Subject Tests
International
International Subject Test—
Math 1 Practice Test
The ACT
®
International Subject Test—Math 1 Practice Test is an official
AIST practice test. The full-length Math 1 Practice Test consists of items
drawn from the International Subject Test Math 1 formative assessment
pool and adheres to the AIST Math 1 Test Specifications.
This PDF file includes Math 1 Practice Test questions and answer keys.
Taking the AIST Official full-length practice test is the best way to
prepare for the two sessions of the AIST Math 1 test.
Math 1
60 Minutes—50 Questions
For each question, first decide which answer is correct. Then, click the circle
next to your answer to select that answer. If you decide to change your answer,
click the circle next to your new answer.
You are permitted to use an approved calculator on this test. You may use your
calculator for any problems you choose. Some of the problems may require a
calculator; some of the problems may best be solved without using a calculator.
A Reference Sheet has been included in this Math 1 Practice Test, beginning
on the next page.
Note: Unless otherwise indicated, all of the following assumptions apply to
these problems.
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 the arithmetic mean.
Your score will be based only on the number of questions you answer correctly
during the time allowed. 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 will NOT be penalized for guessing. It is to your advantage to
answer every question even if you must guess.
If you finish before time ends, you should use the time remaining to reconsider
questions you are uncertain about.
i
© 2023 by ACT, Inc. All rights reserved.
No part of the AIST Math 1 Practice Test can be copied,
reproduced, sold, scanned, emailed, or otherwise transferred.
ii
Interior Angles of Polygons
Circles
Right Triangles
Sequence and Series
Interest
=
2
3
2
2
2
=
2
2
= =
2
a
2
= c
2
C
C
n
a
1
n
=
� (
a
1
n
P(
r
t
=
=
=
d
=
=
z3.14
n
n
=
=
Subject Tests
International
Math 1 Reference Sheet
iii
Interior Angles of Polygons
Circles
Right Triangles
Sequence and Series
Interest
=
2
3
2
2
2
=
2
2
=
=
2
a
2
=
c
2
C
C
n
a
1
n
=
� (
a
1
n
P(
r
t
=
=
=
d
=
=
z3.14
n
n
=
=
iv
Interior Angles of Polygons
Circles
Right Triangles
Sequence and Series
Interest
=
2
3
2
2
2
=
2
2
= =
2
a
2
= c
2
C
C
n
a
1
n
=
� (
a
1
n
P(
r
t
=
=
=
d
=
=
z3.14
n
n
=
=
Miscellaneous
Key to Symbols
1
© 2023 by ACT, Inc. All rights reserved.
No part of the AIST Math 1 Practice Test can be copied,
reproduced, sold, scanned, emailed, or otherwise transferred.
1. What is the complete factorization of the expression x
2
− 16 ?
A. (x + 4
)
2
B. (x − 4
)
2
C. (x − 4
)
(x + 4
)
D. (x + 1
)
(x − 16
)
2. Catherine has a bag of beads. She has 30 red beads, 25 blue beads, and 27 green
beads. If she randomly draws 1 bead from the bag, what is the probability it will be
blue?
A.
57
_
82
B.
30
_
82
C.
27
_
82
D.
25
_
82
3. The graph of a quadratic function has x -intercepts at (−4,0
)
and (1,0
)
. What are the
zeros of this quadratic function?
A. 4 and 1
B. 4 and −1
C. −4 and 1
D. −4 and −1
4. Two lines intersect to form this figure. What is the value of x ?
(4x + 30)°
(2x)°
A. 10
B. 20
C. 25
D. 35
5. What is the value of
(
x − 3
)
(
x + 6x
)
_
x
when x = −1 ?
A. 20
B. 14
C. −10
D. −28
Interior Angles of Polygons
Circles
Right Triangles
Sequence and Series
Interest
=
2
3
2
2
2
=
2
2
= =
2
a
2
= c
2
C
C
n
a
1
n
=
� (
a
1
n
P(
r
t
=
=
=
d
=
=
z3.14
n
n
=
=
2
© 2023 by ACT, Inc. All rights reserved.
No part of the AIST Math 1 Practice Test can be copied,
reproduced, sold, scanned, emailed, or otherwise transferred.
6. A juicer can extract an amount of apple juice equal to 85% of the weight of the
apples. Which equation models the amount of juice, a , that the juicer can extract from
x pounds of apples?
A. a =
0.85
_
x
B. a = 85x
C. a = 0.85x
D. a =
85
_
x
7. In this figure, nABC ≅ ?
A. nADC
B. nACD
C. nCAD
D. nCDA
8. Teresa invested $1,000 in an account that yields 5% annual interest. Use the formula
I = prt to find the amount of interest Teresa earned after 5 years.
