TEXAS SUCCESS INITIATIVE ASSESSMENT 2.0
Mathematics
Sample Questions
TEXAS SUCCESS INITIATIVE ASSESSMENT 2.0
1
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Texas Success Initiative Assessment 2.0
(TSIA2) Mathematics Sample Questions
The TSIA2 Mathematics test covers four main categories:
Quantitative Reasoning, which includes calculating ratios, proportions, and percents,
as well as identifying, manipulating, and interpreting linear equations and expressions.
Algebraic Reasoning, which includes solving equations (linear, quadratic, polynomial,
exponential, rational, and radical), evaluating functions, and solving algebraic
problems in context.
Geometric and Spatial Reasoning, which includes converting units within
measurement systems, solving geometric problems (perimeter, area, surface area,
and volume), performing transformations, and applying right triangle trigonometry.
Probabilistic and Statistical Reasoning, which includes classifying data, constructing
appropriate representations of data, computing and interpreting probability, and
describing measures of center and spread of data.
The Use of Calculators
When you take an actual mathematics test online, a basic, square root, or graphing
calculator is allowed for some questions. If a question allows for the use of a calculator, a
calculator icon will appear on the screen, along with the question. For each of the sample
items in this packet, it is noted which calculator you can use—[basic], [square root], or
[graphing]—to solve the problem.
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TEXAS SUCCESS INITIATIVE ASSESSMENT 2.0
2
Sample Questions
Directions for questions 1–20
For each of the questions below, choose the best answer
from the four choices given.
1. If there are 2.2 pounds in 1 kilogram, how many
pounds are there in x kilograms? [basic]
A.
x
2.2
B. 2.2x
C. 2.2 + x
D.
x
2.2
2.
Monday Tuesday Wednesdayursday
5
4
3
2
1
0
Number of Customers
(in hundreds)
CUSTOMERS AT A STORE
e bar graph above shows the number of customers
who shopped at a store Monday through ursday of
one week. If the number of customers on Friday was
a one-h increase from the number of customers on
ursday, how many customers shopped at the store
on Friday? [basic]
A. 480
B. 500
C. 525
D. 600
3. Last year, a bakery sold w loaves of bread. is year,
the bakery sold three more than twice the number of
loaves of bread sold last year. If next year the bakery
plans on selling twice the number of loaves of bread
sold this year, how many loaves of bread does the
bakery expect to sell next year? [basic]
A. 2w
B. 2w + 3
C. 4w + 3
D. 4w + 6
4. If 7p − 4 = 8, what is the value of p? [basic]
A.
4
7
B.
7
12
C.
7
12
D.
7
4
5. Running at an average rate of 6 miles per hour, how
many minutes would it take Kyle to run 3 miles?
[basic]
A. 18
B. 30
C. 40
D. 45
6.
01234
e dot plot above identies the number of pets living
with each of 20 families in an apartment building.
What fraction of the families have more than two pets?
[basic]
A.
3
20
B.
1
5
C.
1
4
D.
9
20
TEXAS SUCCESS INITIATIVE ASSESSMENT 2.0
3
7.
r
h
e formula for the volume of the right circular
cylinder shown is
V = πr
2
h.
If r = 2b and h = 5b + 3 , what is the volume of the
cylinder in terms of b? [basic]
A.
10πb
2
+ 6πb
B.
20πb
3
+ 12πb
2
C.
20π
2
b
3
+ 12π
2
b
2
D.
50πb
3
+ 20πb
2
+ 90πb
8. Richard bought 3 slices of cheese pizza and 2 sodas
for $8.75. Jordan bought 2 slices of cheese pizza and 4
sodas for $8.50. How much would an order of 1 slice of
cheese pizza and 3 sodas cost? [basic]
A. $3.25
B. $5.25
C. $7.75
D. $17.25
9. If 5c − 2 = 3c, then 24c =
[basic]
A. 6
B
. 8
C. 16
D. 24
10. In the xy-plane, the slope of the line y = mx − 4 is
less than the slope of the line y = x − 4. Which of the
following must be true about m? [basic]
A. m = −1
B. m = 1
C. m < 1
D. m > 1
11. A hi
story class is made up of 12 tenth graders and 9
eleventh graders. e tenth graders averaged 77 on the
midterm exam, and the eleventh graders averaged 91
on the midterm exam. What was the average grade on
the midterm exam for the entire class? [basic]
A. 82
B. 83
C. 84
D. 85
12. Which of the following is NOT equivalent to
(3x − 12)(x + 4)? [square root]
A.
3(x
2
– 8x + 16)
B.
3(x
2
– 16)
C.
3x
2
– 48
D. 3x(x + 4) – 12(x + 4)
13. If the cost of carpeting a oor is $2.50 per square foot,
how much will it cost to carpet a rectangular oor that
is 10 feet by 12 feet? [basic]
A
. $112.00
B. $120.00
C. $250.00
D. $300.00
14. If n is the least of two consecutive odd integers, which
of the following represents the sum of the two integers?
