UGA Math Placement Test Prep 2026/2027 – Complete High-Yield Practice Questions, Verified Answers, and Step-by-Step Mathematical Rationales (Grade A+)

UGA MATH PLACEMENT TEST QUESTIONS AND
VERIFIED ANSWERS (2026–)

Complete Practice Test Bank | 250 Questions |
University of Georgia



1. Find the 10th term of the arithmetic sequence: 3, 7, 11, 15, …

A) 39
B) 43
C) 35
D) 47

Correct Answer: A) 39

Rationale: The common difference is 4. Using the formula aₙ = a₁ + (n−1)d: a₁₀ = 3 +
(10−1)(4) = 3 + 36 = 39 .




2. Find the 6th term of the geometric sequence: 2, 6, 18, 54, …

A) 162
B) 486
C) 1458
D) 108

Correct Answer: B) 486

Rationale: The common ratio is 3. Using the formula aₙ = a₁(r)ⁿ⁻¹: a₆ = 2(3)⁶⁻¹ = 2(3)⁵ =
2(243) = 486 .

,3. Write a numerical expression for: "sixteen minus the quotient of twelve and
six."

A) 16 − 6 ÷ 12
B) 12 ÷ 6 − 16
C) 16 ÷ 12 − 6
D) 16 − 12 ÷ 6

Correct Answer: D) 16 − 12 ÷ 6

Rationale: "The quotient of twelve and six" is 12 ÷ 6. "Sixteen minus" that quotient gives
16 − 12 ÷ 6 .




4. Evaluate: 6a + 2b − 6c + 4, if a=3, b=5, and c=−1

A) 179
B) 84
C) 155
D) 38

Correct Answer: D) 38

Rationale: Substitute the values: 6(3) + 2(5) − 6(−1) + 4 = 18 + 10 + 6 + 4 = 38 .




5. In which quadrant would the point (9, −10) be located?

A) Quadrant I
B) Quadrant II
C) Quadrant III
D) Quadrant IV

Correct Answer: D) Quadrant IV

Rationale: Points with positive x and negative y are in Quadrant IV .

,6. Simplify: 3(x + 1) − 4(2x − 5) + 10x

A) 5x − 32
B) 21x + 23
C) 5x + 23
D) 5x − 17

Correct Answer: C) 5x + 23

Rationale: 3x + 3 − 8x + 20 + 10x = (3x − 8x + 10x) + (3 + 20) = 5x + 23 .




7. Write and solve: "The difference of a number x and ten is negative four."

A) x + 10 = −4; x = 5
B) x − 10 = −4; x = 6
C) x − 10 = −4; x = −6
D) x + 10 = −4; x = −5

Correct Answer: B) x − 10 = −4; x = 6

Rationale: "Difference of x and ten" means x − 10. Set equal to −4 and solve: x = 6 .




8. Write and solve: "The quotient of negative sixty and a number x is four."

A) −60/x = 4; x = −15
B) −60x = 4; x = 15
C) −60/x = 4; x = 15
D) −60x = 4; x = −15

Correct Answer: A) −60/x = 4; x = −15

Rationale: "Quotient of negative sixty and x" is −60/x. Set equal to 4 and solve: −60/x = 4
→ x = −15 .

, 9. Solve: x² − 5x + 6 = 0

A) x = 2, 3
B) x = −2, −3
C) x = 1, 6
D) x = −1, −6

Correct Answer: A) x = 2, 3

Rationale: Factor: (x − 2)(x − 3) = 0, so x = 2 or x = 3 .




10. Solve the inequality: −3x > 12

A) x > −4
B) x < −4
C) x > 4
D) x < 4

Correct Answer: B) x < −4

Rationale: Divide by −3 and flip the inequality sign: x < −4 .




11. Write the equation y = 2x − 5 in standard form.

A) 2x − y = 5
B) 2x + y = −5
C) −2x + y = −5
D) x + y = 5

Correct Answer: A) 2x − y = 5

Rationale: y = 2x − 5 → −2x + y = −5 → multiply by −1: 2x − y = 5 .




12. Simplify: (x²)(x⁵)