ACT Math Practice Test 3

Difficulty Level – 2: Medium

Directions: Solve each problem and then click on the correct answer. You are permitted to use a calculator on this test.

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Question 1
If x is an even integer and y is an odd integer, which of the following must be an odd integer?

A
2x + 2y
B
2x − 2y
C
x + y + 1
D
x + y + 2
E
x − 2y
Question 1 Explanation: 
The correct answer is (D). To solve this problem, choose an even integer for x and an odd integer for y and evaluate each of the answer choices. Set x = 0 and y = 1 → only x + y + 2 will evaluate to an odd integer.
Question 2
35% of 15% of x is equivalent to which of the following?

A
0.0525x
B
0.125x
C
0.25x
D
0.525x
E
5.25x
Question 2 Explanation: 
The correct answer is (A). 35% of 15% of a number is 0.35 * 0.15 of that number:
0.35 * 0.15 = 0.0525x
Question 3
A farmer has a rectangular field that measures 125 feet by 200 feet. He wants to enclose the field with a fence. What is the total length, in feet, he will need for the job?

A
350
B
450
C
550
D
650
E
750
Question 3 Explanation: 
The correct answer is (D). This question is really asking for the perimeter of the field. Add up all of the sides to find the perimeter:
(125 * 2) + (200 * 2) = 650
Question 4
A21math

The equation above is equivalent to which of the following?

A
13 x y3 z3
B
23 x3 y5 z5
C
43 x2 y2 z2
D
34 x4 y2 z2
E
83 x4 y2 z3
Question 4 Explanation: 
The correct answer is (B). Evaluate the expression to find the most simplified form. First evaluate the coefficients:
4 * 2 * 13 * 14 = 23
x * x2 = x3
y * y2 * y2 = y5
z * z3 * z = z5
Combine each of these terms to get answer choice (B).
Question 5
What is the slope intercept form of (13x − 5x) + 12 − 2y = 6?

A
y = 3x − 9
B
y = 4x + 3
C
y = −4x − 3
D
y = 6x + 2
E
y = −6x + 5
Question 5 Explanation: 
The correct answer is (B). Recall that slope-intercept form is y = mx + b where m is the slope and b is the y-intercept. Solve for y:
8x − 2y = −6
2y = 8x + 6
Divide everything by 2:
y = 4x + 3
Question 6
A and B are reciprocals (when multiplied together their product is 1). If A < −1, then B must be which of the following?

A
B > 1
B
B < 0
C
0 < B < 1
D
−1 < B < 0
E
B < −1
Question 6 Explanation: 
The correct answer is (D). If the product of two numbers is positive, the two numbers must have the same sign. That is, if ab > 0, then either a > 0 and b > 0, or a < 0 and b < 0.

We are told that A < −1 (which implies that A < 0).
So we know that B < 0.
Q101a
If we take reciprocals on both sides of the last inequality, we must flip the inequality sign. Hence: B > −1

So we know that B < 0, and B > −1. We can represent this as a compound inequality: −1 < B < 0
Question 7
Magazine subscriptions cost $9.99 a month per magazine after an initial contract fee of $24.99. Which expression represents the cost of m magazines?

A
$9.99 + $24.99m
B
$9.99m + $24.99
C
$24.99 - $9.99m
D
$24.99 + m + $9.99
E
$33.98m
Question 7 Explanation: 
The correct answer is (B). Consider the given information: the initial contract fee is a one time price that will be added to the number, m, of magazines times the cost per magazine so, 9.99m + 24.99.
Question 8
If ƒ(x) = −3x3 + 4x2 − x + 2 and g(x) = 2x2 − x, what is ƒ(g(−1))?

A
−46
B
−22
C
0
D
22
E
46
Question 8 Explanation: 
The correct answer is (A). This question asks about function composition.
Begin by evaluating g(−1) = 2 + 1 = 3
Now evaluate ƒ(3) = −3 * 27 + 36 − 3 + 2 = −46
Question 9
The coordinates (−3, 5) and (3, 5) designate the diameter of a circle, what is its circumference?

A
π
B
2π
C
4π
D
6π
E
12π
Question 9 Explanation: 
The correct answer is (D). The circumference of a circle is the distance around defined by π * diameter. The diameter in this case can be found through the difference between the x values:
3 − (−3) = 6, so π * 6 is the circumference.
Question 10
Richard wants to try every possible combination of meals available at his favorite restaurant. They offer 4 appetizers, 5 entrees, and 3 desserts. How many total meals will Richard have tried by the time he finishes?

A
12
B
15
C
20
D
60
E
120
Question 10 Explanation: 
The correct answer is (D). To find the total number of combinations, we multiply the total number of options for each meal available:
4 * 5 * 3 = 60
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