Colorado Engineer Intern Examination
Practice Exam 2026 | 100 Questions &
Answers with Detailed Rationales |
Complete Exam Prep & Study Guide
1. Mathematics
If f(x)=3x2−4x+5, what is f′(x)?
A. 3x−4
B. 6x−4
C. 6x+4
D. 3x2−4
Answer: 6x−4
Rationale: The derivative of 3x2 is 6x, the derivative of −4x is −4, and the
derivative of a constant is zero.
2. Mathematics
Evaluate the integral ∫4x3dx.
A. x4+C
B. 4x4+C
C. x4/4+C
D. 12x2+C
,Answer: x4+C
Rationale: Using the power rule for integration, 4∫x3dx=4(x4/4)=x4+C.
3. Mathematics
What is the determinant of the matrix [2134]?
A. 5
B. 8
C. 11
D. 14
Answer: 5
Rationale: For a 2 × 2 matrix, the determinant is ad−bc. Thus, (2)(4)−(3)(1)=5.
4. Mathematics
What is the solution to 2x+7=19?
A. 5
B. 6
C. 7
D. 8
Answer: 6
Rationale: Subtracting 7 gives 2x=12, and dividing by 2 gives x=6.
5. Mathematics
What is the magnitude of the vector v=3i+4j?
A. 3
B. 4
C. 5
D. 7
Answer: 5
,Rationale: The magnitude is 32+42=25=5.
6. Probability
A fair six-sided die is rolled once. What is the probability of obtaining an even
number?
A. 1/6
B. 1/3
C. 1/2
D. 2/3
Answer: 1/2
Rationale: There are three even outcomes—2, 4, and 6—out of six equally likely
outcomes, giving 3/6=1/2.
7. Statistics
What measure of central tendency is obtained by arranging data in order and
selecting the middle value?
A. Mean
B. Mode
C. Median
D. Variance
Answer: Median
Rationale: The median is the middle value when observations are arranged in
numerical order.
8. Engineering Economics
If $1,000 is invested at 5% annual simple interest for 3 years, what is the interest
earned?
A. $50
B. $100
, C. $150
D. $157.63
Answer: $150
Rationale: Simple interest is I=Prt. Therefore, I=(1000)(0.05)(3)=150.
9. Engineering Economics
What does a positive net present value generally indicate for an investment?
A. The project must be rejected
B. The project has no cash flow
C. The project is economically favorable at the selected discount rate
D. The project has zero initial cost
Answer: The project is economically favorable at the selected discount rate
Rationale: A positive NPV means the present value of expected benefits exceeds
the present value of costs at the chosen discount rate.
10. Ethics
An engineer discovers that a design contains a serious safety defect. What is the
most appropriate first professional action?
A. Ignore the defect
B. Conceal the defect from the client
C. Take reasonable action to address the safety concern
D. Approve the design immediately
Answer: Take reasonable action to address the safety concern
Rationale: Protection of public health, safety, and welfare is a fundamental
engineering responsibility.
11. Statics
Practice Exam 2026 | 100 Questions &
Answers with Detailed Rationales |
Complete Exam Prep & Study Guide
1. Mathematics
If f(x)=3x2−4x+5, what is f′(x)?
A. 3x−4
B. 6x−4
C. 6x+4
D. 3x2−4
Answer: 6x−4
Rationale: The derivative of 3x2 is 6x, the derivative of −4x is −4, and the
derivative of a constant is zero.
2. Mathematics
Evaluate the integral ∫4x3dx.
A. x4+C
B. 4x4+C
C. x4/4+C
D. 12x2+C
,Answer: x4+C
Rationale: Using the power rule for integration, 4∫x3dx=4(x4/4)=x4+C.
3. Mathematics
What is the determinant of the matrix [2134]?
A. 5
B. 8
C. 11
D. 14
Answer: 5
Rationale: For a 2 × 2 matrix, the determinant is ad−bc. Thus, (2)(4)−(3)(1)=5.
4. Mathematics
What is the solution to 2x+7=19?
A. 5
B. 6
C. 7
D. 8
Answer: 6
Rationale: Subtracting 7 gives 2x=12, and dividing by 2 gives x=6.
5. Mathematics
What is the magnitude of the vector v=3i+4j?
A. 3
B. 4
C. 5
D. 7
Answer: 5
,Rationale: The magnitude is 32+42=25=5.
6. Probability
A fair six-sided die is rolled once. What is the probability of obtaining an even
number?
A. 1/6
B. 1/3
C. 1/2
D. 2/3
Answer: 1/2
Rationale: There are three even outcomes—2, 4, and 6—out of six equally likely
outcomes, giving 3/6=1/2.
7. Statistics
What measure of central tendency is obtained by arranging data in order and
selecting the middle value?
A. Mean
B. Mode
C. Median
D. Variance
Answer: Median
Rationale: The median is the middle value when observations are arranged in
numerical order.
8. Engineering Economics
If $1,000 is invested at 5% annual simple interest for 3 years, what is the interest
earned?
A. $50
B. $100
, C. $150
D. $157.63
Answer: $150
Rationale: Simple interest is I=Prt. Therefore, I=(1000)(0.05)(3)=150.
9. Engineering Economics
What does a positive net present value generally indicate for an investment?
A. The project must be rejected
B. The project has no cash flow
C. The project is economically favorable at the selected discount rate
D. The project has zero initial cost
Answer: The project is economically favorable at the selected discount rate
Rationale: A positive NPV means the present value of expected benefits exceeds
the present value of costs at the chosen discount rate.
10. Ethics
An engineer discovers that a design contains a serious safety defect. What is the
most appropriate first professional action?
A. Ignore the defect
B. Conceal the defect from the client
C. Take reasonable action to address the safety concern
D. Approve the design immediately
Answer: Take reasonable action to address the safety concern
Rationale: Protection of public health, safety, and welfare is a fundamental
engineering responsibility.
11. Statics
