CSU/UC Mathematics Diagnostic Testing Project (MDTP) — Questions and Answers

Question 1: Which measure of central tendency is most affected by extreme values?

Median
Mode
Mean (Correct answer)
Range

Correct answer: Mean

The mean is the measure of central tendency most significantly affected by extreme values, also known as outliers. Because the mean is calculated by summing all values, a single unusually high or low value can disproportionately pull the average towards it. In contrast, the median is more resistant to the influence of outliers.

Question 2: The graph of y = f(x - 2) is a shift of y = f(x) in which direction?

2 units right (Correct answer)
2 units left
2 units down
2 units up

Correct answer: 2 units right

Replacing x with x - 2 shifts the graph 2 units to the right.

Question 3: What is sin(90°)?

1 (Correct answer)
1/2
0
√2/2

Correct answer: 1

At 90°, the point on the unit circle is (0, 1), so sin(90°) = 1, the maximum value of sine.

Question 4: A box has 3 defective and 7 good items. What is the probability a randomly selected item is good?

0.5
0.7 (Correct answer)
0.9
0.3

Correct answer: 0.7

P(good) = 7/10 = 0.7.

Question 5: What is 15% of 240?

24
32
48
36 (Correct answer)

Correct answer: 36

15% of 240 = 0.15 × 240 = 36.

Question 6: Compute: (-3/4) × (-8/9)

3/8
-3/8
2/3 (Correct answer)
-2/3

Correct answer: 2/3

(-3/4) × (-8/9) = 24/36 = 2/3 (negative × negative = positive).

Question 7: What is the least common multiple (LCM) of 12 and 18?

36 (Correct answer)
24
6
216

Correct answer: 36

The LCM of 12 and 18 is 36 since 36 is the smallest number divisible by both.

Question 8: A scatter plot is most useful for determining:

The spread of data
The relationship between two variables (Correct answer)
The most frequent value
The mean of a data set

Correct answer: The relationship between two variables

A scatter plot is a graphical tool specifically designed to display the relationship between two quantitative variables. By plotting individual data points, it allows for visual identification of patterns, trends, and the strength and direction of correlation between the variables. It helps determine if there's a positive, negative, or no relationship.

Question 9: What is 2/3 - 1/4?

1/12
3/7
1/7
5/12 (Correct answer)

Correct answer: 5/12

LCD of 3 and 4 is 12: 8/12 - 3/12 = 5/12.

Question 10: Which of the following is a point estimate?

Population mean
Sample mean (Correct answer)
Population variance
Population standard deviation

Correct answer: Sample mean

A point estimate is a single value that is used to estimate an unknown population parameter. The sample mean is a common point estimate for the population mean, providing the best single guess for the true population average based on the observed sample data. Other examples include the sample proportion for the population proportion.

Question 11: In a data set, the range is defined as:

The most frequently occurring value
The sum of all values
The difference between the highest and lowest values (Correct answer)
The middle value when the data is ordered

Correct answer: The difference between the highest and lowest values

The range is a simple measure of data dispersion that indicates the spread of a data set. It is calculated by subtracting the lowest value from the highest value in the set. This provides a quick and easy way to understand the total span of the data.

Question 12: Which statement about the function y = 1/x is true?

It has a horizontal asymptote at y = 1
It is defined at x = 0
It is an even function
It has a vertical asymptote at x = 0 (Correct answer)

Correct answer: It has a vertical asymptote at x = 0

y = 1/x is undefined at x = 0 and has a vertical asymptote there.

Question 13: Which is the scientific notation for 0.00047?

4.7 × 10⁻³
4.7 × 10⁻⁴ (Correct answer)
4.7 × 10³
47 × 10⁻⁵

Correct answer: 4.7 × 10⁻⁴

Moving the decimal 4 places right: 0.00047 = 4.7 × 10⁻⁴.

Question 14: What is the primary purpose of the Mathematics Diagnostic Testing Project (MDTP)?

To test students' reading comprehension
To evaluate students' physical fitness
To assess students' mathematical skills and knowledge (Correct answer)
To measure students' artistic abilities

Correct answer: To assess students' mathematical skills and knowledge

The Mathematics Diagnostic Testing Project (MDTP) is specifically designed to evaluate students' mathematical skills and knowledge. Its primary purpose is to provide a comprehensive assessment of a student's understanding across various mathematical concepts. This diagnostic information helps identify areas of strength and weakness.

Question 15: What is the primary goal of inferential statistics?

To calculate the mean of a data set
To make inferences about a population based on a sample (Correct answer)
To organize data
To describe data

Correct answer: To make inferences about a population based on a sample

The primary goal of inferential statistics is to make generalizations or inferences about a larger population based on data collected from a smaller sample. This involves using statistical methods to draw conclusions, make predictions, and test hypotheses about population parameters. It extends findings beyond the observed data.