A. $26,000
B. $25,000
C. $1,250
D. $250
9. In this figure, nABC has a right angle at B and the measure of ∠BAC is 30° . If
‾
AC is
12 units long, how many units long is
‾
BC ?
A.
√
_
3
B. 4
C. 6
D. 6
√
_
3
3
© 2023 by ACT, Inc. All rights reserved.
No part of the AIST Math 1 Practice Test can be copied,
reproduced, sold, scanned, emailed, or otherwise transferred.
10. Alphonso bends a wire that is 36 cm long to form a rectangle. The length of the
rectangle is 2 times its width. What is the width, in centimeters, of the rectangle?
A. 4.5
B. 6.0
C. 7.2
D. 12.0
11. What is the equation, in standard form, of the line that passes through (−5,6) and has
a slope of 2 ?
A. −2x + y = −4
B. −2x + y = 11
C. −2x + y = 16
D. −5x + 6y = 2
12. What point is the x -intercept of the graph of the function f (x
)
= − x
2
+ 4x − 4 ?
A. (−4,0)
B. (−2,0)
C. (2,0)
D. (4,0)
13. In the figure, if
‾
GE and
‾
DF are parallel, what is m∠BDC ?
A. 110°
B. 40°
C. 30°
D. 10°
4
© 2023 by ACT, Inc. All rights reserved.
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reproduced, sold, scanned, emailed, or otherwise transferred.
14. Which graph represents the inequality
6y + 15
_
3
≤ 4x + 9 ?
A.
B.
15. What is the completely simplified form of 5
√
_
7 −
√
_
63 + 7
√
_
(21
)
(3
)
?
A. 59
√
_
7
B. 35
√
_
7
C. 26
√
_
7
D. 23
√
_
7
16. The local newspaper sells ads at a constant rate per square inch. A 3 -inch-by- 4 -inch
ad costs $25 . Susan has a budget of $150 to run a 9 -inch-by- 12 -inch ad. Can she
purchase a 9 -inch-by- 12 -inch ad and stay within her budget?
A. Yes, because the ad will cost $75 .
B. Yes, because the ad will cost $108 .
C. No, because the ad will cost $200 .
D. No, because the ad will cost $225 .
C.
D.
5
© 2023 by ACT, Inc. All rights reserved.
No part of the AIST Math 1 Practice Test can be copied,
reproduced, sold, scanned, emailed, or otherwise transferred.
17. Kane made this model of an office building.
2x −
2
?
3
x
2
+ x + 1
The expression 3 x
2
+ x + 1 represents the building’s total height in feet. The
expression 2x − 2 represents the distance, in feet, between the top of the building and
the floor of the cafeteria. What is the distance between the ground and the floor of the
cafeteria?
A. 3 x
2
− x + 3
B. 3 x
2
− x − 1
C. 3 x
2
− 3x − 2
D. 3 x
2
+ x − 3
18. What is the value of
√
_
4 x
3
when x = 9 ?
A. 6
B. 18
C. 54
D. 108
19. In circle B , m∠ABC = 30° . What is m∠CDA ?
A. 60°
B. 30°
C. 15°
D. 10°
6
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reproduced, sold, scanned, emailed, or otherwise transferred.
20. Rosa can wash 15 cars in 6 hours. If Joel and Tony help Rosa and work at the same
rate as she does, how many hours will it take them to wash 15 cars?
A. 2
B. 3
C. 5
D. 9
21. Which number line shows the solution set of this compound inequality?
2x − 9 ≤ 3 and 3 (x + 8
)
> 18
A.
B.
C.
D.
22. A tree planted on level ground is supported by cords of equal length and is
perpendicular to the ground as shown in this figure. The cords are tied to the tree
3 feet above the ground and are staked at points C and Z , which are equidistant from
the tree. Which statement explains how you can prove ∠C ≅ ∠Z ?
A. ∠C ≅ ∠Z by the AA theorem.
B. nABC ≅ nXYZ by the AAS theorem, and ∠C ≅ ∠Z because corresponding parts of
congruent triangles are congruent.
C. ∠C ≅ ∠Z by the ASA theorem.
D. nABC ≅ nXYZ by the SSS postulate, and ∠C ≅ ∠Z because corresponding parts
of congruent triangles are congruent.
7
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No part of the AIST Math 1 Practice Test can be copied,
reproduced, sold, scanned, emailed, or otherwise transferred.
23. When a student subtracts 18 from a number, the result is
1
_
4
of the number. What is
the number?
A. 6
B. 18
C. 24
D. 36
24. Evaluate this expression for x =
1
_
2
and y =
1
_
3
:
x
2
y −
(
x
2
− y
2
)
+ x y
2
A. 0
B.
1
_
23
C.
2
_
35
D.
2
_
9
25. Dina found that
x
2
_
4
− 4x + 16 represents the area of a square. Which expression
represents a side of this square?
