1.
Praxis Core Math: Numbers and Quantity
If \( x \) and \( y \) are two distinct prime numbers, which of the following represents the total number of factors for the product \( xy \)?
1 out of 56
2.
Praxis Core Math: Numbers and Quantity
What is the \( n^{th} \) term of the sequence defined by \( a_n = 3^n - 2^n \)?
2 out of 56
3.
Praxis Core Math: Numbers and Quantity
What is the value of \( x \) in the equation \( 2^{3x - 1} = 8^x \)?
3 out of 56
4.
Praxis Core Math: Numbers and Quantity
What is the sum of the infinite geometric series \( 8, 4, 2, 1, \ldots \)?
4 out of 56
5.
Praxis Core Math: Numbers and Quantity
Given that \( a \) is a positive integer, which of the following represents the sum of the first \( n \) terms of the sequence \( 2a, 4a, 6a, \ldots, 2na \)?
5 out of 56
6.
Praxis Core Math: Numbers and Quantity
What is the least common multiple (LCM) of \( 12 \) and \( 18 \)?
6 out of 56
7.
Praxis Core Math: Numbers and Quantity
If \( \frac{5}{3x} = \frac{15}{9x - 6} \), what is the value of \( x \)?
7 out of 56
8.
Praxis Core Math: Numbers and Quantity
If \( \frac{x}{4} = \frac{y}{3} \) and \( y = 12 \), what is the value of \( x \)?
8 out of 56
9.
Praxis Core Math: Numbers and Quantity
If the ratio of \( x \) to \( y \) is \( 3:4 \) and \( y = 20 \), what is the value of \( x \)?
9 out of 56
10.
Praxis Core Math: Numbers and Quantity
What is the decimal equivalent of the fraction \( \frac{7}{8} \)?
10 out of 56
11.
Praxis Core Math: Numbers and Quantity
The expression \( \frac{8^x}{4^{x+1}} \) simplifies to which of the following?
11 out of 56
12.
Praxis Core Math: Numbers and Quantity
What is the value of \( x \) in the equation \( 4^{2x+1} = 64 \)?
12 out of 56
13.
Praxis Core Math: Numbers and Quantity
If the ratio \( \frac{x}{y} \) is equivalent to \( \frac{2}{3} \) and \( x + y = 30 \), what is the value of \( x \)?
13 out of 56
14.
Praxis Core Math: Numbers and Quantity
Find the sum of the arithmetic series \( 3 + 7 + 11 + \ldots + 47 \).
14 out of 56
15.
Praxis Core Math: Numbers and Quantity
If \( \log_5(x) = 3 \), what is the value of \( x \)?
15 out of 56
16.
Praxis Core Math: Numbers and Quantity
What is the result of simplifying the expression \( \sqrt{50} - \sqrt{18} \)?
16 out of 56
17.
Praxis Core Math: Numbers and Quantity
If the prime factors of \( n \) are 2, 3, and 5, which of the following must be a factor of \( n \)?
17 out of 56
18.
Praxis Core Math: Numbers and Quantity
If \( a, b \), and \( c \) are consecutive even integers and \( a < b < c \), what is \( c \) in terms of \( a \)?
18 out of 56
19.
Praxis Core Math: Numbers and Quantity
What is the solution set for the inequality \( 3x - 4 > 2x + 5 \)?
19 out of 56
20.
Praxis Core Math: Numbers and Quantity
What is the cube root of \( -27 \)?
20 out of 56
21.
Praxis Core Math: Data Interpretation and Representation Statistics and Probability
In a class of 30 students, 18 play football, 15 play basketball, and 10 play both. How many students do not play either of the two sports?
21 out of 56
22.
Praxis Core Math: Data Interpretation and Representation Statistics and Probability
In a survey, 70\% of respondents prefer tea over coffee. If 3 respondents are randomly selected, what is the probability that exactly 2 of them prefer tea over coffee?
22 out of 56
23.
Praxis Core Math: Data Interpretation and Representation Statistics and Probability
A set of data is normally distributed with a mean of 50 and a standard deviation of 5. What percentage of the data falls between 45 and 55?
23 out of 56
24.
Praxis Core Math: Data Interpretation and Representation Statistics and Probability
A histogram shows the frequency distribution of the weights of 60 cats. If the mean weight is 10 pounds and the median weight is 9 pounds, which of the following is true about the distribution?
24 out of 56
25.
Praxis Core Math: Data Interpretation and Representation Statistics and Probability
The median of the data set 3, 7, 9, 14, x, 17, 22, 25, 28 is 15. What is the value of x?
25 out of 56
26.
Praxis Core Math: Data Interpretation and Representation Statistics and Probability
A fair six-sided die is rolled twice. What is the probability that the sum of the two rolls is 9?
26 out of 56
27.
Praxis Core Math: Data Interpretation and Representation Statistics and Probability
A set of data is normally distributed with a mean of 50 and a standard deviation of 5. What percentage of the data falls between 45 and 55?
27 out of 56
28.
Praxis Core Math: Data Interpretation and Representation Statistics and Probability
A box contains 5 red balls, 3 green balls, and 2 blue balls. What is the probability of randomly drawing two balls of different colors?