Question 16: Simplify: (3x²y)(2xy³)

5x³y⁴
6x²y⁶
5x²y³
6x³y⁴ (Correct answer)

Correct answer: 6x³y⁴

Multiply coefficients (3 × 2 = 6) and add exponents for like bases: x²⁺¹ = x³ and y¹⁺³ = y⁴.

Question 17: What is the range of y = sin(x)?

[−1, 1] (Correct answer)
[0, 2π]
[0, 1]
(−∞, ∞)

Correct answer: [−1, 1]

The sine function oscillates between −1 and 1 inclusive, so its range is [−1, 1].

Question 18: What is the solution set of x² - 5x + 6 = 0?

{-1, -6}
{-2, -3}
{1, 6}
{2, 3} (Correct answer)

Correct answer: {2, 3}

Factoring gives (x - 2)(x - 3) = 0, so x = 2 or x = 3.

Question 19: If sin(θ) = 3/5 and θ is in the first quadrant, what is cos(θ)?

4/5 (Correct answer)
3/4
2/5
5/4

Correct answer: 4/5

Using the Pythagorean identity: cos(θ) = √(1 - sin²θ) = √(1 - 9/25) = √(16/25) = 4/5.

Question 20: If sin(θ) = 1/2, what is one value of θ in the interval [0°, 360°)?

30° (Correct answer)
45°
90°
60°

Correct answer: 30°

sin(30°) = 1/2, making 30° one solution for the equation in the given interval.

Question 21: How can teachers use the results of the MDTP?

To compare students' performance across different schools
To identify specific areas where students need additional support and instruction (Correct answer)
To assign final grades for the course
To determine which students should be advanced to the next grade level

Correct answer: To identify specific areas where students need additional support and instruction

Teachers utilize MDTP results as a diagnostic tool to pinpoint specific mathematical concepts where students may be struggling or excelling. This detailed feedback allows educators to tailor their instruction, provide targeted support, and address individual learning gaps effectively. It helps in customizing educational strategies rather than just assigning grades.

Question 22: What is 5/8 × 4/3?

20/11
9/24
20/24
5/6 (Correct answer)

Correct answer: 5/6

5/8 × 4/3 = 20/24 = 5/6 after dividing numerator and denominator by 4.

Question 23: What is the ratio of 2 hours to 45 minutes in simplest form?

8:3 (Correct answer)
8:1
4:3
2:45

Correct answer: 8:3

2 hours = 120 minutes; 120:45 simplifies by dividing by 15 to give 8:3.

Question 24: Which of the following is true about the angles in an equilateral triangle?

The angles vary depending on the side lengths
All angles are 60 degrees (Correct answer)
All angles are 90 degrees
Two angles are equal, and one is different

Correct answer: All angles are 60 degrees

An equilateral triangle is characterized by having all three sides of equal length. As a direct consequence of this, all three interior angles are also equal. Since the sum of angles in any triangle is 180 degrees, each angle in an equilateral triangle must measure 60 degrees (180 / 3 = 60).

Question 25: What is cos(π/3)?

1/2 (Correct answer)
1
√3/2
√2/2

Correct answer: 1/2

π/3 radians = 60°, and cos(60°) = 1/2 from the standard 30-60-90 triangle.

Question 26: Simplify: 18/24

6/8
3/4 (Correct answer)
9/12
2/3

Correct answer: 3/4

GCF of 18 and 24 is 6; 18 ÷ 6 = 3 and 24 ÷ 6 = 4, so the simplified form is 3/4.

Question 27: Which property is illustrated by: (2/3) × (3/2) = 1?

Distributive property
Associative property
Commutative property
Multiplicative inverse property (Correct answer)

Correct answer: Multiplicative inverse property

Multiplying a number by its reciprocal gives 1, which is the multiplicative inverse property.

Question 28: Which of the following is a rational number?

√9 (Correct answer)
√2
π
e

Correct answer: √9

√9 = 3, which is an integer and therefore rational; the others are irrational.

Question 29: What is the value of tan(45°)?

1/√3
√3
1 (Correct answer)
0

Correct answer: 1

tan(45°) = sin(45°)/cos(45°) = (√2/2)/(√2/2) = 1.

Question 30: What is the value of tan(45°)?

√3
1 (Correct answer)
0
1/2

Correct answer: 1

tan(45°) = sin(45°)/cos(45°) = (√2/2)/(√2/2) = 1.

CSU/UC Mathematics Diagnostic Testing Project (MDTP)

The MDTP is a joint CSU/UC project that measures student readiness for mathematics courses ranging from pre-algebra through calculus. It provides diagnostic reports identifying strengths and weaknesses across key math domains to guide course placement.

Questions

35 min

Time Limit

70%

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Sources & references

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mdtp.ucsd.edu — Registration, test dates · verified Oct 2026
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