PRAXIS CORE -MATH (5732) |ACTUAL QUESTIONS
AND VERIFIED ANSWERS|BRAND NEW 2026-2027
UPDATE|GRADED A+
Question 1
Sarah rolls a fair, six-sided number cube, numbered 1 through 6, five times and rolls a 3, 4,
1, 4, and 4 in that order. What is the probability that she will roll a 4 on her sixth roll?
A. 1/16
B.1/3
C. 1/2
D. 3/5
E. 5/6
CORRECT ANSWER
Option (A) is correct. Because the number cube is fair, each roll is independent of the
others and equally likely. Since there is one number 4 on the six-sided cube, the
probability of rolling a 4 on any roll is 16 .
Question 2
Which of the following expressions is equivalent to the expression 21−6x21−6x for all
values of x ? A. 5−2(8−3x)5−2(8−3x)
B. 6+3(5−2x)6+3(5−2x)
C. 25−(4−6x)25−(4−6x)
D. 3(4−2x)−93(4−2x)−9
E. 7(3−2x)−8x7(3−2x)−8x
CORRECT ANSWER
Option (B) is correct. Using the distributive property, 6+3(5−2x)=6+15−6x=21−6x. None of
the other selections is equivalent to this.
1
,Question 3
Justine observed that the more time she spent studying for a test the higher her test score
was. Which of the following graphs could be the graph of the relationship Justine observed
between the time she studied for a test and her test score?
CORRECT ANSWER
Option (C) is correct. For a graph to indicate that more time studying results in a higher
test score, an increase in time will also show an increase in the test score. Of the five
options, only (C) shows a graph that has this property.
Question 4
A right circular cylinder with base B is shown. If a plane that is neither parallel nor
perpendicular to base B passes through the cylinder, which of the following could be the
shape of the intersection of the plane and the cylinder?
A. An ellipse with circumference less than the circumference of B
B. An ellipse with circumference greater than the circumference of B
C. An ellipse with circumference equal to the circumference of B
D. A circle with circumference less than the circumference of B
E. A circle with circumference greater than the circumference of B
CORRECT ANSWER
Option (B) is correct. A plane that is parallel to the base intersects the cylinder in a circle,
but because the intersecting plane is not parallel, the intersection is an ellipse. One of
the axes of the ellipse is equal to the diameter of the base, but the other axis (in the
direction of the tilt) is larger than the diameter. That means that the circumference of the
ellipse is greater than the circumference of the base.
Question 5
If 5(2x+1)=3(x+4)−55(2x+1)=3(x+4)−5, what is the value of x ?
2
,CORRECT ANSWER
Correct Answer: 2/7
Solve the equation by first using the distributive property: 5(2x+1)=3(x+4)−5 becomes
10x+5=3x+12−5. Combining similar terms yields the equation 10x+5=3x+7. After subtracting
3x from both sides of the equation to get 7x + 5 = 7, subtracting 5 from both sides yields the
equivalent equation 7x =2. The answer is found by dividing each side of this equation by 7.
Question 6
In which of the following are the numbers ordered from least to greatest?
A. −1,−1/2,1/9,1/5
B. −1/2,−1,1/5,1/9
C. 1/5,1/9,−1,−1/2
D. −1/2,1/5,1/9,−1
CORRECT ANSWER
Option (A) is correct. The numbers should be ordered from left to right on the number
line from the most negative number to the largest positive number: −1<−12<19<15.
Question 7
If x/6 is between 3 and 4, which of the following could be the value of x ?
A. 14
B. 17
C. 20
D. 25
E. 26
CORRECT ANSWER
3
, Option (C) is correct. When the numbers 3 and 4 are written as fractions with a
denominator of 6, we need to find a value of x which satisfies the inequality
18/6<x/6<24/6 . This requires a number that lies between 18 and 24. The only number
among the given choices that does this is 20.
Question 8
Wilma completed an 81-mile trip in 90 minutes. The graph above indicates the total
number of miles Wilma traveled at 15-minute intervals. According to the graph, how many
miles did Wilma travel in the last 45 minutes of her trip?
A. 39
B. 42
C. 55
D. 70
E. 81
CORRECT ANSWER
Option (B) is correct. The last 45 minutes of Wilma's trip refers to the interval from t=45
to t=90, where Wilma traveled from a distance of 39 miles to a distance of 81 miles as
shown on the graph. Subtracting 81−39=42 yields the number of miles Wilma traveled.
Question 9
If triangle ABC in the xy-plane shown above is shifted 7 units to the right and 4 units up,
what would be the coordinates of point A after the shift?
