Your FREE Praxis Core Mathematics (5733) Practice Test 2026 – 140+ Q&A

Praxis Core Math Practice Questions

1. If $x$ and $y$ are two distinct prime numbers, which of the following represents the total number of factors for the product $xy$?
   • 2
   • 3
   • 4
   • 5

   Correct answer: 4

   Correct answer: 4. Explanation: The product of two distinct prime numbers has exactly 4 factors: 1, $x$, $y$, and $xy$.

2. Given that $a$ is a positive integer, which of the following represents the sum of the first $n$ terms of the sequence $2a, 4a, 6a, \ldots, 2na$?
   • $na^2$
   • $n^2a$
   • $na(n + 1)$
   • $a(n)(n + 1)$

   Correct answer: $a(n)(n + 1)$

   Correct answer: $a(n)(n + 1)$. Explanation: The sequence is an arithmetic sequence with a common difference of $2a$.

3. What is the least common multiple (LCM) of $12$ and $18$?
   • 36
   • 54
   • 72
   • 108

   Correct answer: 36

   Correct answer: 36. Explanation: The prime factorization of $12$ is $2^2 \times 3$ and of $18$ is $2 \times 3^2$.

4. What is the sum of the infinite geometric series $8, 4, 2, 1, \ldots$?
   • 16
   • 15
   • 14
   • 13

   Correct answer: 16

   Correct answer: 16. Explanation: The sum of an infinite geometric series is given by $\frac{a}{1 - r}$, where $a$ is the first term and $r$ is the common ratio.

5. What is the $n^{th}$ term of the sequence defined by $a_n = 3^n - 2^n$?
   • $3n - 2n$
   • $3^{n-1} - 2^{n-1}$
   • $n(3 - 2)$
   • $3^n - 2^n$

   Correct answer: $3^n - 2^n$

   Correct answer: $3^n - 2^n$. Explanation: The $n^{th}$ term is defined by the formula $a_n = 3^n - 2^n$.

6. If $\frac{x}{4} = \frac{y}{3}$ and $y = 12$, what is the value of $x$?
   • 16
   • 15
   • 14
   • 13

   Correct answer: 16

   Correct answer: 16. Explanation: Substitute $y = 12$ into the equation to get $\frac{x}{4} = \frac{12}{3}$.

7. If the ratio of $x$ to $y$ is $3:4$ and $y = 20$, what is the value of $x$?
   • 15
   • 25
   • 30
   • 35

   Correct answer: 15

   Correct answer: 15. Explanation: The ratio $3:4$ means $\frac{x}{y} = \frac{3}{4}$.

8. What is the decimal equivalent of the fraction $\frac{7}{8}$?
   • 0.875
   • 0.885
   • 0.895
   • 0.905

   Correct answer: 0.875

   Correct answer: 0.875. Explanation: The fraction $\frac{7}{8}$ can be converted to a decimal by division, yielding $0.875$.

9. If the ratio $\frac{x}{y}$ is equivalent to $\frac{2}{3}$ and $x + y = 30$, what is the value of $x$?
   • 10
   • 12
   • 15
   • 18

   Correct answer: 12

   Correct answer: 12. Explanation: Using the ratio and the sum, create a system of equations and solve for $x$.

10. If $\log_5(x) = 3$, what is the value of $x$?
    • 15
    • 125
    • 243
    • 625

    Correct answer: 125

    Correct answer: 125. Explanation: Rewrite the logarithmic equation as an exponential equation.

11. If the prime factors of $n$ are 2, 3, and 5, which of the following must be a factor of $n$?
    • 60
    • 30
    • 15
    • 10

    Correct answer: 30

    Correct answer: 30. Explanation: Identify the least common multiple of the prime factors.

12. If $a, b$, and $c$ are consecutive even integers and $a < b < c$, what is $c$ in terms of $a$?
    • $a + 2$
    • $a + 4$
    • $2a$
    • $2a + 2$

    Correct answer: $a + 4$

    Correct answer: $a + 4$. Explanation: Determine the relationship between consecutive even integers.

13. What is $\sqrt[3]{-27}$?
    • -9
    • -3
    • 3
    • 9

    Correct answer: -3

    Correct answer: -3. Explanation: Calculate $\sqrt[3]{-27}$, a root of a negative number.

14. 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?
    • $68\%$
    • $95\%$
    • $99.7\%$
    • $50\%$

    Correct answer: $68\%$

    Correct answer: $68\%$. Explanation: In a normal distribution, approximately $68\%$ of the data lies within one standard deviation of the mean.

15. If the probability of an event A is 0.2 and the probability of an event B is 0.4, what is the probability of either A or B occurring, assuming the two events are independent?
    • 0.24
    • 0.48
    • 0.52
    • 0.8

    Correct answer: 0.52

    Correct answer: 0.52. Explanation: The probability of either A or B is $P(A) + P(B) - P(A \cap B)$. Since A and B are independent, $P(A \cap B) = P(A) \times P(B) = 0.2 \times 0.4 = 0.08$. Therefore, the probability is $0.2 + 0.4 - 0.08 = 0.52$.

16. 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?
    • 7
    • 10
    • 12
    • 15

    Correct answer: 7

    Correct answer: 7. Explanation: Use the inclusion-exclusion principle. The total number of students playing either sport is $18 + 15 - 10 = 23$. Therefore, $30 - 23 = 7$ students do not play either sport.

17. 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?
    • 0.343
    • 0.441
    • 0.189
    • 0.027

    Correct answer: 0.441

    Correct answer: 0.441. Explanation: Use the binomial probability formula for $n = 3$, $k = 2$, and $p = 0.7$.

18. 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?
    • It is symmetric.
    • It is positively skewed.
    • It is negatively skewed.
    • It cannot be determined.

    Correct answer: It is positively skewed.

    Correct answer: It is positively skewed. Explanation: When the mean is greater than the median, the distribution is positively skewed.

19. What is the range of the data set 8, 3, 7, 14, 10, 6, 2, 9?
    • 6
    • 8
    • 10
    • 12

    Correct answer: 12

    Correct answer: 12. Explanation: The range is the difference between the maximum and minimum values in the data set.

20. If a data set has a standard deviation of zero, what can be concluded about the data?
    • All data points are the same.
    • The data points are evenly distributed.
    • There is no variance in the data.
    • The data cannot be analyzed.

    Correct answer: All data points are the same.

    Correct answer: All data points are the same. Explanation: A standard deviation of zero means there is no spread in the data; all values are identical.

21. 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?
    • 0.48
    • 0.68
    • 0.14
    • 0.2

    Correct answer: 0.48

    Correct answer: 0.48. Explanation: The probability of two independent events both happening is the product of their individual probabilities.

22. 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?
    • 15
    • 18
    • 20
    • 22

    Correct answer: 18

    Correct answer: 18. Explanation: Use the average formula and solve for the unknown number.

23. 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?
    • $\frac{5}{10} \times \frac{4}{9}$
    • $\frac{3}{10} \times \frac{2}{9}$
    • $\frac{5}{10} \times \frac{3}{9}$
    • $\frac{3}{10} \times \frac{5}{9}$

    Correct answer: $\frac{5}{10} \times \frac{4}{9}$

    Correct answer: $\frac{5}{10} \times \frac{4}{9}$. Explanation: Calculate the probability of drawing one red ball and then another red ball without replacement.

24. The median of a set of seven distinct numbers is 24, and the smallest number in the set is 14. If the range of the numbers is 20, what is the maximum value in the set?
    • 44
    • 34
    • 28
    • 54

    Correct answer: 34

    Correct answer: 34. Explanation: The range equals the maximum minus the minimum. With the smallest number 14 and a range of 20, the maximum is $14 + 20 = 34$. This is consistent with a median of 24 (the fourth value).

25. 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?
    • 5
    • 10
    • 15
    • 20

    Correct answer: 5

    Correct answer: 5. Explanation: Adding a constant to all data points in a dataset does not change its standard deviation.

