Sample Math Algebra Assessment

Transcription

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Math Algebra
Assessment
Test Code: 220231
Teacher Key
Directions: Record all answers on your answer sheet using a #2 pencil. Fill in
ovals on your answer sheet completely. There is only one correct answer per
question. Additional marks, whether intended or unintended, will cause the
question to be marked as incorrect.
For this test, you may write in your test booklet. You may answer the questions in any order.
You may go back to any passage if there is additional time at the end of the test.
Permission to duplicate this assessment for non-profit use by the school is granted with proper attribution to
GAINS Interim Measures, LTD.
011111
Teacher Key
MATHEMATICS TEST Interim
Algebra 20-23
EXPLANATION OF THE TEACHER KEY: This key is for Algebra Test 220231. The meaning
of 2023 is that it contains items that students who score in the range of 20 -23 on the Explore,
Plan, or ACT should be able to answer correctly. There are 12 standards in the 20 -23 range
on the ACT that pertain to Algebra II. Each item stem is shown as the student will see it. The
meaning of “1” is that this is the first version of the test. Two versions are available for this
test.
To the right of each item stem the following information is included:
Correct answer choice letter
ACT Strand
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Content Area
College Readiness Standard (CRS)
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Calculator use
Formulas that may be used in the completion of the item (i.e., a 2 + b 2 = c 2)
A table below contains the steps the student might take to produce an answer. The correct
answer is labeled “Correct”.
.
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Sample Item from the Teacher Key
1. The average (arithmetic mean) of 3 numbers is 60. If
two of the numbers are 50 and 60, what is the third
number?
A.
B.
C.
D.
E.
50
55
60
65
70
DO YOUR FIGURING HERE.
Answer
E
Content Area
Algebra
ACT Strand
II. Probability, Statistics, & Data Analysis
CRS
Calculator
20-23 a. Calculate the missing data value, given
the average and all data values but one
Addition, Subtraction, Multiplication
Formula
Average
A. Lowest value given
B. Mean of 50 and 60 only
C. Median
D. Mean of 60 and 70
E. Correct
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The item stem begins “The average ...”
The right column shows that the correct answer choice is “E”.
The Content Area is “Algebra”.
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The ACT Strand for this item is “II. Probability, Statistics, & Data Analysis”. There are 8 strands (Basic Operations
& Applications; Probability, Statistics, & Data Analysis; Numbers: Concepts & Properties; Expressions, Equations,
& Inequalities; Graphical Representations; Properties of Plane Figures; Measurement; and Functions).
The College Readiness Standard is “20-23 a”. Calculate the missing data value, given the average and all data values
but one.
It is suggested that a calculator should be used for this problem “Calculator for addition, subtraction, multiplication.”
It is suggested that the formula associated with this item is “Average”.
Answer choice “E” is 70. The answer choice is labeled “Correct.”
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MATHEMATICS TEST
45 Minutes—36 Questions
DIRECTIONS: Solve each problem, choose the correct
answer, and then fill in the corresponding oval on your
answer document.
Do not linger over problems that take too much time.
Solve as many as you can; then return to the others in
the time you have left for this test.
You are permitted to use a calculator on this test. You
may use your calculator for any problems you choose,
1. The average (arithmetic mean) of 3 numbers is 60. If
two of the numbers are 50 and 60, what is the third
number?
but some of the problems may best be done without
using a calculator.
Note: Unless otherwise stated, all of the following should
be assumed.
1. Illustrative figures are NOT necessarily drawn to scale.
2. Geometric figures lie in a plane.
3. The word line indicates a straight line.
4. The word average indicates arithmetic mean.
Answer
E
Content Area Algebra
ACT Strand
50
CRS
B.
55
Calculator
Formula
Average
C.
60
D.
65
E.
70
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A.
A. Lowest value given
B. Mean of 50 and 60 only
C. Median
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D. Mean of 60 and 70
E. Correct
Answer
2. Rebecca, who is 2 years old, has a toy computer
designed to teach children the alphabet. The keyboard
has 26 keys, 1 for each of the 26 capital letters of the
alphabet. When she presses a key at random, what is
the probability that it will be a letter found in
REBECCA?
F.
5
26
G.
6
26
H.
5
21
J.
7
26
K.