A. (1, -2)
B. (4, -2)
C. (4, 2)
D. (5, -2)
E. (5, 2)
CORRECT ANSWER
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AND VERIFIED ANSWERS|BRAND NEW 2026-2027
UPDATE|GRADED A+
Question 1
Sarah rolls a fair, six-sided number cube, numbered 1 through 6, five times and rolls a 3, 4,
1, 4, and 4 in that order. What is the probability that she will roll a 4 on her sixth roll?
A. 1/16
B.1/3
C. 1/2
D. 3/5
E. 5/6
CORRECT ANSWER
Option (A) is correct. Because the number cube is fair, each roll is independent of the
others and equally likely. Since there is one number 4 on the six-sided cube, the
probability of rolling a 4 on any roll is 16 .
Question 2
Which of the following expressions is equivalent to the expression 21−6x21−6x for all
values of x ? A. 5−2(8−3x)5−2(8−3x)
B. 6+3(5−2x)6+3(5−2x)
C. 25−(4−6x)25−(4−6x)
D. 3(4−2x)−93(4−2x)−9
E. 7(3−2x)−8x7(3−2x)−8x
CORRECT ANSWER
Option (B) is correct. Using the distributive property, 6+3(5−2x)=6+15−6x=21−6x. None of
the other selections is equivalent to this.
1
,Question 3
Justine observed that the more time she spent studying for a test the higher her test score
was. Which of the following graphs could be the graph of the relationship Justine observed
between the time she studied for a test and her test score?
CORRECT ANSWER
Option (C) is correct. For a graph to indicate that more time studying results in a higher
test score, an increase in time will also show an increase in the test score. Of the five
options, only (C) shows a graph that has this property.
Question 4
A right circular cylinder with base B is shown. If a plane that is neither parallel nor
perpendicular to base B passes through the cylinder, which of the following could be the
shape of the intersection of the plane and the cylinder?
A. An ellipse with circumference less than the circumference of B
B. An ellipse with circumference greater than the circumference of B
C. An ellipse with circumference equal to the circumference of B
D. A circle with circumference less than the circumference of B
E. A circle with circumference greater than the circumference of B
CORRECT ANSWER
Option (B) is correct. A plane that is parallel to the base intersects the cylinder in a circle,
but because the intersecting plane is not parallel, the intersection is an ellipse. One of
the axes of the ellipse is equal to the diameter of the base, but the other axis (in the
direction of the tilt) is larger than the diameter. That means that the circumference of the
ellipse is greater than the circumference of the base.
Question 5
If 5(2x+1)=3(x+4)−55(2x+1)=3(x+4)−5, what is the value of x ?
2
,CORRECT ANSWER
Correct Answer: 2/7
Solve the equation by first using the distributive property: 5(2x+1)=3(x+4)−5 becomes
10x+5=3x+12−5. Combining similar terms yields the equation 10x+5=3x+7. After subtracting
3x from both sides of the equation to get 7x + 5 = 7, subtracting 5 from both sides yields the
equivalent equation 7x =2. The answer is found by dividing each side of this equation by 7.
Question 6
In which of the following are the numbers ordered from least to greatest?
A. −1,−1/2,1/9,1/5
B. −1/2,−1,1/5,1/9
C. 1/5,1/9,−1,−1/2
D. −1/2,1/5,1/9,−1
CORRECT ANSWER
Option (A) is correct. The numbers should be ordered from left to right on the number
line from the most negative number to the largest positive number: −1<−12<19<15.
Question 7
If x/6 is between 3 and 4, which of the following could be the value of x ?
A. 14
B. 17
C. 20
D. 25
E. 26
CORRECT ANSWER
3
, Option (C) is correct. When the numbers 3 and 4 are written as fractions with a
denominator of 6, we need to find a value of x which satisfies the inequality
18/6<x/6<24/6 . This requires a number that lies between 18 and 24. The only number
among the given choices that does this is 20.
Question 8
Wilma completed an 81-mile trip in 90 minutes. The graph above indicates the total
number of miles Wilma traveled at 15-minute intervals. According to the graph, how many
miles did Wilma travel in the last 45 minutes of her trip?
A. 39
B. 42
C. 55
D. 70
E. 81
CORRECT ANSWER
Option (B) is correct. The last 45 minutes of Wilma's trip refers to the interval from t=45
to t=90, where Wilma traveled from a distance of 39 miles to a distance of 81 miles as
shown on the graph. Subtracting 81−39=42 yields the number of miles Wilma traveled.
Question 9
If triangle ABC in the xy-plane shown above is shifted 7 units to the right and 4 units up,
what would be the coordinates of point A after the shift?
A. (1, -2)
B. (4, -2)
C. (4, 2)
D. (5, -2)
E. (5, 2)
CORRECT ANSWER
4