26. In a class of 30 students, 18 are wearing glasses. What is the probability that a randomly selected student from the class is wearing glasses?
    • $\frac{3}{5}$
    • $\frac{2}{3}$
    • $\frac{3}{4}$
    • $\frac{4}{5}$

    Correct answer: $\frac{3}{5}$

    Correct answer: $\frac{3}{5}$. Explanation: The probability is the number of students wearing glasses divided by the total number of students.

27. 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?
    • $\frac{4}{15}$
    • $\frac{2}{3}$
    • $\frac{5}{15}$
    • $\frac{10}{15}$

    Correct answer: $\frac{2}{3}$

    Correct answer: $\frac{2}{3}$. Explanation: The probability is calculated by dividing the number of non-blue balls by the total number of balls.

28. What is the range of the data set: 3, 7, 7, 10, 12, 15, 17?
    • 10
    • 12
    • 14
    • 15

    Correct answer: 14

    Correct answer: 14. Explanation: The range is the difference between the highest and lowest values in the data set.

29. If the mode of a set of data is 23 and the mean is 25, which of the following can be inferred about the distribution?
    • It is symmetric.
    • It is positively skewed.
    • It is negatively skewed.
    • No inference can be made.

    Correct answer: It is positively skewed.

    Correct answer: It is positively skewed. Explanation: A higher mean compared to the mode suggests a longer tail on the right side (positive skew).

30. Given the quadratic equation $x^2 - 4x + 4 = 0$, what are the roots?
    • 0 and 4
    • 2 and -2
    • 2 and 2
    • -2 and -2

    Correct answer: 2 and 2

    Correct answer: 2 and 2. Explanation: The equation is a perfect square trinomial, factorizing to $(x-2)^2 = 0$.

31. If the sides of a square are lengthened by 40%, by what percent does the area increase?
    • $40\%$
    • $60\%$
    • $80\%$
    • $96\%$

    Correct answer: $96\%$

    Correct answer: $96\%$. Explanation: Area increases by the square of the side length increase, $(1.4)^2 = 1.96$, or $96\%$.

32. The sum of the interior angles of a polygon is 1080 degrees. How many sides does the polygon have?
    • 6
    • 7
    • 8
    • 9

    Correct answer: 8

    Correct answer: 8. Explanation: Use the formula $(n-2)\times 180^\circ$ for the sum of interior angles, where $n$ is the number of sides.

33. If $f(x) = x^2 - 5x + 6$, what are the x-intercepts of the graph of $f$?
    • 2 and 3
    • -2 and -3
    • 2 and -3
    • -2 and 3

    Correct answer: 2 and 3

    Correct answer: 2 and 3. Explanation: Set $f(x) = 0$ and solve for $x$. The equation factorizes to $(x-2)(x-3) = 0$.

34. What is the equation of the circle with a center at $(3,-4)$ and a radius of 5?
    • $(x-3)^2 + (y+4)^2 = 25$
    • $(x+3)^2 + (y-4)^2 = 25$
    • $(x-3)^2 + (y-4)^2 = 5$
    • $(x+3)^2 + (y+4)^2 = 5$

    Correct answer: $(x-3)^2 + (y+4)^2 = 25$

    Correct answer: $(x-3)^2 + (y+4)^2 = 25$. Explanation: Use the standard form of a circle equation $(x-h)^2 + (y-k)^2 = r^2$.

35. If $\sin \theta = \frac{1}{2}$ and $0 \leq \theta \leq \frac{\pi}{2}$, what is $\cos \theta$?
    • $\frac{\sqrt{3}}{2}$
    • $\frac{1}{2}$
    • $\frac{\sqrt{2}}{2}$
    • $\frac{1}{\sqrt{2}}$

    Correct answer: $\frac{\sqrt{3}}{2}$

    Correct answer: $\frac{\sqrt{3}}{2}$. Explanation: In the first quadrant, use the Pythagorean identity $\sin^2 \theta + \cos^2 \theta = 1$.

36. What is the area of a right triangle with legs of length 6 and 8?
    • 24
    • 28
    • 48
    • 52

    Correct answer: 24

    Correct answer: 24. Explanation: Use the formula for the area of a triangle $\frac{1}{2} \times \text{base} \times \text{height}$.

37. Find the vertex of the parabola given by $y = 2x^2 - 4x + 3$.
    • (1, 1)
    • (-1, -1)
    • (1, -1)
    • (-1, 1)

    Correct answer: (1, 1)

    Correct answer: (1, 1). Explanation: Use the formula $-\frac{b}{2a}$ to find the x-coordinate of the vertex and substitute to find y.

38. Which equation represents a line parallel to the line given by $y = -2x + 3$?
    • $y = -2x - 3$
    • $y = 2x + 3$
    • $y = -\frac{1}{2}x + 3$
    • $y = -2x + 5$

    Correct answer: $y = -2x + 5$

    Correct answer: $y = -2x + 5$. Explanation: Parallel lines have the same slope.

39. What is the volume of a cylinder with radius 3 and height 4?
    • $36\pi$
    • $48\pi$
    • $72\pi$
    • $144\pi$

    Correct answer: $36\pi$

    Correct answer: $36\pi$. Explanation: Volume of a cylinder = $\pi r^2 h = \pi \times 3^2 \times 4 = 36\pi$.

40. The line $y = mx + b$ passes through the points (1, 2) and (3, 8). What is the value of $m$?
    • 2
    • 3
    • 4
    • 6

    Correct answer: 3

    Correct answer: 3. Explanation: Calculate the slope using the two given points.

41. What is the length of the hypotenuse of a right triangle with legs of lengths 7 and 24?
    • 25
    • 28
    • 31
    • 35

    Correct answer: 25

    Correct answer: 25. Explanation: Use the Pythagorean theorem, $a^2 + b^2 = c^2$.

42. If the area of a trapezoid is 60 square units and the lengths of the bases are 5 units and 15 units, what is the height?
    • 6 units
    • 8 units
    • 10 units
    • 12 units

    Correct answer: 6 units

    Correct answer: 6 units. Explanation: Use the formula for the area of a trapezoid.

43. In the equation $ax^2 + bx + c = 0$, if $a + b + c = 0$, what is one of the roots?
    • -1
    • 0
    • 1
    • 2

    Correct answer: 1

    Correct answer: 1. Explanation: Use the property that if $a + b + c = 0$, then $x = 1$ is a root.

44. If $\tan \theta = \sqrt{3}$ and $0 \leq \theta \leq \frac{\pi}{2}$, what is $\sin \theta$?
    • $\frac{\sqrt{3}}{2}$
    • $\frac{1}{2}$
    • $\frac{\sqrt{2}}{2}$
    • $1$

    Correct answer: $\frac{\sqrt{3}}{2}$

    Correct answer: $\frac{\sqrt{3}}{2}$. Explanation: Use trigonometric identities to find $\sin \theta$ from $\tan \theta$.

45. Which of the following numbers is prime?
    • 91
    • 57
    • 51
    • 53

    Correct answer: 53

    The number 53 is prime. A prime number is a whole number greater than 1 whose only factors are 1 and itself. The value 53 has no divisors other than 1 and 53, while 51 equals 3 times 17, 57 equals 3 times 19, and 91 equals 7 times 13, so each of those is composite.

46. Why is the number 1 not considered a prime number?
    • Because 1 is an even number
    • Because 1 cannot be divided evenly by any number
    • Because a prime number must have exactly two distinct factors, and 1 has only one
    • Because 1 is a negative number

    Correct answer: Because a prime number must have exactly two distinct factors, and 1 has only one

    The number 1 is not prime because a prime number must have exactly two distinct positive factors, and 1 has only one factor, which is itself. Primes such as 2, 3, and 5 each have exactly two factors, namely 1 and the number itself. Since 1 fails this two-factor requirement, it is classified as neither prime nor composite.