7
19
F
Content Area Basic Statistics & Probability Concepts
ACT Strand
CRS
Calculator
20-23 c. Determine the probability of a simple
event
None
Formula
Probability of random event
F. Correct
G. Does not account for one of the repeating letters
H. Uses letters not used for the denominator
J. Does not account for E and C repeating in name
K.
1
Does not account for E and C repeating in name and uses
letters not used for the denominator
2
2
3. Mrs. Sacchitello’s statistics class is examining how many of each type of cookie are purchased in the cafeteria. Three
groups recorded the number of cookies that were purchased during a week. The first group was assigned chocolate
chip cookies, the second group was assigned peanut butter cookies and the final group was assigned oatmeal raisin
cookies. The bar graphs from each group are shown below (all scales are equal). Which line graph displays the
results of all three groups?
Chocolate Chip Cookies
Peanut Butter Cookies
90
Oatmeal Raisin Cookies
90
90
82
80
75
80
70
70
60
60
Number of Cookies Sold
70
55
48
50
40
30
70
60
50
80
52
50
45
40
35
30
60
51
50
40
30
22
20
20
20
10
10
10
0
0
0
Monday
Tuesday
Wednesday
Thursday
Friday
Monday
Tuesday
Wednesday
Thursday
Friday
22
18
10
Monday
Tuesday
Wednesday
Thursday
Friday
Cookies Sold
90
80
A.
70
60
50
40
30
20
Answer
A
Content Area
Basic Statistics & Probability Concepts
ACT Strand
CRS
20-23 b. Translate from one representation of
data to another (e.g., a bar graph to a circle
graph)
10
0
Monday
Tuesday
Wednesday
Thursday
Friday
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Cookies Sold
80
70
B.
60
50
40
Calculator
None
Formula
None
A. Correct
30
10
0
Monday
Tuesday
Wednesday
Thursday
Friday
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B. Number of cookies sold on Monday
20
C. Only shows 2 cookies
D. Number of cookies sold is in reverse order
Cookies Sold
90
E. Only shows chocolate chip cookies
80
C.
70
60
50
40
30
20
10
0
Monday
Tuesday
Wednesday
Thursday
Friday
Cookies Sold
90
80
D.
70
60
50
40
30
20
10
0
Monday
Tuesday
Wednesday
Thursday
Friday
Cookies Sold
90
80
E.
70
60
50
40
30
20
10
0
Monday
Tuesday
Wednesday
Thursday
Friday
2
2
4. Joey has 4 pairs of batting pants, 6 baseball jerseys,
and 2 pairs of baseball spikes in his closet. How
many different uniforms, composed of a pair of
batting pants, a jersey and a pair of spikes, can he
choose from this closet?
F.
2
G.
6
H.
J.
12
26
K.
48
Answer
K
2
ACT Strand
II. Probability, Statistics & Data
CRS
Calculator
20-23 d. Exhibit knowledge of simple counting
techniques.
Reduce Fractions
Formula
Probability of a given event
F. Number of spikes
G. Number of jerseys
H. 4 + 6 + 2
J. 4 × 6 + 2
K. 4 ×6 × 2 Correct
5. What is the 8th term in this sequence of “triangular”
numbers, defined by the figures below:
1, 3, 6, 10, …?
B.
26
C.
36
D.
40
E.
80
ACT Strand
III. Numbers: Concepts & Properties
CRS
Calculator
20-23 a. Exhibit knowledge of elementary
number concepts including rounding, the
ordering of decimals, pattern identification,
absolute value, primes, and greatest common
factor
Multiplication, addition, division
Formula
xn
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8
C
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A.
Answer
n(n 1)
2
A. Number term to find
B. 10 + 4 × 4
C. Correct
D. Addition error
E. 10 × 8
6. When x = -1, what is the value of
F.
-10
G.
-2
H.
2
J.
9
K.