[basic]
A. n + 1
B. n + 2
C. 2n + 1
D. 2n + 2
15.
[graphing]
A.
x
5
y
2
B.
y
2
x
5
C.
x
5
y
2
D.
x
5
y
–3
x
–5
y
y
3
–1
( )
=
TEXAS SUCCESS INITIATIVE ASSESSMENT 2.0
4
16. Reyna has 5 coins worth 10 cents each and 4 coins
worth 25 cents each. If she chooses two of these coins
at random, what is the probability that the two coins
combined will be worth at least 35 cents? [basic]
A.
5
18
B.
5
9
C.
13
18
D.
71
72
17. In the xy-plane, what is the y-intercept of the graph of
the equation
1
2
–
y = 6
x (x + 3)
( )
? [square root]
A. –9
B. –
1
2
C. 3
D. 9
18.
x
x + 1
e area of the triangle above is 21. What is the value
of x? [square root]
A. 3
B. 6
C. 7
D. 11
19. For which of the following values of x is the function
f(x) =
4 x–
2
NOT dened as a real number?
[square root]
A. −2
B. 0
C. 2
D. 4
20. Under ideal conditions, the population of a certain
spe
cies doubles every nine years. If the population
started with 100 individuals, which of the following
expressions gives the population of the species t years
aer the population started, assuming that the
population has been living under ideal conditions?
[graphing]
A.
2 × 100
9t
B.
t
9
2 × 100
C.
100 × 2
9t
D.
t
9
100
× 2
TEXAS SUCCESS INITIATIVE ASSESSMENT 2.0
5
Answer Key
1. B
2. A
3. D
4. C
5. B
6. B
7. B
8. B
9. D
10. C
11. B
12. A
13. D
14. D
15. C
16. C
17. A
18. B
19. D
20. D
TEXAS SUCCESS INITIATIVE ASSESSMENT 2.0
6
Rationales
1. Choice B is the correct answer. If there are 2.2 pounds in 1 kilogram, then there are
2.2x pounds in x kilograms.
2. Choice A is the correct answer. According to the graph,
400 customers shopped
at the store on Thursday. The number of customers at the store on Friday was a
one-fth increase from the number of customers on Thursday. Thus, the number of
customers on Friday was
400 +
1
5
(400) = 400 + 80 = 480.
3. Choice D is the correct answer. Last year, a bakery sold
w loaves of bread. This year,
the bakery sold three more than twice the number of loaves of bread sold last year,
which is
2w + 3 . Next year, the bakery plans on selling twice the number of loaves of
bread sold this year, which is 2(2w + 3) = 4w + 6 loaves of bread.
4. Choice C is the correct answer. If
7p − 4 = 8, then 7p = 12, so p =
7
12
.
5. Choice B is the correct answer. There are 60 minutes in one hour, so a rate of 6 miles
in one hour is equivalent to a rate of
=
6
60
=
1
10
1
10
=
6
60
mile in one minute. Therefore, at this rate,
Kyle runs one mile in 10 minutes. It follows that it would take Kyle 3 × 10 = 30 minutes
to run 3 miles.
6. Choice B is the correct answer. According to the dot plot, families that have more
than two pets have either three pets or four pets. Since
3 families have three pets and
1 family has four pets, a total of 4 families have more than two pets. Since there are
a total of
20 families, the fraction of families with more than two pets is
4
20
, which is
equivalent to
1
5
.
7. Choice B is the correct answer. Substituting the values r = 2b and h = 5b + 3
into the formula for the volume of the cylinder gives
V = π(2b)
2
(5b + 3) = 4πb
2
(5b + 3) =
20πb
3
+ 12πb
2
.
8. Choice B is the correct answer. Let
c dollars be the cost of a slice of cheese pizza
and s dollars be the cost of a soda. From the information given, the system can be
written as:
3c + 2s = 8.75
2c + 4s = 8.5
This is equivalent to:
c + 4s = 17.5
2c + 4s = 8.5
Subtracting the second equation from the rst equation gives 4c = 9, so c = 2.25.
Solving the equation (2)(2.25) + 4s = 8.5 for s gives s = 1 . It follows that the cost of 1
soda is $1.00. Therefore, the cost of an order of 1 slice of cheese pizza and 3 sodas
would be
$2.25 + 3($1.00) = $5.25.
9. Choice D is the correct answer. If
5c − 2 = 3c, then 2c = 2, so c = 1. Therefore,
24c = (24)(1) = 24.
TEXAS SUCCESS INITIATIVE ASSESSMENT 2.0
7
10. Choice C is the correct answer. If an equation of a line in the xy-plane is in
slope-intercept form, the slope is the coecient of x, so the slope of the line
y = mx − 4 is m , and the slope of the line y = x − 4 is 1. The slope of the line y = mx − 4
is less than the slope of the line y = x − 4, so it must be true that m < 1.