28 out of 56
29.
Praxis Core Math: Data Interpretation and Representation Statistics and Probability
What is the range of the data set 8, 3, 7, 14, 10, 6, 2, 9?
29 out of 56
30.
Praxis Core Math: Data Interpretation and Representation Statistics and Probability
If a data set has a standard deviation of zero, what can be concluded about the data?
30 out of 56
31.
Praxis Core Math: Data Interpretation and Representation Statistics and Probability
A dataset has a mean of 50 and a standard deviation of 5. If all data points increase by 10, what will be the new standard deviation?
31 out of 56
32.
Praxis Core Math: Data Interpretation and Representation Statistics and Probability
In a classroom, the probability that a student owns a laptop is 0.6 and the probability that a student owns a smartphone is 0.8. Assuming independence, what is the probability that a student owns both a laptop and a smartphone?
32 out of 56
33.
Praxis Core Math: Data Interpretation and Representation Statistics and Probability
The median of a set of seven distinct numbers is 24. If the range of the numbers is 20, what is the maximum possible value in the set?
33 out of 56
34.
Praxis Core Math: Data Interpretation and Representation Statistics and Probability
What is the range of the data set: 3, 7, 7, 10, 12, 15, 17?
34 out of 56
35.
Praxis Core Math: Data Interpretation and Representation Statistics and Probability
A set of five numbers has an average of 10. If the largest number is removed, the average of the remaining numbers is 8. What is the value of the number that was removed?
35 out of 56
36.
Praxis Core Math: Data Interpretation and Representation Statistics and Probability
The median of five numbers is 14. If one of the numbers, which is greater than 14, is removed, what will be the effect on the median?
36 out of 56
37.
Praxis Core Math: Data Interpretation and Representation Statistics and Probability
A box contains 4 red balls, 5 blue balls, and 6 green balls. If a ball is picked at random, what is the probability that it is not blue?
37 out of 56
38.
Praxis Core Math: Data Interpretation and Representation Statistics and Probability
In a box of colored balls, there are 5 red, 3 blue, and 2 green balls. If two balls are drawn randomly without replacement, what is the probability that both balls are red?
38 out of 56
39.
Praxis Core Math: Algebra and Geometry
The sum of the interior angles of a polygon is 1080 degrees. How many sides does the polygon have?
39 out of 56
40.
Praxis Core Math: Algebra and Geometry
What is the slope of the line perpendicular to the line with the equation \( 3x - 4y = 12 \)?
40 out of 56
41.
Praxis Core Math: Algebra and Geometry
If \( f(x) = x^2 - 5x + 6 \), what are the x-intercepts of the graph of \( f \)?
41 out of 56
42.
Praxis Core Math: Algebra and Geometry
What is the equation of the circle with a center at \( (3,-4) \) and a radius of 5?
42 out of 56
43.
Praxis Core Math: Algebra and Geometry
If the sides of a square are lengthened by 40%, by what percent does the area increase?
43 out of 56
44.
Praxis Core Math: Algebra and Geometry
If \( \sin \theta = \frac{1}{2} \) and \( 0 \leq \theta \leq \frac{\pi}{2} \), what is \( \cos \theta \)?
44 out of 56
45.
Praxis Core Math: Algebra and Geometry
The line \( y = mx + b \) passes through the points (1, 2) and (3, 8). What is the value of \( m \)?
45 out of 56
46.
Praxis Core Math: Algebra and Geometry
What is the volume of a cylinder with radius 3 and height 4?
46 out of 56
47.
Praxis Core Math: Algebra and Geometry
What is the area of a right triangle with legs of length 6 and 8?
47 out of 56
48.
Praxis Core Math: Algebra and Geometry
Find the vertex of the parabola given by \( y = 2x^2 - 4x + 3 \).
48 out of 56
49.
Praxis Core Math: Algebra and Geometry
If \( \tan \theta = \sqrt{3} \) and \( 0 \leq \theta \leq \frac{\pi}{2} \), what is \( \sin \theta \)?
49 out of 56
50.
Praxis Core Math: Algebra and Geometry
Solve for \( x \): \( 2x^2 - 5x - 3 = 0 \)
50 out of 56
51.
Praxis Core Math: Algebra and Geometry
In the equation \( ax^2 + bx + c = 0 \), if \( a + b + c = 0 \), what is one of the roots?
51 out of 56
52.
Praxis Core Math: Algebra and Geometry
What are the solutions to the inequality \( 3x - 7 < 2(x + 4) \)?
52 out of 56
53.
Praxis Core Math: Algebra and Geometry
Given the quadratic equation \( x^2 - 4x + 4 = 0 \), what are the roots?
53 out of 56
54.
Praxis Core Math: Algebra and Geometry
Which equation represents a line parallel to the line given by \( y = -2x + 3 \)?
54 out of 56
55.
Praxis Core Math: Algebra and Geometry
If \( f(x) = 3x^2 - 2x + 1 \), what is \( f(-2) \)?
55 out of 56
56.
Praxis Core Math: Algebra and Geometry
Solve for \( x \) in the equation \( \log_2(x-1) + \log_2(x+1) = 3 \).
56 out of 56