47. What is the product of the fractions 2/3 and 9/10 in simplest form?
    • 18/30
    • 11/13
    • 3/5
    • 6/13

    Correct answer: 3/5

    The product is 3/5. To multiply fractions, multiply the numerators together (2 times 9 equals 18) and the denominators together (3 times 10 equals 30), giving 18/30, then divide both terms by their greatest common factor of 6 to simplify to 3/5. Adding numerators and denominators instead of multiplying would not give a correct product.

48. A recipe calls for 3/4 cup of flour, but a baker wants to make 2/3 of the recipe. How much flour is needed?
    • 1/2 cup
    • 1 5/12 cup
    • 5/7 cup
    • 17/12 cup

    Correct answer: 1/2 cup

    The baker needs 1/2 cup of flour. To find a fraction of an amount, multiply the two fractions: 2/3 times 3/4 equals 6/12, which simplifies to 1/2. Multiplying numerators (2 times 3 equals 6) and denominators (3 times 4 equals 12) and then reducing gives the result.

49. What is the result of dividing 3/4 by 2/5?
    • 5/6
    • 3/10
    • 15/8
    • 6/20

    Correct answer: 15/8

    The quotient is 15/8. To divide fractions, multiply the first fraction by the reciprocal of the second: 3/4 times 5/2 equals 15/8. Flipping the divisor and multiplying is the key step; simply multiplying 3/4 by 2/5 would instead give 3/10, which is the product, not the quotient.

50. A ribbon that is 5/6 of a yard long is cut into pieces that are each 5/24 of a yard. How many pieces can be cut?
    • 4 pieces
    • 3 pieces
    • 6 pieces
    • 2 pieces

    Correct answer: 4 pieces

    There are 4 pieces. To find how many equal parts fit into a length, divide the whole by the size of one part: 5/6 divided by 5/24 equals 5/6 times 24/5, which equals 120/30, or 4. Dividing fractions means multiplying by the reciprocal of the divisor.

51. What is the sum of 3/4 and 5/6?
    • 19/12
    • 8/10
    • 4/5
    • 15/24

    Correct answer: 19/12

    The sum is 19/12. To add fractions, rewrite them with a common denominator; the least common denominator of 4 and 6 is 12, so 3/4 becomes 9/12 and 5/6 becomes 10/12, and 9/12 plus 10/12 equals 19/12. Adding numerators and denominators separately to get 8/10 is incorrect.

52. What is the result of subtracting 1/4 from 11/12?
    • 2/3
    • 5/6
    • 10/12
    • 10/8

    Correct answer: 2/3

    The difference is 2/3. To subtract fractions, use a common denominator; the least common denominator of 12 and 4 is 12, so 1/4 becomes 3/12, and 11/12 minus 3/12 equals 8/12, which simplifies to 2/3. The unreduced form 8/12 is equivalent but not in simplest terms.

53. What is the greatest common factor of 48 and 60?
    • 240
    • 24
    • 12
    • 6

    Correct answer: 12

    The greatest common factor of 48 and 60 is 12. The prime factorization of 48 is 2 times 2 times 2 times 2 times 3, and 60 is 2 times 2 times 3 times 5; the shared prime factors are two 2s and one 3, whose product is 12. The value 240 is the least common multiple, not the greatest common factor.

54. A teacher has 54 pencils and 72 erasers and wants to make identical supply kits using all items with none left over. What is the greatest number of kits that can be made?
    • 9 kits
    • 6 kits
    • 18 kits
    • 12 kits

    Correct answer: 18 kits

    The greatest number of kits is 18, found by taking the greatest common factor of 54 and 72. The factor 18 divides 54 exactly 3 times and 72 exactly 4 times, so each kit holds 3 pencils and 4 erasers. A larger number such as 12 does not divide 54 evenly, so it cannot be used.

55. What is the least common multiple of 8 and 12?
    • 24
    • 96
    • 48
    • 4

    Correct answer: 24

    The least common multiple of 8 and 12 is 24. Listing multiples of 8 gives 8, 16, 24 and multiples of 12 gives 12, 24, so 24 is the smallest value appearing in both lists. The value 4 is the greatest common factor, not the least common multiple, and 96 is a common multiple but not the least.

56. Two runners start a circular track together. One completes a lap every 6 minutes and the other every 9 minutes. After how many minutes will they next cross the start line at the same time?
    • 54 minutes
    • 15 minutes
    • 3 minutes
    • 18 minutes

    Correct answer: 18 minutes

    They meet again after 18 minutes, which is the least common multiple of 6 and 9. Multiples of 6 are 6, 12, 18 and multiples of 9 are 9, 18, so 18 is the smallest time both complete whole laps. The value 54 is a common multiple but not the least, so it is not the first meeting time.

57. A car travels 240 miles using 6 gallons of gasoline at a constant rate of fuel use. How many gallons are needed to travel 400 miles at the same rate?
    • 12 gallons
    • 15 gallons
    • 10 gallons
    • 8 gallons

    Correct answer: 10 gallons

    The car needs 10 gallons. First find the constant rate: 240 miles divided by 6 gallons equals 40 miles per gallon. Then divide the new distance by that rate: 400 divided by 40 equals 10 gallons. Using a constant rate means the miles-per-gallon stays the same across the trip.

58. A pump moves water at a constant rate and fills 144 gallons in 3 hours. How many gallons will it fill in 5 hours at the same rate?
    • 180 gallons
    • 216 gallons
    • 240 gallons
    • 288 gallons

    Correct answer: 240 gallons

    The pump fills 240 gallons. A constant rate means the amount per hour is steady, so first divide to find it: 144 gallons divided by 3 hours equals 48 gallons per hour. Then multiply by the new time: 48 times 5 equals 240. The constant-rate assumption lets the same per-hour value apply to both time spans.

59. At a store, 6 identical notebooks cost 13.50 dollars. What is the unit rate in dollars per notebook?
    • 2.00 dollars
    • 3.00 dollars
    • 2.25 dollars
    • 2.50 dollars

    Correct answer: 2.25 dollars

    The unit rate is 2.25 dollars per notebook. A unit rate gives the cost for a single item, found by dividing the total cost by the number of items: 13.50 divided by 6 equals 2.25. Dividing the number of notebooks by the price would instead give notebooks per dollar.

60. A printer produces 350 pages in 14 minutes. What is its printing rate in pages per minute?
    • 35 pages per minute
    • 20 pages per minute
    • 25 pages per minute
    • 28 pages per minute

    Correct answer: 25 pages per minute

    The rate is 25 pages per minute. A unit rate expresses output per single unit of time, so divide the number of pages by the number of minutes: 350 divided by 14 equals 25. Multiplying instead of dividing would not produce a per-minute rate.

61. What is the difference between a ratio and a proportion?
    • A proportion compares two quantities, while a ratio sets them equal
    • There is no difference; the terms mean the same thing
    • A ratio compares two quantities, while a proportion is an equation stating that two ratios are equal
    • A ratio is always larger than a proportion

    Correct answer: A ratio compares two quantities, while a proportion is an equation stating that two ratios are equal

    The correct distinction is that a ratio compares two quantities, while a proportion is an equation stating that two ratios are equal. For example, 2 to 3 is a ratio, and the statement 2/3 equals 4/6 is a proportion because it sets two equal ratios in balance. A proportion is built from ratios, so the two ideas are related but not identical.

62. In a photograph, the ratio of width to height is 4 to 3. If an enlarged copy is 24 inches wide, how tall is it if the proportion is kept?
    • 14 inches
    • 18 inches
    • 21 inches
    • 16 inches

    Correct answer: 18 inches

    The enlarged copy is 18 inches tall. Setting up a proportion preserves the ratio: 4/3 equals 24/h, so cross-multiply to get 4h equals 72, and h equals 18. A proportion keeps the width-to-height relationship the same as the original 4-to-3 ratio.

