MAT 091 Module 3 Exam | Basic Algebra Exam Q&A | Portage Learning

MAT 091 Module 3 | Mathematics Exam Q&A | Portage
Learning
Here are 100 original multiple-choice practice questions for MAT 091 Module 3 |
Mathematics. This set assumes Module 3 covers quadratic equations, radicals,
rational expressions, functions, graphing, exponents, scientific notation, and
variation. These are not official exam questions and are not copied from any textbook,
test bank, or copyrighted source.



Question 1: Solve: 𝑥 2 − 7𝑥 + 12 = 0

A. 𝑥 = 3,4
B. 𝑥 = −3, −4
C. 𝑥 = 2,6
D. 𝑥 = −2, −6

Correct answer: A

Rationale: (𝑥 − 3)(𝑥 − 4) = 0, so 𝑥 = 3or 𝑥 = 4.



Question 2: Solve: 𝑥 2 = 49

A. 𝑥 = 7
B. 𝑥 = −7
C. 𝑥 = ±7
D. No real solution

Correct answer: C

Rationale: Take the square root of both sides: 𝑥 = ±7.



Question 3: Solve: 𝑥 2 − 5𝑥 = 0

A. 𝑥 = 0,5
B. 𝑥 = 0, −5
C. 𝑥 = 5
D. 𝑥 = −5

Correct answer: A

Rationale: 𝑥(𝑥 − 5) = 0, so 𝑥 = 0or 𝑥 = 5.

,Question 4: Solve: 2𝑥 2 + 3𝑥 − 2 = 0
1
A. 𝑥 = 2 , −2
1
B. 𝑥 = − 2 , 2
C. 𝑥 = 1, −2
D. 𝑥 = 2, −1

Correct answer: A
1
Rationale: (2𝑥 − 1)(𝑥 + 2) = 0, so 𝑥 = 2or 𝑥 = −2.



Question 5: Find the discriminant of 𝑥 2 + 4𝑥 + 5 = 0

A. −4
B. 4
C. 36
D. −36

Correct answer: A

Rationale: 𝑏 2 − 4𝑎𝑐 = 16 − 20 = −4.



Question 6: If the discriminant is 0, how many real solutions does a quadratic equation
have?

A. 0
B. 1
C. 2
D. Infinitely many

Correct answer: B

Rationale: A zero discriminant means one repeated real solution.



Question 7: Solve using the quadratic formula: 𝑥 2 − 4𝑥 − 1 = 0

A. 2 ± √5
B. 2 ± √3
C. 4 ± √5
D. −2 ± √5

Correct answer: A

, 4±√16+4 4±2√5
Rationale: 𝑥 = = = 2 ± √5.
2 2




Question 8: Solve: (𝑥 − 3)2 = 16

A. 𝑥 = 7, −1
B. 𝑥 = 7,1
C. 𝑥 = −7, −1
D. 𝑥 = 4, −4

Correct answer: A

Rationale: 𝑥 − 3 = ±4, so 𝑥 = 7or 𝑥 = −1.



Question 9: Complete the square: 𝑥 2 + 6𝑥 + ___

A. 6
B. 9
C. 12
D. 36

Correct answer: B

Rationale: Half of 6 is 3; 32 = 9.



Question 10: Find the vertex of 𝑦 = (𝑥 − 2)2 + 3

A. (2, 3)
B. (−, 23)
C. (2, −3)
D. (3, 2)

Correct answer: A

Rationale: Vertex form 𝑦 = (𝑥 − ℎ)2 + 𝑘gives vertex (ℎ, 𝑘) = (2, 3).



Question 11: Find the axis of symmetry of 𝑦 = 𝑥 2 − 6𝑥 + 5

A. 𝑥 = 3
B. 𝑥 = −3
C. 𝑥 = 6
D. 𝑥 = −6