
Prisms

What is the volume of a
rectangular prism with a
length of 16 inches, a height
or 4 inches, and a width of 12
inches?
A.
B.
C.
D.
48 in.³
768 in.³
1810 in.³
2413 in.³
39
Practice…
Geometry
Identifying, using, and/or describing properties of angles,
triangles, quadrilaterals, circles, pyramids, cubes, prisms,
spheres, cones and/or cylinders..
Parallelograms

(Short Response)
Is it possible for two parallelograms to have the same area but not
be congruent? Explain why or why not.
Scoring Rubric:
**[2 points] Yes, two parallelograms can have the same area but not be congruent.
Let one parallelogram have a base of 6 units and a height of 4 units. Its area is 24
square units. Let another parallelogram have a base of 8 units and a height of 3
units. Its area is also 24 units, but the two parallelograms are not congruent.
*[1 point] Yes, two parallelograms can have the same area but not be congruent. No
explanation or example is given.
*[1 point] Yes, two parallelograms can have the same area but not be congruent. A
poor or incorrect explanation is given.
[0 points] A zero response is completely incorrect, irrelevant, or incoherent or is a
correct response that was obtained by an obviously incorrect procedure.
41
Practice…
Geometry
Identifying, using, and/or describing properties of angles,
triangles, quadrilaterals, circles, pyramids, cubes, prisms,
spheres, cones and/or cylinders..
Angles

Which angles are
complementary?
1
5
A.
B.
C.
D.
2
4
<2 and <3
<3 and <4
<4 and <5
<1 and <2

The ratio of two
supplementary angles is 2:7.
What is the measure of the
smaller angle?
A.
B.
C.
D.
10°
14°
20°
40°
3
42
Practice…
Geometry
Identifying, using, and/or describing properties of angles,
triangles, quadrilaterals, circles, pyramids, cubes, prisms,
spheres, cones and/or cylinders..
Net

Which of the following figures is the net of a square based pyramid?
A. 1
C. 3
B. 2
D. 4
43
Practice…
Geometry
Identifying, using, and/or describing properties of angles,
triangles, quadrilaterals, circles, pyramids, cubes, prisms,
spheres, cones and/or cylinders..
Regular Polygons

(Extended Response)
The top of the picnic table shown
has the shape of a regular polygon.
a. Sketch and classify the polygon. Is it
convex or concave?
b. Draw a single segment that divides
the polygon in your sketch into two
trapezoids.
c. Find the sum of the measures of the
angles of the polygon.
Solution:
a–b.
The polygon is a regular hexagon. It is convex.
c. 360 + 360 = 720
The sum of the measures of the angles of the polygon is 720°.
44
Practice…
Geometry
Identifying, using, and/or describing properties of angles,
triangles, quadrilaterals, circles, pyramids, cubes, prisms,
spheres, cones and/or cylinders.
Angles & Lines

Line p is parallel to line k in the
figure shown below
p
k

In the diagram below, line l
is parallel to line m and
line p is parallel to line q?
m
2
3
4
1
5
j
l
Which statement about the lines in
the figure is true?
A. Line k is parallel to line m.
B. Line m is parallel to line j.
C. Line p is perpendicular to line k.
D. Line j is perpendicular to line p.
p
q
m
Which angle has the same
measure as <1?
A. <2
B. <3
C. <4
D. <5
46
Geometry
Practice…
Computing measures of sides of right triangles using the
Pythagorean Theorem.
Pythagorean Theorem

Mr. Kyle drives eight miles
south and then six miles
east. What was the
diagonal distance from his
starting point?

What is the length of the
missing side in this triangle?
20
12
A.
B.
C.
D.
2 miles
10 miles
14 miles
48 miles
x
A.
B.
C.
D.
14
15
16
18
47
Geometry
Practice…
Plot and/or identify ordered pairs on a coordinate plane.
Coordinate System