10
6x 4
?
x
Answer
K
ACT Strand
IV. Expressions, Equations, & Inequalities
CRS
20-23 a. Evaluate algebraic expressions by
substituting integers for unknown quantities
Calculator
Formula
Evaluating Variable Expressions
F. Rules of addition of integers
G. Rules of addition of integers
H. Rules of addition integers
J. Subtracted denominator from numerator and ignored signs
K. Correct
3
2
7. Add: ( x
2
3x) ( x
2
x)
A. 6x6
B. 5x2 + 4x3
C. 2x2 + 3x + 1
2
D. 2x + 4x
2
Answer
D
ACT Strand IV. Expressions, Equations, & Inequalities
CRS
20-23 b. Add and subtract simple algebraic
expressions
Calculator
Formula
Addition
Combining Like Terms
E. x4 + 3x2
A. All coefficients and exponents are summed
B. (2 + 3) x² + (2² x²x)
C. ( x² + 3x)+( x² + 1)
D. Correct
E. (x² × x²) + (3x × x)
8. Solve for r: 4r – 14 = 14.
1
4
H.
J.
K.
0
7
24
CRS
20-23 c. Solve routine first-degree equations
Calculator
Formula
Addition of Integers, Division
Solving equations in the form ax + b = c
Subtracts 4 – 14 on left to get -10r = 14, then divides both
sides by -10
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F. -1.4
Answer
J
F.
G. Multiplies 4 × -14 on left, then divides both sides by that
H. Cancels 14s before dividing
J. Correct
K.
4
Subtracts 4 –14 on left to get -10r = 14, then adds 10 to each
side
2
9. Fred walked m miles on Tuesday. On Wednesday, he
walked 3 fewer than twice the number of miles he
walked on Tuesday. Which expression represents the
number of miles Fred walked on Wednesday?
Answer
C
Content Area Pre-Algebra
CRS
Calculator
Formula
A. 2(3 – m)
2
20-23 d. Perform straightforward word-tosymbol translations
None
Mathematics Vocabulary; Writing Expressions
B. 2(m – 3)
A. Chose incorrect operation
C. 2m – 3
B. Chose incorrect operation
D. 3 – 2m
C. Correct
E. 3m – 2
D. Chose incorrect operation
E. Chose incorrect operation
3x² + x – 6
3x² + 7x – 6
3x² – 6
-18x²
4x + 1
Calculator
Multiplication, Addition, Subtraction
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F.
G.
H.
J.
K.
Answer
G
CRS
20-23 e. Multiply two binomials
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10. Expand by multiplication: (x + 3)(3x – 2) = ?
Formula
FOIL
F. 3x² + 3x – 2x – 6
G. 3x² – 2x + 9x – 6 Correct
H. Middle terms are omitted
J. All coefficients are multiplied (1)(3)(3)(-2)(x)(x)
K. (x + 3) + (3x – 2)
5
2
Answer
11. Which point is located at (2, -4)?
M
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x
ACT Strand
V. Graphical Representations
CRS
20-23 a. Locate points in the coordinate plane
Calculator
Graphing Calculator
Formula
Graphing Points in the Coordinate Plane
A. Switched x and y
N
B. (-2, 4)
P
A.
B.
C.
D.
E.
C. (2, 4)
K
L
M
N
P
12. If f ( x)
2
Content Area Coordinate Geometry
y
L
E
D. (-4, -2)
E. Correct
Answer
4 x 2, then f(-2) = ?
G
-64
G.
H.
J.
-16
8
16
K.
64
ACT Strand
VIII. Functions
CRS
20-23 a. Evaluate quadratic functions, expressed
in function notation, at integer values
Programmed Order of Operation
Calculator
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F.
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Formula
F. -(4)2(-2)2
G. -4(-2)2 Correct
H. (-4)(-2)
J. Incorrect sign
K. (-4)2(-2)2
13. In a math course, a student scored 95 on one test, 92
on the second test, 83 on the third test, 75 on the
fourth test, 87 on the fifth test and 70 on the last test.
If the student has the opportunity to drop the test
with the lowest score, what is the student’s average
in the math class? Note: Teachers rounds scores to
nearest whole number.
A.
Answer
D
ACT Strand
CRS
Calculator
Addition, Subtraction, Multiplication, Division
Formula
Average
72
A. 5 scores divided by 6
84
B.
C. 85
D. 86
E. 100
B. Did not drop lowest score
C. Median
D. Correct
E. Sum of 6 scores divided by 5
6
2
Answer
14. Washington High School has 1823 students. If the
classes are divided as represented in the circle graph
below, how many junior students attend Washington
High School?