63. A paint mixture uses blue and yellow in a ratio of 3 to 7. If a batch contains 40 ounces total, how many ounces are yellow?
    • 12 ounces
    • 30 ounces
    • 21 ounces
    • 28 ounces

    Correct answer: 28 ounces

    The batch contains 28 ounces of yellow. The ratio 3 to 7 means the total is divided into 3 plus 7, or 10, equal parts; each part is 40 divided by 10, which equals 4 ounces. Yellow takes 7 parts, so 7 times 4 equals 28 ounces. Blue takes the remaining 3 parts, or 12 ounces.

64. Convert the fraction 5/16 to a decimal.
    • 0.3125
    • 0.516
    • 0.31
    • 0.625

    Correct answer: 0.3125

    The decimal is 0.3125. To convert a fraction to a decimal, divide the numerator by the denominator: 5 divided by 16 equals 0.3125. The value 0.625 is the decimal for 10/16, which is twice as large as 5/16.

65. Convert the decimal 0.85 to a fraction in simplest form.
    • 85/10
    • 8/5
    • 85/1000
    • 17/20

    Correct answer: 17/20

    The decimal 0.85 equals 17/20 in simplest form. The digits 85 are in the hundredths place, so 0.85 equals 85/100, and dividing both numerator and denominator by their greatest common factor of 5 gives 17/20. Writing 85/10 would represent 8.5, which is ten times too large.

66. What is 18 percent of 250?
    • 50
    • 32
    • 45
    • 68

    Correct answer: 45

    18 percent of 250 is 45. To find a percent of a number, convert the percent to a decimal by dividing by 100, so 18 percent becomes 0.18, then multiply: 0.18 times 250 equals 45. Forgetting to move the decimal and multiplying by 18 would give a value far too large.

67. A test has 400 questions, and a student answers 140 of them. What percent of the questions did the student answer?
    • 46 percent
    • 35 percent
    • 28 percent
    • 40 percent

    Correct answer: 35 percent

    The student answered 35 percent. To find what percent one number is of another, divide the part by the whole and multiply by 100: 140 divided by 400 equals 0.35, which is 35 percent. The value 28 percent would result from dividing by 500 rather than the correct total of 400.

68. A bakery's daily bread sales increased from 60 loaves to 75 loaves. What was the percent increase?
    • 80 percent
    • 15 percent
    • 25 percent
    • 20 percent

    Correct answer: 25 percent

    The percent increase is 25 percent. To find percent increase, find the change (75 minus 60 equals 15), divide by the original amount (15 divided by 60 equals 0.25), then multiply by 100. The value 15 is the increase in loaves, not the percent, and 20 percent would come from dividing by the new value of 75 instead of the original 60.

69. A company's monthly expenses dropped from 250 dollars to 200 dollars. What was the percent change?
    • A decrease of 15 percent
    • A decrease of 25 percent
    • A decrease of 20 percent
    • A decrease of 50 percent

    Correct answer: A decrease of 20 percent

    The percent change is a decrease of 20 percent. To calculate percent change, find the difference (200 minus 250 equals negative 50), divide by the original amount (negative 50 divided by 250 equals negative 0.20), then multiply by 100 to get negative 20 percent. The negative sign indicates a decrease, and dividing by the original 250 rather than the new 200 is essential.

70. Convert the fraction 9/25 to a percent.
    • 44 percent
    • 9 percent
    • 36 percent
    • 25 percent

    Correct answer: 36 percent

    The fraction 9/25 equals 36 percent. To convert a fraction to a percent, scale it so the denominator is 100 by multiplying both terms by 4, giving 36/100, which is 36 percent. Equivalently, divide 9 by 25 to get 0.36 and multiply by 100. The value 9 percent ignores the conversion entirely.

71. The distance from Earth to the Sun is about 93,000,000 miles. Which expression shows this distance in scientific notation?
    • 93 times 10 to the 6th power
    • 9.3 times 10 to the 7th power
    • 9.3 times 10 to the 6th power
    • 0.93 times 10 to the 8th power

    Correct answer: 9.3 times 10 to the 7th power

    In scientific notation the distance is 9.3 times 10 to the 7th power. Scientific notation writes a number as one nonzero digit before the decimal point times a power of ten; moving the decimal in 93,000,000 seven places to the left gives 9.3, so the exponent is 7. The form 93 times 10 to the 6th power has two digits before the decimal and is not standard scientific notation.

72. What does the number 5.6 times 10 to the negative 4 power equal in standard decimal form?
    • 0.056
    • 0.00056
    • 56000
    • 0.0056

    Correct answer: 0.00056

    The value equals 0.00056. A negative exponent in scientific notation means the number is less than 1, and the exponent of negative 4 means the decimal point in 5.6 moves four places to the left, producing 0.00056. A positive exponent would instead make the number large, such as 56000.

73. A hiking trail is 12.5 kilometers long. How many meters is this?
    • 125,000 meters
    • 125 meters
    • 12,500 meters
    • 1,250 meters

    Correct answer: 12,500 meters

    The trail is 12,500 meters. To convert kilometers to meters, use the fact that 1 kilometer equals 1,000 meters, then multiply: 12.5 times 1,000 equals 12,500. Because a meter is a smaller unit than a kilometer, the number of meters is larger than the number of kilometers.

74. A bottle contains 2.5 liters of juice. How many milliliters is this?
    • 250 milliliters
    • 25,000 milliliters
    • 2,500 milliliters
    • 25 milliliters

    Correct answer: 2,500 milliliters

    The bottle contains 2,500 milliliters. To convert liters to milliliters, use the relationship that 1 liter equals 1,000 milliliters, then multiply: 2.5 times 1,000 equals 2,500. Converting to a smaller metric unit increases the numerical value.

75. How many quarts are in 3 gallons?
    • 6 quarts
    • 9 quarts
    • 12 quarts
    • 24 quarts

    Correct answer: 12 quarts

    There are 12 quarts in 3 gallons. To convert units, use the U.S. customary fact that 1 gallon equals 4 quarts, then multiply: 3 times 4 equals 12. The value 24 would result from incorrectly using 8 quarts per gallon instead of 4.

76. Round the number 0.2249 to the nearest hundredth.
    • 0.22
    • 0.23
    • 0.225
    • 0.2

    Correct answer: 0.22

    Rounded to the nearest hundredth, 0.2249 is 0.22. The hundredths digit is 2, and the digit immediately to its right is 4, which is less than 5, so the hundredths digit stays the same and the rest is dropped. The later digits 49 do not cause rounding up because only the digit in the thousandths place determines it.

77. Which list orders the values 5/8, 0.7, 2/3, and 0.66 from least to greatest?
    • 5/8, 2/3, 0.66, 0.7
    • 2/3, 5/8, 0.66, 0.7
    • 5/8, 0.66, 2/3, 0.7
    • 0.66, 5/8, 2/3, 0.7

    Correct answer: 5/8, 0.66, 2/3, 0.7

    The correct order is 5/8, 0.66, 2/3, 0.7. Converting each to a decimal allows comparison on a common basis: 5/8 equals 0.625, 0.66 stays 0.66, 2/3 is about 0.667, and 0.7 stays 0.7. Arranging from smallest to largest gives 0.625, 0.66, 0.667, then 0.7. Placing 0.66 before 5/8 is wrong because 0.625 is less than 0.66.

78. A teacher records the number of books each of 5 students read over the summer: 6, 8, 8, 10, 13. What is the mean number of books read?
    • 10
    • 8
    • 11
    • 9

    Correct answer: 9

    The mean is 9 books. To find the mean of a data set, add all the values (6 + 8 + 8 + 10 + 13 = 45) and divide by how many values there are (45 divided by 5 = 9). The mean is the arithmetic average and is not the same as the most frequent value, which here is 8.

79. Find the median of the data set: 12, 15, 19, 22, 27, 31.
    • 19
    • 21
    • 20.5
    • 22

    Correct answer: 20.5

    The median is 20.5. Because this ordered data set has an even number of values (six), the median is the average of the two middle values, which are 19 and 22: (19 + 22) divided by 2 equals 20.5. With an even count there is no single middle number, so you must average the two center values.