Which building is located at
(-2, 3)?
Library

At what point does the line
intersect the y-axis?
A.
B.
C.
D.
(5, 0)
(0, 5)
(0,-3)
(-3, 0)
Market
School
Bank
A.
B.
C.
D.
School
Library
Market
Bank
49
Algebraic Concepts
Vocabulary Review
Linear equation is an equation whose graph in a coordinate plane
1. A ______________
is a straight line.
Absolute value is the distance of a number from zero on a number
2. _____________
line; shown by | |.
of equations is a group of two or more equations that
3. A(n) System
__________________
contain two or more variables.
4. A phrase that contains operations, numbers, and/or variables is a(n)
Expression
____________.
5. A relationship that has exactly one output for each input is called a
Function
________.
Word Bank:
Function
Function table
System of equations
Absolute value
Expression
Inverse operations
Terms
Equation
Inequality
Linear function
50
Algebraic Concepts
Vocabulary Review
Inequality shows the relationship between quantities that are not
6. An _________
equal.
7. A sentence that shows that two expressions are equivalent is a(n)
Equation
________.
Terms in an expression are set apart by plus or minus signs.
8. ______
9. A table of ordered pairs that represent solutions of a function is called a
Function table
_____________.
Inverse operations undo each other; addition and subtraction,
10._________________
multiplication and division.
Word Bank:
Function
Function table
System of equations
Absolute value
Expression
Inverse operations
Terms
Equation
Inequality
Linear function
51
Algebraic Concepts
Practice…
Analyzing, extending or developing descriptions of patterns or
functions.
Patterns

Fiona created a pattern
using numbers as shown
below.
0, 2, 6, 12
The pattern continues. What is
the next number in the
pattern?
A.
B.
C.
D.
14
18
20
24

List the next two values in
this sequence:
4, 10, 22, __, __
A.
B.
C.
D.
34, 46
34, 48
40, 62
46, 94
52
Algebraic Concepts
Practice…
Analyzing, extending or developing descriptions of patterns or
functions.
Functions

A.
B.
C.
D.
What is the solution of
x > -3?.
3
x < -1
x > -1
x < -9
x > -9

The table below shows a
relationship between the
values of x and y.
x
y
-7
-10
-2
-5
3
0
8
5
Which equation describes the
relationship?
A. y = x – 3
B. y = x +3
C. y = -x -3
D. y = -x +3
53
Practice…
Algebraic Concepts
Select and/ or use a strategy to simplify an expression, solve
an equation or inequality and/ or check the solution for
accuracy.
Solving Equations

A.
B.
C.
D.
Dora owns a card store.
After a full week, she made
$250.00 by selling cards (c).
Using the equation
1.25c = 250, how many
cards did Dora sell that
week?
125
200
251
312

In which equation is m = 28
the solution?
A. m – 3 = 5
5
B. m – 3 = 5
5
C. m – 3 = 5
5
D. (m – 3)5 = 5
54
Practice…
Algebraic Concepts
Selecting and/ or using a strategy to simplify an expression,
solve an equation or inequality and/ or check the solution for
accuracy.
Expressions

If k can be replaced by any
number, how many different
values can the expression
k + 6 have?
A.
B.
C.
D.
One
Six
Seven
Infinitely many
Inequalities
There is $150 in Dave’s bank
account. He deposits $200 into the
account each month. Dave needs
at least $700 to buy a used car.
The inequality below can be solved
for x to find the number of deposits
Dave must make to reach his goal.
200x + 150 ≥ 700
How many deposits must Dave make?

A.
B.
C.
D.
x ≥ 2.75
x ≤ 2.75
x ≥ 4.25
x ≤ 4.25
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Practice…
Algebraic Concepts
Selecting and/ or using a strategy to simplify an expression,
solve an equation or inequality and/ or check the solution for
accuracy.
Checking for Accuracy
(Short Response)

Brett was given the problem: “Evaluate 2x² + 5 when x = 3.” Brett wrote
that the answer was 41. Was Brett correct? Explain your answer.
Scoring Rubric:
**[2 points] No, and an appropriate explanation is given or the expression is
evaluated correctly.
*[1 point] No, and the correct order of operations is used to evaluate 2(3)² + 5,
but one computational error is made.
*[1 point] One conceptual error is made in evaluating the expression, but the
question is answered appropriately.
*[1 point] Appropriate work is shown, but the question is not answered.
[0 points] No, but no explanation or an inappropriate explanation is given.
[0 points] A zero response is completely incorrect, irrelevant, or incoherent or is
a correct response that was obtained by an obviously incorrect procedure.
56
Algebraic Concepts
Practice…
Creating and/ or interpreting expressions, equations or
inequalities that model problem situations.
Inequalities