Freshmen
26%
ACT Strand
CRS
Calculator
20-23 b. Translate from one representation of
data to another (e.g., a bar graph to a circle
graph)
Multiply
Formula
None
F. Percent
G. Number of seniors
H. Number of sophomores
J. Number of freshmen
Juniors
27%
Freshmen
Seniors
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270
398
452
475
492
Juniors
K. Correct
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F.
G.
H.
J.
K.
Sophomores
25%
Sophomores
2
Washington High School Students
Seniors
22%
K
7
2
15. What is the probability that a 12-sided die will give
the numbers 5, 6, or 7 when rolled?
A.
B.
C.
D.
E.
1:6
1:3
1:4
4:1
9:12
Answer
C
2
ACT Strand
CRS
event
Reduce Fractions
Calculator
Formula
Probability of a given event; identify
numerator and denominator
A. 2:12
B. 4:12
C. Correct
D. Number of possibilities used as numerator
E. Added the three numbers and used as numerator
5
G.
H.
J.
K.
8
13
20
40
K
ACT Strand
CRS
Calculator
techniques
Multiplication
Formula
Combinations
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F.
Answer
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16. Andrew has 8 shirts and 5 pairs of pants. If all the
shirts can be worn with any of the pairs of pants,
how many different pant-shirt outfits can he choose
from?
F. Number of pairs of pants
G. Number of shirts
H. 5 + 8
J. 4 × 6 × 2
K. (8)(5) Correct
8
2
Answer
2
17. If a = | b | and b = -4, then what is 3a ?
D
2
A.
-24
ACT Strand
B.
C.
D.
E.
-13
24
48
144
CRS
number concepts including rounding the
absolute value, primes and greatest common
factor
Scientific/Graphing Calculators for Absolute
Value
Absolute Value, Order of Operation
Calculator
Formula
A. 3(-4)(2)
B. 3 – 42
C. 3(4)(2)
D. 3(4)2 Correct
E. 3(-4) = -12; (-12)2
Answer
18. What is the value of 2d – 5 + g when d = 5 and g = -2?
H
K.
18
ACT Strand
CRS
Calculator
Formula
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-4
-2
3
7
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F.
G.
H.
J.
F. 2(-2) – 5 + 5
G. 2(5 – 5) – 2
H. 2(5) – 5 + (-2) Correct
J. 2(5) – 5 + 2
K. Uses 5 as place digit: 25 – 5 –2
C
19. What is the sum of the two polynomials in the following Answer
addition problem?
2 x 2 3x 5
ACT Strand
CRS
A.
2x2 + 9x + 4
Calculator
expressions
Addition, Subtraction of Like Terms
B.
C.
3x2 + 9x – 5
3x2 + 9x + 4
Formula
Combining Like Terms, Adding Polynomials
x2 6x 1
D.
E.
A. Omitted x2
4
3x + 9x + 4
3x4 + 9x2 + 4
B. -5 – 1, Wrong sign on 5 omitted -1
C. Correct
D. Added exponents in first term
E. Added exponents in first 2 terms
9
2
20. Cultural Canines charges $25 for dog training, plus $10
times the skill level of the dog. They calculate the skill
level by dividing the number of classes the dog has
attended by 2. A dog who has attended x classes is
charged $75. Which of the following equations allows
you to solve for x?
F.
G.
H.
J.
K.
$25 x
$10
2
$25 x
$10
2
ACT Strand
CRS
Calculator
Subtraction/Division
Formula
Translation of words into numbers, variables
and operations
F. Interchanges charges and uses incorrect operation
$75
G. Interchanges charges
$10 x
$25
$75
2
$10 + $25(x –2) = $75
$25 + $10(x –2) = $75
H. Correct
J. Interchanges charges and uses incorrect operation
K. Incorrect operation
Answer
ACT Strand
CRS
Calculator
None
Formula
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2y – 15
2y + 15
2(y - 15)
2(y + 15)
y 15
2
A
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E.
H
2
$75
21. Martha has 15 more minutes of reading to do until she
has read twice as many minutes today as yesterday.
Which expression shows how many minutes Martha
has read so far today?
A.
B.
C.
D.
Answer
A. Correct
B. Chose incorrect operation
C. Chose incorrect operation
Answer
22. For all x and y, (3x – y)(x2 + y) = ?
H
2
2
2
ACT Strand
3x3 +3xy – x2y + y2
CRS
H.