80. A coach records the ages of players on a team: 14, 16, 16, 15, 16, 14, 17. What is the mode of this data set?
    • 14
    • 16
    • 17
    • 15

    Correct answer: 16

    The mode is 16. The mode is the value that appears most frequently in a data set; here 16 occurs three times, more than any other value. Finding the mode simply requires counting how often each value appears and choosing the one with the highest count.

81. For the data set 4, 7, 7, 9, 11, 7, 15, 4, what are the mean, median, and mode, respectively?
    • Mean 8, median 8, mode 4
    • Mean 8, median 7, mode 7
    • Mean 9, median 7, mode 4
    • Mean 7, median 7, mode 7

    Correct answer: Mean 8, median 7, mode 7

    The mean is 8, the median is 7, and the mode is 7. The mean is the sum (4+7+7+9+11+7+15+4 = 64) divided by 8 values, giving 8. Ordered, the data are 4, 4, 7, 7, 7, 9, 11, 15, so the median is the average of the two middle values (7 and 7), which is 7, and the mode is 7 because it appears three times.

82. A class of 9 students earned these quiz scores: 22, 30, 35, 41, 41, 44, 50, 58, 95. Which measure of central tendency is most affected by the score of 95?
    • The mean
    • The mode
    • The median
    • The range is unaffected

    Correct answer: The mean

    The mean is most affected by the unusually high score of 95. The mean uses every value in its calculation, so a single extreme value pulls it up noticeably, while the median (which depends only on position, here 41) and the mode are resistant to extreme values. This is why the median is often preferred for skewed data.

83. A data set of home prices in a neighborhood has a mean of 410,000 dollars but a median of 290,000 dollars. What does this difference most likely indicate?
    • A few very high-priced homes are pulling the mean upward
    • The data set has no variation
    • Half the homes cost less than 410,000 dollars
    • Most homes cost exactly 410,000 dollars

    Correct answer: A few very high-priced homes are pulling the mean upward

    A few very high-priced homes are pulling the mean upward. When the mean is much larger than the median, the data are right-skewed, meaning a small number of large values inflate the average while the median stays near the typical value. For skewed data like incomes or home prices, the median better represents a typical value than the mean does.

84. What is the range of the data set: 23, 45, 12, 67, 34, 8, 51?
    • 55
    • 43
    • 67
    • 59

    Correct answer: 59

    The range is 59. The range of a data set is found by subtracting the smallest value from the largest value: 67 minus 8 equals 59. The range measures the total spread of the data but ignores how the values in between are distributed.

85. Which statement correctly describes what standard deviation measures?
    • The most common value in a data set
    • The total number of data points
    • The middle value of an ordered data set
    • How spread out the values are around the mean

    Correct answer: How spread out the values are around the mean

    Standard deviation measures how spread out the values in a data set are around the mean. A small standard deviation means the values cluster tightly near the mean, while a large standard deviation means they are widely scattered. It is a measure of variability, not of central location like the mean or median.

86. In a data set of test scores, most values fall between 70 and 85, but one student scored 12. The value 12 is best described as which of the following?
    • An outlier
    • The mode
    • The median
    • The first quartile

    Correct answer: An outlier

    The value 12 is an outlier. An outlier is a data value that lies far outside the pattern of the rest of the data, here much lower than the cluster of scores between 70 and 85. Outliers can strongly distort the mean and the range, which is why they are identified and examined separately.

87. For a data set, the first quartile is 20 and the third quartile is 40. Using the 1.5 times IQR rule, which of these values would be flagged as an outlier?
    • 65
    • 75
    • 45
    • 55

    Correct answer: 75

    The value 75 would be flagged as an outlier. The interquartile range is Q3 minus Q1, or 40 minus 20 = 20, so 1.5 times the IQR is 30. The upper fence is Q3 + 30 = 40 + 30 = 70, and any value above 70 is an outlier; 75 exceeds 70 while 65, 55, and 45 do not.

88. Find the first quartile (Q1) of the data set: 3, 5, 8, 9, 12, 14, 17, 20.
    • 6.5
    • 5
    • 9
    • 8

    Correct answer: 6.5

    The first quartile is 6.5. With 8 values, the lower half is 3, 5, 8, 9, and Q1 is the median of that half: the average of 5 and 8, which is 6.5. The first quartile is the median of the lower portion of the data, not simply the second value.

89. A box plot displays a five-number summary. Which set of values does a box plot show?
    • Only the mean and the standard deviation
    • Minimum, first quartile, median, third quartile, and maximum
    • Mean, mode, median, range, and standard deviation
    • The frequency of every individual value

    Correct answer: Minimum, first quartile, median, third quartile, and maximum

    A box plot shows the minimum, first quartile, median, third quartile, and maximum, which together form the five-number summary. The box spans from Q1 to Q3 (the interquartile range), a line inside marks the median, and the whiskers extend to the minimum and maximum. Reading a box plot lets you quickly judge center and spread without seeing every data point.

90. On a box plot, the box stretches from 30 to 50 and the line inside the box is at 38. What does the line at 38 represent?
    • The mean of the data
    • The range of the data
    • The maximum value
    • The median of the data

    Correct answer: The median of the data

    The line at 38 represents the median of the data. In a box plot, the line inside the box always marks the median (the second quartile), while the box edges mark Q1 and Q3. The fact that the median is closer to the lower edge (30) than the upper edge (50) suggests the data are slightly right-skewed.

91. A histogram shows the number of students scoring in each 10-point interval on a test. The tallest bar is over the interval 70 to 79. What does that tallest bar indicate?
    • Exactly 70 students took the test
    • The highest score on the test was in the 70s
    • The average score was exactly 79
    • More students scored in the 70 to 79 interval than in any other

    Correct answer: More students scored in the 70 to 79 interval than in any other

    The tallest bar indicates that more students scored in the 70 to 79 interval than in any other interval. In a histogram, the height of each bar shows the frequency (count) of data values that fall within that interval, so the tallest bar is the most common range. Histogram bars represent ranges of values, not individual scores.

92. A stem-and-leaf plot has a stem of 4 with leaves 2, 5, and 8. What data values do these represent?
    • 4.2, 4.5, and 4.8
    • 42, 45, and 48
    • 4, 2, 5, and 8
    • 402, 405, and 408

    Correct answer: 42, 45, and 48

    The values are 42, 45, and 48. In a stem-and-leaf plot, the stem represents the leading digit or digits and each leaf is the final digit, so a stem of 4 with leaves 2, 5, and 8 produces 42, 45, and 48. This format preserves every original data value while showing the overall shape of the distribution.

93. A pie chart shows how a family's monthly budget is divided. If the slice for housing takes up one-fourth of the circle and the total budget is 4,800 dollars, how much is spent on housing?
    • 480 dollars
    • 960 dollars
    • 1,200 dollars
    • 2,400 dollars

    Correct answer: 1,200 dollars

    The family spends 1,200 dollars on housing. A pie chart shows parts of a whole, so a slice taking up one-fourth of the circle represents one-fourth of the total: 4,800 divided by 4 equals 1,200. Each slice's size is proportional to its share of the whole, which is what makes pie charts useful for showing percentages of a total.

94. A scatter plot of hours studied versus test score shows points that rise from lower left to upper right. What does this pattern indicate?
    • That all students scored the same
    • No relationship between the variables
    • A positive correlation between the variables
    • A negative correlation between the variables

    Correct answer: A positive correlation between the variables

    This pattern indicates a positive correlation between the variables. When the points on a scatter plot trend upward from lower left to upper right, larger values of one variable tend to occur with larger values of the other, here meaning more study hours are associated with higher scores. A downward trend would indicate a negative correlation.

95. On a scatter plot, a line of best fit is drawn through the data. What is the purpose of this line?
    • To show the range of the data
    • To connect every data point exactly in order
    • To mark the single highest data point
    • To model the overall trend and allow predictions from the data

    Correct answer: To model the overall trend and allow predictions from the data

    The line of best fit models the overall trend in the data and allows predictions. It is a straight line drawn so that the data points are balanced as evenly as possible above and below it, summarizing the general direction of the relationship. It does not pass through every point; instead it captures the trend so values can be estimated for inputs between or beyond the observed data.