A.
B.
C.
D.
When Bernie earns 5 times
more than the amount (a) of
money he has plus another
$1,000, he will have at least
$16,000 to start a small
business. Which statement
represents this situation?
5a + 1,000 ≥ 16,000
5 + 1,000a ≤ 16,000
5a +1,000 ≤ 16,000
5 + 1,000a ≥ 16,000
Expressions

Which expression represents
4 times the sum of x squared
and 6?
A.
B.
C.
D.
4x² + 6
4(x² + 6)
4(x + 6)²
(4x + 6)²
57
Algebraic Concepts
Practice…
Creating and/ or interpreting expressions, equations or
inequalities that model problem situations.
Creating Equations

A.
B.
C.
D.
A wooden box with 8 DVDs
inside weighs 4.2 kilograms.
The box weighs 0.6 kg when
empty. Using w to represent
the weight of one DVD, which
of the following describes this
situation?
8w = 4.2
8w + 0.6 = 4.2
8w – 0.6 = 4.2
8(w + 0.6) = 4.2

Which equation shows that
the sum of x and 2 is twice
as much as 6?
A.
B.
C.
D.
x=2·2·6
x + 2 · 2 =6
2(x +2) = 6
x+2=2·6
58
Algebraic Concepts
Practice…
Represent relationships with tables or graphs on the coordinate
plane.
Functions

Given the function y = ½x -2,
which set of numbers
completes the table?
x
Tables

Which linear function is
graphed below?
A.
B.
C.
D.
y=x+3
y² = 3x
y=3
x=3
y
-4
-2
0
A.
B.
C.
D.
{4, 3, 2}
{-4, -3, -2}
{-4, 3, 2}
{4, -3, -2}
59
Data Analysis & Probability
Vocabulary Review
Correlation describes the relationship between two sets of data.
1. ___________
2. A graphic method for showing a summary using median, quartiles and
Box-and-whisker plot
extremes of data is known as a(n) ____________________.
3. A(n) Permutation
___________ is a possible order or arrangement of a set of items.
Experimental probability is based on the results of a
4. A statement of _____________________
series of trials.
5. Two events that cannot occur at the same time are known as
Mutually exclusive events
_______________________.
Word Bank:
Compound event
Stem-and-leaf plot
Theoretical probability
Box-and-whisker plot
Experimental probability
Independent events
Permutation
Mutually exclusive
events
Scatter plot
60
Correlation
Data Analysis & Probability
Vocabulary Review
probability is a statement of the probability of an event
6. Theoretical
___________________
without doing an experiment or analyzing.
event is made up of two or more simple events.
7. A Compound
_______________
8. Two events in which the outcome of one event does not affect the
Independent events
outcome of the other event are known as _________________.
9. A graph with points plotted to show a relationship between two
Scatter plot
variables is called a ___________.
Stem-and-leaf plot displays groups of data arranged by place
10.A(n) ________________
value.
Word Bank:
Compound event
Stem-and-leaf plot
Theoretical probability
Box-and-whisker plot
Experimental probability
Independent events
Permutation
Mutually exclusive
events
Scatter plot
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Correlation
Data Analysis & Probability
Practice…
Choosing, displaying or interpreting data.
Charts

Stem-and-Leaf Plots
According to the graph, what
percent of the students chose
generic brands?

Favorite Sneakers at
Sherman High School Brand
A, 8%
Brand B,
5%
Generic
brands
Brand E,
27%
Brand C,
15%
Brand D,
30%
A.
B.
C.
D.
15%
14%
17%
16%
A.
B.
C.
D.
The table below shows test
scores for a class. How
many students scored in the
80’s?
Stem
Leaf
9
0 1 1 5 7
8
0 0 2 4 6 7 9
7
7 7 8 9
6
9
5
2 3
4
4
2 students
6 students
7 students
9 students
62
Data Analysis & Probability
Practice…
Choosing, displaying or interpreting data.
Interpreting Data

The test scores for 10 students in Ms. Sampson’s homeroom were
61, 81, 83, 87, 88, 89, 90, 98, and 100. Which frequency table is
accurate for this set of data?
A. 1)
B. 2)
Interval
Frequency
Interval
Frequency
61-70
2
61-70
2
71-80
2
71-80
0
81-90
7
81-90
8
91-100
10
91-100
10
Interval
Frequency
Interval
Frequency
61-70
2
61-70
2
71-80
2
71-80
0
81-90
8
81-90
6
91-100
10
91-100
2
C. 3)
D. 4)
63
Data Analysis & Probability
Practice…
Calculating the probability of an event.
Probability