A.
x
_
2
+ 4
B.
x
_
2
− 4
C.
x
_
2
+ 2
D.
x
_
2
− 2
26. Solve the equation 12 x
2
− 2x = 4 .
A. x =
1
_
2
or −
1
_
2
B. x =
2
_
3
or −
1
_
2
C. x =
2
_
3
or −1
D. x = −
2
_
3
or
1
_
2
8
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No part of the AIST Math 1 Practice Test can be copied,
reproduced, sold, scanned, emailed, or otherwise transferred.
27. Which expression is the completely simplified form of
(
6 x
−8
y
3
)
(
− x
5
y
−1
)
____________
(
2 x
−1
y
2
)
3
?
A. −
3
_
4 y
4
B. −3 x
−37
y
−9
C.
3
_
4 x
10
y
4
D. 3 y
−2
28. Given: nABC with exterior ∠4
Prove: m∠4 = m∠2 + m∠3
Statements Reasons
1. m∠1 + m∠2 + m∠3 = 180°
4. m∠4 + m∠2 + m∠3
2. m∠1 + m∠4 = 180°
3. m∠1 + m∠4 =
m∠1 + m∠2 + m∠3
To complete the proof, what is the correct order of Reasons I−IV ?
I. Substitution Property
II. Definition of Straight Angle
III. Subtraction Property
IV. The sum of the measures of the angles in a triangle is 180° .
A. IV, II, I, III
B. IV, II, III, I
C. II, IV, I, III
D. II, IV, III, I
9
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reproduced, sold, scanned, emailed, or otherwise transferred.
29. The vertices of a parallelogram have coordinates as shown in this figure. What are the
coordinates of B ?
A. (c, b − a)
B. (a − b, c)
C. (b − a, c)
D. (c, a − b)
30. Hexagon ABCDEF is reflected across the x -axis to create A′B′C′D′E′F′ , which is then
rotated 90° counterclockwise about point F′ . Which figure shows the final image?
A.
B.
C.
D.
10
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No part of the AIST Math 1 Practice Test can be copied,
reproduced, sold, scanned, emailed, or otherwise transferred.
31. A total of 140 children participated in a spelling competition. This graph shows the
relation between the number of children, n , who spelled words correctly and the
number of letters, s , in the word spelled.
Which equation most closely approximates the line of best fit?
A. n = −11s + 150
B. n = −20s + 165
C. n = 11s + 150
D. n = 20s + 165
32. Mary solved this system of equations:
⎧
⎪
⎨
⎪
⎩
1
_
2
x +
1
_
4
y = 6
1
_
5
x +
1
_
3
y = 1
What is the solution, (x,y
)
?
A. (8,8)
B. (−15,12)
C. (−5,6)
D. (15,−6)
33. The height of a triangle is 16 inches greater than 8 times the length of its base. If the
area of the triangle is 60 in
2
, what is the length of the base in inches?
A. 2
B. 3
C. 5
D. 7
11
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reproduced, sold, scanned, emailed, or otherwise transferred.
34. An industrial technology student cuts a solid wood cube into 2 congruent pieces along
the diagonals of opposite faces of the cube. The surface area of the cube is 54 in
2
.
What is the surface area, in square inches, of each prism created by the cut?
A. 27
B. 18 + 9
√
_
2
C. 36
D. 27 + 9
√
_
2
35. Which point lies on the locus of points equidistant from (2,3) and (−5,3) ?
A. (6,−1.5)
B. (−1.5,6)
C. (1.5,1)
D. (1,1.5)
36. Clare wants to build a rectangular frame for the base of a shed. She knows ∠ABD is a
right angle. Which statement would not guarantee that the frame is rectangular?
A.
‾
AD and
‾
BC are perpendicular.
B.
‾
AC ∥
‾
BD and
‾
AB ∥
‾
CD .
C.
‾
AC ≅
‾
BD and
‾
AB ≅
‾
CD .
D.
‾
AD and
‾
BC bisect each other.
37. What is the completely simplified form of the expression
12x − 3x − z
3
x
2
y
2
_____________
2 z
3
x y
2
− 18
?
A. −2x
B. −
9x
_
16
C. −
x
_
2
D. −1
12
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No part of the AIST Math 1 Practice Test can be copied,
reproduced, sold, scanned, emailed, or otherwise transferred.
38. Given: Prism 1 ≅ Prism 2
AB = SQ and BC = QR
AD = 9 in
YR = 7 in
The volume of Prism 1 is 189 in
3
. What is the ratio of DH to RT ?
A.
3
_
9
B.
9
_
7
C.
7
_
3
D.
9
_
3
39. Robert sold a TV for k dollars and made a profit of p percent of the amount he paid for
the TV. Which expression shows the amount Robert paid for the TV?
A.
k
(
100 + p
)
_
100
B.
100k
_
100 + p
C.
100p
_
100 + k
D.