3x3 + 3xy – x2y – y2
Calculator
Scientific Calculator
J.
3x x3 + 3xy – x2y2
Formula
Multiplication of Binomials
K.
3x x3 + xy – y2
F.
3x +3xy – xy – y
G.
F. First three terms incorrect
G. Incorrect last term
H. Correct
J. Extra x on first term and omitted last term
K. Extra x on first term and incorrect middle term
10
2
Answer
23. What are the coordinates of point B?
y
A
2
D
ACT Strand V. Graphical Representations
A
CRS
Calculator
Graphing Calculator
Formula
x
B
A. Correct
B. A
C
C. C
E
D. E
A.
B.
C.
D.
E.
E. D
(-4, -1)
(-4, 1)
(-1, -4)
(1, -4)
(1, 4)
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24. What is the value of F(-3,2) when the operation
F(a,b) = 5a2 + 5ab – 4ab2 ?
F(-3,2) = -87
F(-3,2) = -82
F(-3,2) = -27
F(-3,2) = 3
F(-3,2) = 63
K
ACT Strand VIII. Functions
CRS
20-23 a. Evaluate quadratic functions,
expressed in function notation, at integer values
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F.
G.
H.
J.
K.
Answer
Calculator
Formula
F. -45 – 30 – 12
G. Uses a = 2 and b = -3
H. -45 – 30 + 48
J. 45 – 30 – 12
K. Correct
25. For a 5-day period of time, the average daily
temperature in Orlando, Florida was recorded as 85°.
The entries are: Monday, 83°, Tuesday, 90°,
Thursday, 81°, Friday, 83°. The entry for Wednesday
is missing. What must the temperature for Wednesday
have been?
A. 81°
B. 82°
C. 85°
D. 88°
E. 90°
Answer
ACT Strand II. Probability, Statistics, & Data Analysis
CRS
Calculator
Multiplication
Formula
Average
A.
B.
C.
D.
E.
11
D
Lowest number in list
Subtraction Error
Weekly average
Correct
Highest number in list
2
2
26. The graph to the right represents the average number of minutes spent on homework (Monday – Thursday) during
the month. Which chart below best represents the average number of minutes spent during the first week of the
month (assume all scales are equal)?
Average Time Spent on Homework
100
90
80
70
60
Minutes
F.
50
40
30
20
10
0
Monday
Tuesday
Wednesday
Thursday
100
90
80
70
60
Minutes
G.
50
40
30
Answer
20
0
Monday
Tuesday
Wednesday
Thursday
100
90
80
70
60
Minutes
F
ACT Strand
CRS
20-23 b. Translate from one representation of data
to another (e.g., a bar graph to a circle graph)
Calculator
None
Formula
None
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H.
m
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10
50
40
30
F. Correct
20
10
0
Monday
Tuesday
Wednesday
Thursday
G. Week 2
H. Week 3
J. Week 4
100
90
K. Only displays 2 days
80
70
60
Minutes
J.
50
40
30
20
10
0
Monday
Tuesday
Wednesday
Thursday
100
95
90
Minutes
K.
85
80
75
Monday
Tuesday
12
2
27. The pet store sells birds, hamsters and fish. The ratio of
birds to the store’s total pets is 64:240, and the ratio of
hamsters to the store’s total pets is 3:24. If one pet is
chosen at random from the entire store, what is the
probability that it will be a fish?
A.
30
240
B.
67
264
C.
64
240
D.
94
240
E.
146
240
ACT Strand
CRS
event
Calculator
Reduce Fractions
Formula
Probability of a given event: Identify
numerator and denominator, Ratio
B.
64 3
240 24
C. Probability of choosing a bird
D. Probability of not choosing a fish
E. Correct
Answer
J
ACT Strand
CRS
techniques
Calculator
Multiplication
Formula
Combinations
F. Number of categories
e
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J. 168
K. 300
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3
18
56
E
2
A. Probability of choosing a hamster
28. Lilly is decorating cupcakes. She has 3 flavors of
frosting, 8 colors of sprinkles, and 7 types of candy. If
each cupcake can have only 1 type of frosting, 1 color
of sprinkles, and 1 type of candy, how many different
ways can she decorate the cupcakes?
F.
G.
H.
