Math Praxis Practice Test (5003) Questions and Answers
3. Which of the following expressions is equivalent to the expression 21−6x for all
values of x ?
5−2(8−3x)
6+3(5−2x)
25−(4−6x)
3(4−2x)−9
7(3−2x)−8x
6+3(5−2x)
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.
5. 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?
An ellipse with circumference less than the circumference of B
An ellipse with circumference greater than the circumference of B
An ellipse with circumference equal to the circumference of B
A circle with circumference less than the circumference of B
A circle with circumference greater than the circumference of B
Correct Answer: B
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.
6. If 5(2x+1)=3(x+4)−5, what is the value of x ?
,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.
8. If x6 is between 3 and 4, which of the following could be the value of x ?
14
17
20
25
26
25
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
186<x6<246. This requires a number that lies between 18 and 24. The only number
among the given choices that does this is 20.
10. 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?
(1, -2)
(4, -2)
(4, 2)
(5, -2)
(5, 2)
A Start (-2)(-2)
(5, 2)
11. 1.4, 1.8, 2.2, 2.0, 1.0, 1.9, 1.2, 2.1, 1.7
What is the median of the numbers in the list above?
, 1.2
1.4
1.7
1.8
1.9
1.8
Option (D) is correct. The median of an ordered set of data is the number positioned
where there are an equal number less than the number and greater than the number
(that is, the number in the "middle"). Rearranging the nine numbers from least to
greatest, the list becomes 1.0, 1.2, 1.4, 1.7, 1.8, 1.9, 2.0, 2.1, 2.2, where 1.8 is the fifth
(middle) number in the list.
12. If 1/7x−2=1, then x=
-7
3
9
15
21
Correct Answer: E
Option (E) is correct. Solve this equation by first adding 2 to both sides, resulting in an
equivalent equation 1/7x=3. Multiplying both sides of this equation by 7 yields
7(1/7x)=7(3) or x=21.
13. 1/4, 9/8, 2/3, 1/2, k, π
Question:
The five numbers shown above are listed in order from least to greatest. Which of
the following could be the value of k
Indicate all such values.
A. 2
B. .516
C. 238
3. Which of the following expressions is equivalent to the expression 21−6x for all
values of x ?
5−2(8−3x)
6+3(5−2x)
25−(4−6x)
3(4−2x)−9
7(3−2x)−8x
6+3(5−2x)
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.
5. 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?
An ellipse with circumference less than the circumference of B
An ellipse with circumference greater than the circumference of B
An ellipse with circumference equal to the circumference of B
A circle with circumference less than the circumference of B
A circle with circumference greater than the circumference of B
Correct Answer: B
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.
6. If 5(2x+1)=3(x+4)−5, what is the value of x ?
,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.
8. If x6 is between 3 and 4, which of the following could be the value of x ?
14
17
20
25
26
25
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
186<x6<246. This requires a number that lies between 18 and 24. The only number
among the given choices that does this is 20.
10. 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?
(1, -2)
(4, -2)
(4, 2)
(5, -2)
(5, 2)
A Start (-2)(-2)
(5, 2)
11. 1.4, 1.8, 2.2, 2.0, 1.0, 1.9, 1.2, 2.1, 1.7
What is the median of the numbers in the list above?
, 1.2
1.4
1.7
1.8
1.9
1.8
Option (D) is correct. The median of an ordered set of data is the number positioned
where there are an equal number less than the number and greater than the number
(that is, the number in the "middle"). Rearranging the nine numbers from least to
greatest, the list becomes 1.0, 1.2, 1.4, 1.7, 1.8, 1.9, 2.0, 2.1, 2.2, where 1.8 is the fifth
(middle) number in the list.
12. If 1/7x−2=1, then x=
-7
3
9
15
21
Correct Answer: E
Option (E) is correct. Solve this equation by first adding 2 to both sides, resulting in an
equivalent equation 1/7x=3. Multiplying both sides of this equation by 7 yields
7(1/7x)=7(3) or x=21.
13. 1/4, 9/8, 2/3, 1/2, k, π
Question:
The five numbers shown above are listed in order from least to greatest. Which of
the following could be the value of k
Indicate all such values.
A. 2
B. .516
C. 238
