Download The ACT Mathematics Test is a 60-question, 60

The ACT Mathematics Test is a
60-question,
60-minute
test designed to measure the mathematical
skills students have typically acquired in
courses taken by the end of
11th grade
TI – 83’s and TI – 84’s allowed
InSpire 84 Faceplate ONLY
General Tips
• Answer the easy questions first
• Use logic on the more difficult
questions
• Answer every question!
• Review your work
• Be precise
• Erase completely
Test Tip
Watch your Time!
• If you run out of time, use the last three
minutes to bubble
• If you finish early, go back to difficult
problems and check your work
• Circle questions you want to come back to
How is the ACT scored?
•
•
•
•
•
•
5 scores – 4 subject and 1 composite
Score range
= 1 – 36
The college-bound score
= 18
The major-college target
= 25
The big scholarship target
= 30
Check your school’s/scholarship’s
criteria
Pre-Algebra (23%)
14 questions
Questions in this content area are based on basic
operations using whole numbers, decimals,
fractions, and integers; place value; square roots
and approximations; the concept of exponents;
scientific notation; factors; ratio, proportion, and
percent; linear equations in one variable; absolute
value and ordering numbers by value; elementary
counting techniques and simple probability; data
collection, representation, and interpretation; and
understanding simple descriptive statistics.
What is 4% of 1,100?
A.
B.
C.
D.
E.
4
4.4
40
44
440
What is 4% of 1,100?
A.
B.
C.
D.
E.
4
4.4
40
44
440
What is the total cost of 2.5 pounds of
bananas at $0.34 per pound and
2.5 pounds of tomatoes at $0.66 per
pound?
A.
B.
C.
D.
E.
$1.00
$2.40
$2.50
$3.50
$5.00
What is the total cost of 2.5 pounds of
bananas at $0.34 per pound and
2.5 pounds of tomatoes at $0.66 per
pound?
A.
B.
C.
D.
E.
$1.00
$2.40
$2.50
$3.50
$5.00
Elementary Algebra (17%)
10 questions
Questions in this content area are based
on properties of exponents and square
roots, evaluation of algebraic expressions
through substitution, using variables to
express functional relationships,
understanding algebraic operations, and
the solution of quadratic equations by
factoring.
For all x, (x + 4)(x – 5) =?
A.
B.
C.
D.
E.
x2 - 20
x2 – x - 20
2x - 1
2x2 - 1
2x2 – x + 20
For all x, (x + 4)(x – 5) =?
A.
B.
C.
D.
E.
x2 - 20
x2 – x - 20
2x - 1
2x2 - 1
2x2 – x + 20
The relationship between temperature
expressed in degrees Fahrenheit (F)
and degrees Celsius (C) is
F = (9/5)C + 32
If it is 14 degrees Fahrenheit, what is it in
Celsius?
A.
B.
C.
D.
E.
-10o
-12o
-14o
-16o
-18o
The relationship between temperature
expressed in degrees Fahrenheit (F)
and degrees Celsius (C) is
F = (9/5)C + 32
If it is 14 degrees Fahrenheit, what is it in
Celsius?
A.
B.
C.
D.
E.
-10o
-12o
-14o
-16o
-18o
Intermediate Algebra (15%)
9 questions
Questions in this content area are based
on an understanding of the quadratic
formula, rational and radical expressions,
absolute value equations and inequalities,
sequences and patterns, systems of
equations, quadratic inequalities, functions,
modeling, matrices, roots of polynomials,
and complex numbers
If x + y = 1, and x – y = 1, then y = ?
A.
B.
C.
D.
E.
-1
0
1/2
1
2
If x + y = 1, and x – y = 1, then y = ?
A.
B.
C.
D.
E.
-1
0
1/2
1
2
Amy drove the 200 miles to New Orleans
at an average speed 10 miles per hour
faster than her usual average speed. If
she completed the trip in 1 hour less
than usual, what is her usual driving
speed, in miles per hour?
A.
B.