Answer
G. 3 + 8 + 7
H. 8 × 7
J. 3 × 8 × 7 Correct
K. Rounds 8 and 7 to 10
Answer
29. Which is a prime number?
A
A.
B.
5
6
C.
D.
12
21
E.
39
ACT Strand
CRS
number concepts including rounding, the
absolute value, primes, and greatest common
factor
Calculator
None
Formula
Number divisible by 1 and itself
A. Correct
B. 2 × 3 = 6
C. 2 × 2 × 3 = 12
D. 3 × 7 = 21
E. 3 × 13 = 39
13
2
x 5
when x = -3?
30. What is the value of 2
x 4
F. -4
G.
8
5
H.
2
5
8
13
4
5
J.
K.
Answer
G
2
ACT Strand
CRS
Calculator
Formula
Evaluating Variable Expressions using Integers
F. (-3 – 5) / (6 – 4)
G. (-3 – 5) / (9 – 4) Correct
H. (5 – 3) / (9 – 4)
J. (3 + 5) / (9 + 4)
K. (9 – 5) / (9 – 4)
31. Simplify by combining like terms: (w + 3t) – (t – 5) = ? Answer
C
A. wt – 3t – 5w + 15t
-wt – 3t – 5w – 15t
w + 2t + 5
w + 2t – 5
w+8
ACT Strand
CRS
expressions
Calculator
Addition, Subtraction
Formula
Combining Like Terms
e
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B.
C.
D.
E.
2
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2
A. (w – 3t)(t – 5)
B. (w + 3t)(-t – 5)
C. w + 3t – t + 5 Correct
D. 5 instead of -5 is subtracted
E. w + 3 + 5
14
2
32. If 5y + 9 = 4x, then x =?
Answer
K
2
F. y + 9
G.
5
y
4
9
H.
5
y
4
9
J.
5y 9
4
K.
5y 9
4
CRS
Calculator
Addition, Subtraction
Formula
Solve for one variable in terms of another
variable
F. Forgets coefficients of 5 and 4
Subtracts 9 instead of adding and does not divide (y + 9)
G.
by 4
H. Does not divide 9 by 4
J. Subtracts 9
K. Correct
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Sa
B
33. Mark has some tennis balls, b. Which expression shows Answer
6 fewer than three times the number of tennis balls
Mark has?
CRS
Calculator
None
Formula
e
pl
A. 6 – 3b
B. 3b – 6
C. 3(6 – b)
D. 3(b – 6)
E. b – 2(5)
A. Chose incorrect operation
B. Correct
C. Chose incorrect operation
15
2
34. The length and width of a rectangular practice field
must be 3x yards and (2x – 5) yards, respectively.
Which of the following expressions in terms of x gives
the number of square yards of artificial grass needed
to cover the field?
F. 5x – 5
Answer
2
ACT Strand
CRS
Calculator
Multiplication of monomial and binomial
Formula
Area of Rectangle = L x W
G. 4x – 10
H. 15x – 6x
J
F. 3x + (2x – 5)
2
G. (2x – 5) + (2x – 5)
2
J. 6x – 15x
H. (-3x)(2x – 5)
K. 10x – 10
J. (3x)(2x – 5) Correct
K. 3x + 3x + (2x – 5) +(2x – 5) Perimeter
35. One of the following points in the standard (x,y)
coordinate plane has the coordinates (4,-1). Which
one is it?
Answer
E
V. Graphical Representations
CRS
Calculator
Graphing Calculator
Formula
m
Sa
ACT Strand
A. (-1, 4)
e
pl
B. (-4, 1)
C. (-4, -1)
A. F
D. (1, -4)
B. G
E. Correct
C. H
D. J
E. K
36. If f(x) = x2 + 4x + 5, find f(-2).
Answer
H
F.
-17
G.
-7
H.
1
J.
7
K.
17
ACT Strand
VIII. Functions
CRS
20-23 a. Evaluate quadratic functions,
expressed in function notation, at integer values
Calculator
Scientific Calculator with x2 key
Formula
Function Notation, Evaluate Quadratic
Expressions
F. -4 + -8 + -5
G. -4 – 8 + 5
H. 4 – 8 + 5 Correct
J. 4 + 8 – 5 and adds -5
K. 4 + 8 + 5
16

Sample Math Algebra Assessment

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