96. A standard six-sided die is rolled once. What is the probability of rolling an even number?
    • 1/3
    • 2/3
    • 1/6
    • 1/2

    Correct answer: 1/2

    The probability is 1/2. To find a simple probability, divide the number of favorable outcomes by the total number of equally likely outcomes. A die has three even numbers (2, 4, and 6) out of six faces, so the probability is 3/6, which simplifies to 1/2.

97. A bag holds 7 red marbles and 13 blue marbles. If one marble is drawn at random, what is the probability that it is red?
    • 13/20
    • 1/7
    • 7/20
    • 7/13

    Correct answer: 7/20

    The probability of drawing a red marble is 7/20. To calculate a simple probability, divide the number of favorable outcomes by the total number of possible outcomes: there are 7 red marbles out of 20 marbles total, giving 7/20. This fraction is already in lowest terms.

98. A survey of 200 randomly selected voters found that 130 supported a new park. Based on this sample, what is the best inference about the population of all voters?
    • All voters support the park
    • No conclusion about the population can be drawn
    • Exactly 130 voters in the population support the park
    • About 65 percent of the population likely supports the park

    Correct answer: About 65 percent of the population likely supports the park

    The best inference is that about 65 percent of the population likely supports the park. When a sample is randomly selected, its proportion (130 out of 200 = 65 percent) can be used to estimate the corresponding proportion in the whole population. Inferences from a sample give estimates about the population, not exact counts, and random sampling is what makes the estimate reliable.

99. What is the area of a rectangle that is 9 centimeters long and 4 centimeters wide?
    • 26 square centimeters
    • 13 square centimeters
    • 36 square centimeters
    • 18 square centimeters

    Correct answer: 36 square centimeters

    The area is 36 square centimeters. To find the area of a rectangle, multiply length by width: 9 times 4 equals 36. Adding the dimensions (9 plus 4 equals 13) gives perimeter-style thinking, not area, and 26 comes from confusing area with the perimeter formula 2(length plus width).

100. A rectangular garden is 12 meters long and 7 meters wide. How many meters of fencing are needed to enclose the entire garden once?
     • 42 meters
     • 38 meters
     • 19 meters
     • 84 meters

     Correct answer: 38 meters

     The fencing needed is 38 meters. Perimeter is the total distance around a shape, found by adding all sides: 12 plus 7 plus 12 plus 7 equals 38, which equals 2 times (12 plus 7). The value 84 is the area (length times width), not the perimeter, and 19 is only one length plus one width.

101. What is the area of a triangle with a base of 10 inches and a height of 6 inches?
     • 60 square inches
     • 32 square inches
     • 16 square inches
     • 30 square inches

     Correct answer: 30 square inches

     The area is 30 square inches. The area of a triangle equals one-half times base times height: one-half times 10 times 6 equals 30. The value 60 results from forgetting the one-half factor, and 32 would be a perimeter-style miscalculation.

102. A circle has a radius of 5 feet. Using 3.14 for pi, what is the area of the circle to the nearest square foot?
     • 16 square feet
     • 79 square feet
     • 157 square feet
     • 31 square feet

     Correct answer: 79 square feet

     The area is about 79 square feet. The area of a circle equals pi times the radius squared: 3.14 times 5 times 5 equals 78.5, which rounds to 79. The value 31 mistakenly uses the circumference formula (2 times pi times radius), and 16 ignores pi entirely.

103. A circular tabletop has a diameter of 8 feet. Using 3.14 for pi, what is the circumference of the tabletop to the nearest foot?
     • 13 feet
     • 201 feet
     • 50 feet
     • 25 feet

     Correct answer: 25 feet

     The circumference is about 25 feet. Circumference equals pi times the diameter: 3.14 times 8 equals 25.12, which rounds to 25. The value 50 doubles the diameter before multiplying (treating 8 as a radius), and 201 mistakenly computes area using the diameter as a radius squared.

104. A rectangular box is 5 cm long, 3 cm wide, and 4 cm tall. What is its volume?
     • 47 cubic centimeters
     • 94 cubic centimeters
     • 60 cubic centimeters
     • 12 cubic centimeters

     Correct answer: 60 cubic centimeters

     The volume is 60 cubic centimeters. The volume of a rectangular box equals length times width times height: 5 times 3 times 4 equals 60. The value 94 is the surface area, and 12 multiplies only two of the three dimensions.

105. What is the length of the hypotenuse of a right triangle whose legs measure 9 cm and 12 cm?
     • 21 cm
     • 15 cm
     • 11 cm
     • 225 cm

     Correct answer: 15 cm

     The hypotenuse is 15 cm. By the Pythagorean theorem, the square of the hypotenuse equals the sum of the squares of the legs: 9 squared plus 12 squared equals 81 plus 144 equals 225, and $\sqrt{225} = 15$. The value 21 incorrectly adds the legs, and 225 forgets to take the square root.

106. A ladder leans against a wall. The base of the ladder is 5 feet from the wall, and the ladder reaches 12 feet up the wall. How long is the ladder?
     • 7 feet
     • 169 feet
     • 13 feet
     • 17 feet

     Correct answer: 13 feet

     The ladder is 13 feet long. The wall, ground, and ladder form a right triangle where the ladder is the hypotenuse, so 5 squared plus 12 squared equals 25 plus 144 equals 169, and $\sqrt{169} = 13$. The value 17 simply adds 5 and 12, and 169 omits the square root step.

107. What is the slope of the line that passes through the points (2, 3) and (6, 11)?
     • 8
     • 4
     • 1/2
     • 2

     Correct answer: 2

     The slope is 2. Slope equals the change in y divided by the change in x: (11 minus 3) divided by (6 minus 2) equals 8 divided by 4 equals 2. Reversing the ratio to (6 minus 2) over (11 minus 3) gives 1/2, and using only the rise of 8 ignores the run.

108. Which formula gives the slope of a line passing through the points (x1, y1) and (x2, y2)?
     • (x2 minus x1) divided by (y2 minus y1)
     • (x2 plus y2) divided by (x1 plus y1)
     • (y2 plus y1) divided by (x2 plus x1)
     • (y2 minus y1) divided by (x2 minus x1)

     Correct answer: (y2 minus y1) divided by (x2 minus x1)

     The slope formula is (y2 minus y1) divided by (x2 minus x1), often described as rise over run. The vertical change goes in the numerator and the horizontal change in the denominator. Swapping them inverts the slope, and adding coordinates instead of subtracting does not measure a rate of change.

109. Solve for x: 4x minus 7 equals 21.
     • X equals 7
     • X equals 14
     • X equals 5
     • X equals 3.5

     Correct answer: X equals 7

     The solution is x equals 7. Add 7 to both sides to get 4x equals 28, then divide both sides by 4 to get x equals 7. Dividing 21 by 4 before adding 7 gives the incorrect 3.5, and forgetting to divide by 4 leaves 14.

110. Solve for x: 3(x plus 2) equals 5x minus 4.
     • X equals 10
     • X equals 1
     • X equals 5
     • X equals -1

     Correct answer: X equals 5

     The solution is x equals 5. Distribute to get 3x plus 6 equals 5x minus 4, subtract 3x from both sides to get 6 equals 2x minus 4, add 4 to get 10 equals 2x, and divide by 2 to get x equals 5. Failing to distribute the 3 to both terms inside the parentheses is the most common error here.

111. Solve the inequality 2x plus 5 less than 17.
     • X less than 6
     • X less than 11
     • X greater than 6
     • X greater than 11

     Correct answer: X less than 6

     The solution is x less than 6. Subtract 5 from both sides to get 2x less than 12, then divide both sides by the positive number 2 to get x less than 6. Because you divide by a positive number, the inequality sign does not flip; it would only flip if you divided by a negative.