C.
D.
E.
20
30
40
50
60
Amy drove the 200 miles to New Orleans
at an average speed 10 miles per hour
faster than her usual average speed. If
she completed the trip in 1 hour less
than usual, what is her usual driving
speed, in miles per hour?
A.
B.
C.
D.
E.
20
30
40
50
60
Coordinate Geometry (15%)
9 questions
Questions in this content area are based
on graphing and the relations between
equations and graphs, including points,
lines, polynomials, circles, and other curves;
graphing inequalities; slope; parallel and
perpendicular lines; distance; midpoints;
and conics.
What is the slope of the line containing
the points (-2, 7) and (3, -3)?
A.
B.
C.
D.
E.
4
1/4
0
-1/2
-2
What is the slope of the line containing
the points (-2, 7) and (3, -3)?
A.
B.
C.
D.
E.
4
1/4
0
-1/2
-2
A map is laid out in the standard (x, y)
coordinate plane. How long, in units,
is an airplane’s path on the map if
the plane flies along a straight line
from (20, 14) to (5, 10)
A. 1, 201
B. 241
C. 209
D. 7
E. 19
A map is laid out in the standard (x, y)
coordinate plane. How long, in units,
is an airplane’s path on the map if
the plane flies along a straight line
from (20, 14) to (5, 10)
A. 1, 201
B. 241
C. 209
D. 7
E. 19
Plane Geometry (23%)
14 questions
Questions in this content area are based
on the properties and relations of plane
figures, including angles and relations
among perpendicular and parallel lines;
properties of circles, triangles, rectangles,
parallelograms, and trapezoids;
transformations; the concept of proof and
proof techniques; volume; and applications
of geometry to three dimensions.
If the measure of an angle is 37 1/2o,
what it the measure of its supplement?
A.
B.
C.
D.
E.
52 1/2o
62 1/2o
o
37
1/2
127 1/2o
142 1/2o
Can’t be determined
If the measure of an angle is 37 1/2o,
what it the measure of its supplement?
A.
B.
C.
D.
E.
52 1/2o
62 1/2o
o
37
1/2
127 1/2o
142 1/2o
Can’t be determined
A person 2 meters tall casts a shadow
3 meters long. At the same time, a
telephone pole casts a shadow 12
meters long. How many meters tall
is the pole?
A.
B.
C.
D.
E.
4
6
8
11
18
A person 2 meters tall casts a shadow
3 meters long. At the same time, a
telephone pole casts a shadow 12
meters long. How many meters tall
is the pole?
A.
B.
C.
D.
E.
4
6
8
11
18
?
2
3
12
A person 2 meters tall casts a shadow
3 meters long. At the same time, a
telephone pole casts a shadow 12
meters long. How many meters tall
is the pole?
A.
B.
C.
D.
E.
4
6
8
11
18
?
2
3
12
Trigonometry (7%)
4 questions
Questions in this content area are based
on understanding trigonometric relations
in right triangles; values and properties of
trigonometric functions; graphing
trigonometric functions; modeling using
trigonometric functions; use of trigonometric
identities; and solving trigonometric
equations.
What is the sine of angle A in the
triangle?
C
A.
B.
C.
D.
E.
0.30
0.50
0.60
0.75
0.80
10
6
B
8
A
What is the sine of angle A in the
triangle?
C
A.
B.
C.
D.
E.
0.30
0.50
0.60
0.75
0.80
10
6
B
8
A
The hiking path to the top of a mountain
makes, at the steepest place, an angle
of 20o with the horizontal, and it
maintains this constant slope for 500
meters. Which is the closest
approximation to the change in
elevation?
A.
B.
C.
D.
E.
20
170
180
250
470
?
20o
The hiking path to the top of a mountain
makes, at the steepest place, an angle
of 20o with the horizontal, and it
maintains this constant slope for 500
meters. Which is the closest
approximation to the change in
elevation?
A.
B.
C.
D.
E.
20
170
180
250
470
?
20o