100k
_
100 − p
13
© 2023 by ACT, Inc. All rights reserved.
No part of the AIST Math 1 Practice Test can be copied,
reproduced, sold, scanned, emailed, or otherwise transferred.
40. This graph shows the number of books on each of the 8 shelves of a bookcase.
If a librarian moves 4 books from Shelf 4 to Shelf 3 , which measures related to the
numbers of books per shelf will change?
A. Median, mode, and range
B. Mean, mode, and range
C. Median, mean, and range
D. Mode, median, and mean
41. Matt makes 2 promises:
1. If I get a job, I will get a new pair of jeans.
2. If I get a new pair of jeans, I will give away my old pair of jeans.
Assume Matt keeps his promises and that he does not give away his old pair of jeans.
Which of the following is a valid conclusion?
A. He gets a job and a new pair of jeans.
B. He does not get a job and does get a new pair of jeans.
C. He gets a job and does not get a new pair of jeans.
D. He does not get a job and does not get a new pair of jeans.
42. What are the solutions to the equation
⎪
2x + 4
⎪
= 12 −
⎪
x − 5
⎪
?
A. −
11
_
3
and 3
B. −
11
_
3
and
13
_
3
C. −
11
_
3
, 3 , and
13
_
3
D. −
13
_
3
, 13 , and
13
_
3
14
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No part of the AIST Math 1 Practice Test can be copied,
reproduced, sold, scanned, emailed, or otherwise transferred.
43. Rationalize the denominator and simplify the expression
√
_
y
√
_
x + y
_
√
_
xy
.
A.
√
_
x
√
_
x + y
_
x
B.
√
_
x + y
_
√
_
x
C. y
√
_
1 + y
D. 1 +
√
_
y
44. The altitude to the hypotenuse of right triangle nABC divides the hypotenuse into
segments of 9 cm and 16 cm. What is the length, in centimeters, of the longer leg of
nABC ?
A. 12
B. 15
C. 18
D. 20
45. The sine of an angle in a right triangle is
2
_
3
, and the length of the hypotenuse is
37 feet. What is the tangent of this angle?
A.
√
_
5
_
3
B.
2
√
_
5
_
5
C.
√
_
5
_
2
D.
3
_
2
46. A child is standing at point C and flying a kite located at point A , 25 ft above the
ground. As the child lets out more string, the kite rises to point B , directly above
point A . If the angle of elevation changes from 50° to 65° , how much higher, to the
nearest foot, is the kite than it was initially?
A. 5
B. 20
C. 21
D. 45
15
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No part of the AIST Math 1 Practice Test can be copied,
reproduced, sold, scanned, emailed, or otherwise transferred.
47. What are the domain and range for the relation y =
x + 5
_
x − 5
?
A. The domain is the set of all real numbers.
The range is the set of all real numbers.
B. The domain is the set of all real numbers ≠ 5 .
The range is the set of all real numbers ≠ 1 .
C. The domain is the set of all real numbers ≠ −5 .
The range is the set of all real numbers ≠ 1 .
D. The domain is the set of all real numbers.
The range is the set of all real numbers ≠ 5 .
48. Maria’s father is 10 years younger than 3 times Maria’s current age. In 5 years, his
age will be 5 years more than 2 times her age. Which equation can be used to find
Maria’s current age?
A. 3x − 5 = 2x + 5
B. 3x − 10 = 2x + 15
C. 3x − 10 = 2x + 10
D. 3x + 15 = 2x + 5
49. A section of this hemisphere is removed, as indicated by the figure.
(Note: Angle ∠AOB is a central angle of the great circle, and
‾
CO ⊥
‾
AO .)
The radius of the hemisphere is 6 cm, and the volume of the remaining part of the
hemisphere is 120π cm
3
. What is m∠AOB ?
A. 60°
B. 90°
C. 210°
D. 300°
50. What is the value of n in terms of x ?
A. 45 +
1
_
4
x
B. 45 −
1
_
4
x
C. 90 +
1
_
2
x
D. 90 −
1
_
2
x
16
© 2023 by ACT, Inc. All rights reserved.
No part of the AIST Math 1 Practice Test can be copied,
reproduced, sold, scanned, emailed, or otherwise transferred.
International Subject Test—
Math 1 Practice Test
Answer Key
The following table contains the question number and the correct answer (Key)
for each question in this pdf file.
1 C
2 D
3 C
4 C
5 D
6 C
7 D
8 D
9 C
10 B
11 C
12 C
13 D
14 D
15 D
16 D
17 A
18 C
19 C
20 A
21 B
22 D
23 C
24 A
25 B
26 B
27 A
28 A
29 C
30 A
31 A
32 D
33 B
34 D
35 B
36 A
37 C
38 C
39 B
40 A
41 D
42 A
43 A
44 D
45 B
46 B
47 B
48 C
49 A
50 B