112. A student solves the inequality -3x greater than 12 and writes x greater than -4. What is the error?
     • No error was made; x greater than -4 is correct
     • The inequality sign should have been reversed when dividing by a negative, giving x less than -4
     • The sign of -4 should be positive, giving x greater than 4
     • Division by 3 should have been multiplication, giving x greater than 36

     Correct answer: The inequality sign should have been reversed when dividing by a negative, giving x less than -4

     The inequality sign should have been reversed, giving x less than -4. When you divide or multiply both sides of an inequality by a negative number, the direction of the inequality must flip. Dividing -3x greater than 12 by -3 yields x less than -4, not x greater than -4.

113. Solve the system of equations: x plus y equals 10 and x minus y equals 4.
     • X equals 6, y equals 4
     • X equals 3, y equals 7
     • X equals 7, y equals 3
     • X equals 5, y equals 5

     Correct answer: X equals 7, y equals 3

     The solution is x equals 7 and y equals 3. Adding the two equations eliminates y: (x plus y) plus (x minus y) equals 10 plus 4, so 2x equals 14 and x equals 7. Substituting back, 7 plus y equals 10 gives y equals 3, and checking confirms 7 minus 3 equals 4.

114. At a school store, 2 notebooks and 1 pen cost $7, while 1 notebook and 1 pen cost $5. What is the cost of one notebook?
     • $2
     • $5
     • $3
     • $4

     Correct answer: $2

     One notebook costs $2. Let n be a notebook and p a pen: 2n plus p equals 7 and n plus p equals 5. Subtracting the second equation from the first eliminates p and gives n equals 2. Substituting back, a pen costs 5 minus 2 equals $3.

115. Evaluate the expression 3a squared minus 2b when a equals 4 and b equals 5.
     • 134
     • 38
     • 26
     • 18

     Correct answer: 38

     The value is 38. Following order of operations, square first: a squared equals 16, so 3 times 16 equals 48, then subtract 2 times 5 equals 10 to get 48 minus 10 equals 38. The value 134 comes from squaring 3a as a whole (12 squared) instead of just a, which violates order of operations.

116. Simplify the expression 5x plus 3 minus 2x plus 8.
     • 3x plus 11
     • 7x plus 11
     • 7x plus 5
     • 3x plus 5

     Correct answer: 3x plus 11

     The simplified expression is 3x plus 11. Combine the like terms with x: 5x minus 2x equals 3x, then combine the constants: 3 plus 8 equals 11. The result 7x plus 11 incorrectly adds 5x and 2x instead of subtracting.

117. Factor and solve the quadratic equation x squared minus 7x plus 12 equals 0.
     • X equals -3 or x equals -4
     • X equals 3 or x equals 4
     • X equals 2 or x equals 6
     • X equals 1 or x equals 12

     Correct answer: X equals 3 or x equals 4

     The solutions are x equals 3 or x equals 4. The quadratic factors into (x minus 3)(x minus 4) equals 0 because -3 and -4 multiply to 12 and add to -7. Setting each factor to zero gives x equals 3 and x equals 4. Choosing the negative pair would instead solve (x plus 3)(x plus 4) equals 0, which expands to x squared plus 7x plus 12, not the given equation.

118. The quadratic formula solves an equation in the form $ax^2 + bx + c = 0$. Which expression is the quadratic formula for x?
     • $x = \frac{b \pm \sqrt{b^2 - 4ac}}{a}$
     • $x = \frac{-b \pm \sqrt{b^2 + 4ac}}{2a}$
     • $x = \frac{-b}{2a}$
     • $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

     Correct answer: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

     The quadratic formula is $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$. The quantity under the square root, $b^2 - 4ac$, is the discriminant and must be subtracted, not added. The expression $\frac{-b}{2a}$ alone gives only the axis of symmetry, not the solutions.

119. Which of the following expressions is a polynomial?
     • $4x^3 - 2x + 7$
     • $2x^{1/2} - 1$
     • $6x^{-2} + x$
     • $\frac{5}{x} + 3$

     Correct answer: $4x^3 - 2x + 7$

     The expression $4x^3 - 2x + 7$ is a polynomial. A polynomial consists of terms with variables raised to whole-number (non-negative integer) exponents combined by addition or subtraction. Dividing by x, using a fractional exponent like one-half, or using a negative exponent all disqualify an expression from being a polynomial.

120. A line has a slope of 2 and a y-intercept of -3. Which point lies on this line when graphed?
     • (2, -3)
     • (4, 11)
     • (0, 3)
     • (4, 5)

     Correct answer: (4, 5)

     The point (4, 5) lies on the line. The line is y equals 2x minus 3; substituting x equals 4 gives y equals 2 times 4 minus 3 equals 8 minus 3 equals 5. To graph a line in slope-intercept form, start at the y-intercept (0, -3) and rise 2 for every 1 unit right. The point (0, 3) wrongly makes the intercept positive.

121. In the coordinate plane, in which quadrant is the point (-4, -2) located?
     • Quadrant II
     • Quadrant I
     • Quadrant IV
     • Quadrant III

     Correct answer: Quadrant III

     The point (-4, -2) is in Quadrant III. The coordinate plane is divided into four quadrants by the x-axis and y-axis; Quadrant III is the lower-left region where both the x-coordinate and the y-coordinate are negative. A point with a negative x and positive y would be in Quadrant II, and positive x with negative y would be in Quadrant IV.

122. What is the value of $-8 + 5 - (-3)$?
     • -6
     • 0
     • -16
     • 6

     Correct answer: 0

     Correct answer: 0. Subtracting a negative is the same as adding, so the expression becomes -8 + 5 + 3. Combining the terms gives -8 + 8, which equals 0. The value -6 results from incorrectly subtracting 3 instead of adding it.

123. What is the value of $|{-7}| + |4 - 9|$?
     • 2
     • 12
     • -12
     • 3

     Correct answer: 12

     Correct answer: 12. The absolute value of -7 is 7, and 4 - 9 equals -5 whose absolute value is 5, so the sum is 7 + 5 = 12. Absolute value gives the distance from zero and is never negative, so a result of -12 is impossible.

124. Which expression is equal to $2^3 \times 2^4$?
     • $2^{12}$
     • $4^7$
     • $2^7$
     • $2^1$

     Correct answer: $2^7$

     Correct answer: 2 to the 7th power. When multiplying powers with the same base, you add the exponents, so $2^3 \times 2^4 = 2^{3+4} = 2^7$. The choice $2^{12}$ comes from multiplying the exponents instead of adding them, which is incorrect.

125. A shirt originally priced at 40 dollars is marked down by 25 percent. What is the sale price?
     • 30 dollars
     • 15 dollars
     • 35 dollars
     • 10 dollars

     Correct answer: 30 dollars

     Correct answer: 30 dollars. A 25 percent discount on 40 dollars removes 0.25 times 40 = 10 dollars, leaving 40 - 10 = 30 dollars. The value 10 dollars is only the amount of the discount, not the final price.

126. What is the improper fraction $\frac{17}{5}$ written as a mixed number?
     • $3\frac{1}{5}$
     • $2\frac{3}{5}$
     • $3\frac{2}{5}$
     • $4\frac{1}{5}$

     Correct answer: $3\frac{2}{5}$

     Correct answer: 3 and 2/5. Dividing 17 by 5 gives 3 with a remainder of 2, so the mixed number is 3 whole units and 2/5. The choice 3 and 1/5 uses the wrong remainder, since 3 times 5 leaves 2, not 1.

127. Which of the following numbers is divisible by both 3 and 4?
     • 18
     • 24
     • 20
     • 15

     Correct answer: 24

     Correct answer: 24. A number divisible by both 3 and 4 must be a multiple of 12, and 24 equals 12 times 2 while 24 divided by 3 is 8 and divided by 4 is 6 with no remainder. The number 18 is divisible by 3 but not by 4, so it does not qualify.