11. Choice B is the correct answer. Since the
12 tenth graders averaged 77 on the
midterm exam, the sum of their scores was 12 × 77 = 924 ; since the 9 eleventh graders
averaged 91 on the exam, the sum of their scores was 9 × 91 = 819. Therefore, the
sum of the scores of all 12 + 9 = 21 students in the class was 924 + 819 = 1,743, and
their average score on the midterm exam was 1,743 ÷ 21 = 83.
12. Choice A is the correct answer. The expression
(3x − 12)(x + 4) can be rewritten as
3(x − 4)(x + 4) = 3(x
2
− 16), which after applying the distributive property becomes
3x
2
− 48 . Hence, 3(x
2
− 16) and 3x
2
− 48 are equivalent to (3x − 12)(x + 4). A direct
application of the distributive property shows that the expression 3x(x + 4) − 12(x + 4)
is also equivalent to (3x − 12)(x + 4). By contrast, 3(x
2
− 8x + 16), which is equal to
3(x − 4)
2
, is not equivalent to (3x − 12)(x + 4) . For example, for x = 0, the value of
3(x − 4)
2
is 48 and the value of (3x − 12)(x + 4) is −48.
13. Choice D is the correct answer. The oor is 10 feet by 12 feet, so the area of the oor
is (10)(12) = 120 square feet. The cost of carpeting a oor is $2.50 per square foot, so
the cost of carpeting this oor is $2.50 × 120 = $300.00.
14. Choice D is the correct answer. If
n is the least of two consecutive odd integers, then
the greater odd integer is n + 2. It then follows that the sum of the two consecutive
odd integers is n + (n + 2) = 2n + 2.
15. Choice C is the correct answer. The expression inside the parentheses,
x
–5
y
y
3
( )
,
can be rewritten as
x
–5
y
–2
. Since the power of a product is distributed over each
factor, it follows that
x
–5
y
–2
x
5
y
2
–1
=
( )
.
16. Choice C is the correct answer. The only way the two coins Reyna chooses could
not be worth at least
35 cents combined is if both coins are worth 10 cents. For this
to happen, the rst coin Reyna chooses and the second coin she chooses must each
be 10-cent coins. Since 5 of the 9 coins are worth 10 cents each, the probability that
the rst coin chosen is a 10-cent coin is
5
9
. If the rst coin chosen is a 10-cent coin,
there will remain 4 coins worth 10 cents each and 4 coins worth 25 cents each; so
the probability that the second coin will also be a 10-cent coin is
4
8
, or
1
2
. Thus, the
probability that both coins chosen will be
10-cent coins is
× =
5
9
1
2
5
18
. This is the
probability that the two coins chosen will not be worth at least
35 cents combined.
Therefore, the probability that the two coins combined will be worth at least
35 cents
is
=
1
5
18
13
18
–
.
17. Choice A is the correct answer. The
y-intercept of a graph is the y-coordinate
of the point where the graph intersects the y-axis. Setting x = 0 in the equation
1
2
–
y = 6
x (x + 3)
yields
1
2
y = 6
(3) = –9
–
( )
( )
. Therefore, the y-intercept of the graph
of the equation is
−9.
TEXAS SUCCESS INITIATIVE ASSESSMENT 2.0
8
18. Choice B is the correct answer. The area of a triangle can be calculated as half the
product of its base and height,
1
2
A = bh
. Hence, the area of the triangle shown is
(x x + 1)
1
2
2
x
2
+ x
=
. Since the area of the triangle is 21, it follows that
21
=
2
x
2
+ x
, which
is equivalent to
x
2
+ x − 42 = 0 . Solving x
2
+ x − 42 = x + 7 x − 6 = 0 ( )( ) for x gives x = −7,
x = 6. Since the height of a triangle cannot be −7, the value of x must be 6.
19. Choice D is the correct answer. The function
f is not dened as a real number if the
expression under the radical is negative. For
x = 4,
4 4
2
–12== f (4)
–
, which is
not a real number. On the other hand,
4 4 0,==f ( 2) = f (2)
–
–
, and
4 0
2
2==f (0)
–
.
Therefore, of the choices given, the function
f is not dened as a real number for x = 4 .
20. Choice D is the correct answer. At the start of the population, t = 0 , the population
of the species was 100. Under ideal conditions, after nine years, the population will be
100 × 2 = 200; after nine more years, the population will be 200 × 2 = 400 ; and so on.
Hence, after 9p years, where p is a positive integer, the population of the species will
be
100 × 2
p
. Since the number of years elapsed, t, is equal to 9p, it follows that
t
9
p =
.
Therefore,
t years after the population started, the population of the species will be
t
9
100 × 2
.