There are 15 girls and 11
boys in a mathematics class.
If a student is selected at
random to run an errand,
what is the probability that a
boy will be selected?
A.
B.
C.
D.
4/26
11/26
15/26
11/15

There are 9 packages, 5 red
and 4 green. There are
calculators inside 4 of the red
packages and inside 2 of the
green packages. What is the
probability of choosing a
package containing a
calculator from the entire
group of packages?
A.
B.
C.
D.
4/5
2/3
1/2
4/9
64
Data Analysis & Probability
Practice…
Calculating the probability of an event.
Probability

While watching a game at a carnival where participants guess
which of three cups is covering a ball, Jeremy tallies that
following results.
Ball Location
left
middle
right
Frequency
16
18
33
Find the experimental probability of the following as a fraction in its
simplest form AND an approximate percentage.
a. Find the experimental probability of the ball being under the right
cup.
33 or about 50%
67
b. Find the experimental probability of the ball not being under the
middle cup.
49 or about 73%
67
65
Data Analysis & Probability
Practice…
Determining the number of combinations and/ or permutations
for an event.
Permutation
Combination

Sarah and Tom belong to a
soccer league that has 8
teams. Each team will play all
of the other teams twice. How
many games will be played in
all?

A.
B.
C.
D.
16
28
56
64
What is the number of outcomes
for this simulation?
A.
B.
C.
D.
Edward conducts a
simulation using a coin, a
number cube, and a spinner
as shown below.
3
8
12
48
66
Practice…
Data Analysis & Probability
Determining the number of combinations and/ or permutations
for an event.
Combinations

(Short Response)
In Jackson County, Wyoming, license plates are made with two letters
(A through Z) followed by three digits (0 through 9). The plates are
made according to the following restrictions:
•
•

the first letter must be J or W, and the second letter can be any of the 26 letters of the
alphabet
no digit can be repeated
How many different license plates can be made with these restrictions?
Scoring Rubric:
**[2 points] 37,440 and appropriate work is shown, such as 2 x 26 x 10 x 9 x 8
or 2P1 x 26P1 x 10P3.
*[1 point] Appropriate work is show, but one computational error is made.
*[1 point] Appropriate work is shown for at least one restriction, such as 2x26 or
10 x 9 x 8.
*[1 point] 37,440 but no work is shown.
[0 points] A zero response is completely incorrect, irrelevant, or incoherent or is
a correct response that was obtained by an obviously incorrect procedure.
67
Data Analysis & Probability
Practice…
Drawing conclusions, making inferences and/ or evaluate
hypotheses based on statistical and data displays.
Drawing Conclusions

From a batch of 3000 light
bulbs, 100 were selected at
random and tested. If 5 of the
light bulbs in the sample were
found to be defective, about
how many defective light
bulbs would be expected in
the entire bunch?
A.
B.
C.
D.
15
60
150
300
Correlation

The data represented in the
scatter plot below can be
described as having…
A.
B.
C.
D.
Positive correlation
Negative correlation
No correlation
Both positive and negative
68
correlation
Data Analysis & Probability
Practice…
Drawing conclusions, making inferences and/ or evaluate
hypotheses based on statistical and data displays.
Drawing Conclusions

A.
B.
C.
D.
An animal shelter needs to
find homes for 40 dogs and
60 cats. If 15% of the dogs
are female and 25% of the
cats are female, what percent
of the animals are female?
21%
22%
40%
42%
Correlation

Which data sets have a
negative correlation?
A. A person’s eye color and
height
B. A person’s height and weight
C. The distance traveled and
the time it takes to travel
D. The outdoor temperature and
the number of hours a heater
is used
69
Data Analysis & Probability
Practice…
Drawing conclusions, making inferences and/ or evaluate
hypotheses based on statistical and data displays.
Drawing Conclusions

John left his home and walked 3 blocks to his school, as shown in
the accompanying graph.
D
3
B C
2
1
A
Time
What is one possible interpretation of the section of the graph from
point B to point C?
A.
B.
C.
D.
John reached the top of a hill and began walking on level ground.
John waited before crossing a busy street.
John arrived at school and stayed throughout the day.
70
John returned home to get his mathematics homework.
Good luck to all!!!
Feel free to repeat the review as many
times as you like or continue studying
your own additional resources!
71