128. What is the product of $(3 \times 10^4)$ and $(2 \times 10^3)$ written in scientific notation?
     • $6 \times 10^{12}$
     • $5 \times 10^7$
     • $6 \times 10^7$
     • $6 \times 10^{1}$

     Correct answer: $6 \times 10^7$

     Correct answer: 6 times 10 to the 7th power. Multiply the leading numbers, 3 times 2 = 6, and add the exponents of the powers of ten, 4 + 3 = 7, giving $6 \times 10^7$. The choice $6 \times 10^{12}$ incorrectly multiplies the exponents instead of adding them.

129. What is the value of $\sqrt{144}$?
     • 14
     • 12
     • 72
     • 24

     Correct answer: 12

     Correct answer: 12. $\sqrt{144}$ is the number that, when multiplied by itself, equals 144, and $12 \times 12 = 144$. The value 72 is half of 144, not its square root, so it is incorrect.

130. A number rounded to the nearest hundred is 700. Which of the following could be the original number?
     • 643
     • 752
     • 678
     • 755

     Correct answer: 678

     Correct answer: 678. A number rounds to 700 when it lies from 650 up to but not including 750, and 678 falls within that range. The value 643 rounds down to 600 and 752 rounds up to 800, so neither rounds to 700.

131. A teacher gives a quiz to 6 students, and the scores are 7, 9, 9, 12, 14, and 21. If the lowest and highest scores are both removed, by how much does the mean of the remaining four scores differ from the mean of all six scores?
     • 3
     • 1
     • 2
     • 0

     Correct answer: 1

     The correct answer is 1. The mean of all six scores is (7+9+9+12+14+21)/6 = 72/6 = 12. After removing the lowest (7) and highest (21), the remaining scores 9, 9, 12, 14 sum to 44, giving a mean of 44/4 = 11. The means differ by 12 minus 11, which is 1.

132. A spinner is divided into 8 equal sections numbered 1 through 8. What is the probability of the spinner landing on a number that is a multiple of 3?
     • 3/8
     • 1/4
     • 1/8
     • 1/2

     Correct answer: 1/4

     The correct answer is 1/4. The multiples of 3 between 1 and 8 are 3 and 6, giving 2 favorable outcomes out of 8 equally likely sections. The probability is 2/8, which simplifies to 1/4.

133. In a frequency table, 4 students scored 80, 6 students scored 85, and 5 students scored 90 on a test. What is the mean score for these 15 students, to the nearest tenth?
     • 85.0
     • 84.7
     • 85.3
     • 86.0

     Correct answer: 85.3

     The correct answer is 85.3. Multiply each score by its frequency: (4x80)+(6x85)+(5x90) = 320+510+450 = 1280. Divide by the total of 15 students: 1280/15 = 85.33, which rounds to 85.3.

134. Two fair coins are tossed at the same time. What is the probability that the result is exactly one head and one tail?
     • 1/4
     • 3/4
     • 1/3
     • 1/2

     Correct answer: 1/2

     The correct answer is 1/2. The four equally likely outcomes are HH, HT, TH, and TT. Exactly one head and one tail occurs in two of these (HT and TH), giving a probability of 2/4 = 1/2.

135. A bag contains 6 red, 4 green, and 2 yellow marbles. One marble is drawn and NOT replaced, and it is green. What is the probability that a second marble drawn is also green?
     • 4/12
     • 3/11
     • 4/11
     • 1/3

     Correct answer: 3/11

     The correct answer is 3/11. After removing one green marble, 3 green marbles remain out of 11 total marbles. The probability of drawing green on the second draw is therefore 3/11.

136. The five-number summary of a data set is minimum 12, Q1 18, median 25, Q3 34, and maximum 50. What is the interquartile range (IQR) of this data set?
     • 38
     • 25
     • 16
     • 22

     Correct answer: 16

     The correct answer is 16. The interquartile range is found by subtracting the first quartile from the third quartile: Q3 minus Q1 equals 34 minus 18, which is 16.

137. A scatter plot shows that as the outdoor temperature increases, hot chocolate sales decrease. Which type of correlation does this relationship represent?
     • Positive correlation
     • No correlation
     • Perfect correlation
     • Negative correlation

     Correct answer: Negative correlation

     The correct answer is negative correlation. When one variable (temperature) increases while the other variable (hot chocolate sales) decreases, the two variables move in opposite directions, which defines a negative correlation.

138. What is the distance between the points (1, 2) and (7, 10) in the coordinate plane?
     • 10
     • 8
     • 14
     • 100

     Correct answer: 10

     Correct answer: 10. The distance formula gives $\sqrt{(7 - 1)^2 + (10 - 2)^2}$, which is $\sqrt{36 + 64} = \sqrt{100} = 10$.

139. What are the coordinates of the midpoint of the segment joining the points (-2, 5) and (6, -1)?
     • (4, 4)
     • (2, 2)
     • (2, 3)
     • (8, 6)

     Correct answer: (2, 2)

     Correct answer: (2, 2). The midpoint is found by averaging the coordinates: the x-coordinate is (-2 plus 6) divided by 2, which is 2, and the y-coordinate is (5 plus -1) divided by 2, which is 2.

140. Simplify the expression $x^5 \cdot x^3$.
     • $x^2$
     • $x^{15}$
     • $x^8$
     • $2x^8$

     Correct answer: $x^8$

     Correct answer: $x^8$. When multiplying powers with the same base, you add the exponents: 5 plus 3 equals 8, so the result is $x^8$.

141. If $g(x) = 2x^2 - x + 4$, what is the value of $g(3)$?
     • 18
     • 25
     • 21
     • 19

     Correct answer: 19

     Correct answer: 19. Substitute x equals 3 into the function: 2 times 3 squared is 2 times 9, which is 18; then 18 minus 3 plus 4 equals 19.

142. Two triangles are similar. The smaller triangle has a side of length 4 that corresponds to a side of length 10 in the larger triangle. If another side of the smaller triangle is 6, what is the length of the corresponding side in the larger triangle?
     • 15
     • 12
     • 24
     • 9

     Correct answer: 15

     Correct answer: 15. In similar triangles, corresponding sides are proportional. The scale factor is 10 divided by 4, which is 2.5, so the corresponding side is 6 times 2.5, which equals 15.

143. What is the surface area of a cube with edge length 5 units?
     • 125 square units
     • 150 square units
     • 100 square units
     • 30 square units

     Correct answer: 150 square units

     Correct answer: 150 square units. A cube has 6 identical square faces, each with area 5 times 5, which is 25; the total surface area is 6 times 25, which equals 150 square units.

144. Which equation represents a line perpendicular to the line $y = \frac{1}{3}x + 2$?
     • $y = 3x + 5$
     • $y = \frac{1}{3}x - 4$
     • $y = -3x + 1$
     • $y = -\frac{1}{3}x + 2$

     Correct answer: $y = -3x + 1$

     Correct answer: $y = -3x + 1$. Perpendicular lines have slopes that are negative reciprocals. The negative reciprocal of 1/3 is -3, so the line with slope -3 is perpendicular to the given line.

145. Solve for x: $|x - 4| = 9$.
     • X = -5 only
     • X = 13 only
     • X = 5 or x = -13
     • X = 13 or x = -5

     Correct answer: X = 13 or x = -5

     Correct answer: x = 13 or x = -5. An absolute value equation produces two cases: x minus 4 equals 9 gives x equals 13, and x minus 4 equals -9 gives x equals -5.

146. A sphere has a radius of 3 units. Using the formula $V = \frac{4}{3}\pi r^3$, what is its volume in terms of pi?
     • $36\pi$ cubic units
     • $27\pi$ cubic units
     • $12\pi$ cubic units
     • $108\pi$ cubic units

     Correct answer: $36\pi$ cubic units

     Correct answer: $36\pi$ cubic units. Substituting r equals 3 gives (4/3) times pi times 3 cubed, which is (4/3) times pi times 27, equals 36 pi cubic units.