PRECALCULUS FINAL EXAMss
1. Simplify: 𝟑𝒙𝟐 + 𝟓𝒙𝟐
A. 8𝑥
B. 8𝑥 2
C. 15𝑥 4
D. 2𝑥 2
Answer: B
Rationale: Like terms have the same variable and exponent. Since both terms contain 𝑥 2 , add the
coefficients: 3 + 5 = 8. Therefore, the simplified expression is 8𝑥 2 .
2. Solve: 𝟐𝒙 + 𝟓 = 𝟏𝟕
A. 4
B. 5
C. 6
D. 7
Answer: C
Rationale: Subtract 5 from both sides to obtain 2𝑥 = 12. Divide by 2 to get 𝑥 = 6.
3. Factor: 𝒙𝟐 − 𝟗
A. (𝑥 − 9)(𝑥 + 1)
B. (𝑥 − 3)2
C. (𝑥 − 3)(𝑥 + 3)
D. Prime
Answer: C
Rationale: This is a difference of squares. Use the formula 𝑎2 − 𝑏 2 = (𝑎 − 𝑏)(𝑎 + 𝑏).
4. Evaluate: 𝒇(𝒙) = 𝟐𝒙 + 𝟑, find 𝒇(𝟒)
A. 8
B. 10
C. 11
,D. 13
Answer: C
Rationale: Substitute 𝑥 = 4: 2(4) + 3 = 8 + 3 = 11.
5. Find the slope between (𝟏, 𝟐)and (𝟒, 𝟖)
A. 2
B. 3
C. 4
D. 6
Answer: A
Rationale: Use the slope formula:
𝑦2 − 𝑦1
𝑚=
𝑥2 − 𝑥1
8−2 6
Substituting gives = = 2.
4−1 3
6. Solve: 𝒙𝟐 = 𝟒𝟗
A. 7
B. -7
C. ±7
D. 14
Answer: C
Rationale: Both 7 and -7 square to 49, so the solutions are ±7.
7. Evaluate 𝟑𝟒
A. 12
B. 27
C. 64
D. 81
Answer: D
Rationale: 34 = 3 × 3 × 3 × 3 = 81.
, 8. Simplify: √𝟖𝟏
A. 7
B. 8
C. 9
D. 10
Answer: C
Rationale: The principal square root of 81 is 9.
9. Solve: 𝒙𝟐 − 𝟏𝟔 = 𝟎
A. ±4
B. ±8
C. 4
D. -4
Answer: A
Rationale: Add 16 to both sides to get 𝑥 2 = 16, then take square roots.
10. What is the y-intercept of 𝒚 = 𝟑𝒙 − 𝟐?
A. 3
B. -2
C. 1
D. 2
Answer: B
Rationale: In slope-intercept form 𝑦 = 𝑚𝑥 + 𝑏, the y-intercept is 𝑏. Here, 𝑏 = −2.
𝟏
11. Find the domain of 𝒇(𝒙) =
𝒙−𝟐
A. All real numbers
B. 𝑥 ≠ 2
C. 𝑥 > 2
D. 𝑥 < 2
Answer: B
Rationale: The denominator cannot equal zero. Therefore, 𝑥 − 2 ≠ 0, so 𝑥 ≠ 2.
1. Simplify: 𝟑𝒙𝟐 + 𝟓𝒙𝟐
A. 8𝑥
B. 8𝑥 2
C. 15𝑥 4
D. 2𝑥 2
Answer: B
Rationale: Like terms have the same variable and exponent. Since both terms contain 𝑥 2 , add the
coefficients: 3 + 5 = 8. Therefore, the simplified expression is 8𝑥 2 .
2. Solve: 𝟐𝒙 + 𝟓 = 𝟏𝟕
A. 4
B. 5
C. 6
D. 7
Answer: C
Rationale: Subtract 5 from both sides to obtain 2𝑥 = 12. Divide by 2 to get 𝑥 = 6.
3. Factor: 𝒙𝟐 − 𝟗
A. (𝑥 − 9)(𝑥 + 1)
B. (𝑥 − 3)2
C. (𝑥 − 3)(𝑥 + 3)
D. Prime
Answer: C
Rationale: This is a difference of squares. Use the formula 𝑎2 − 𝑏 2 = (𝑎 − 𝑏)(𝑎 + 𝑏).
4. Evaluate: 𝒇(𝒙) = 𝟐𝒙 + 𝟑, find 𝒇(𝟒)
A. 8
B. 10
C. 11
,D. 13
Answer: C
Rationale: Substitute 𝑥 = 4: 2(4) + 3 = 8 + 3 = 11.
5. Find the slope between (𝟏, 𝟐)and (𝟒, 𝟖)
A. 2
B. 3
C. 4
D. 6
Answer: A
Rationale: Use the slope formula:
𝑦2 − 𝑦1
𝑚=
𝑥2 − 𝑥1
8−2 6
Substituting gives = = 2.
4−1 3
6. Solve: 𝒙𝟐 = 𝟒𝟗
A. 7
B. -7
C. ±7
D. 14
Answer: C
Rationale: Both 7 and -7 square to 49, so the solutions are ±7.
7. Evaluate 𝟑𝟒
A. 12
B. 27
C. 64
D. 81
Answer: D
Rationale: 34 = 3 × 3 × 3 × 3 = 81.
, 8. Simplify: √𝟖𝟏
A. 7
B. 8
C. 9
D. 10
Answer: C
Rationale: The principal square root of 81 is 9.
9. Solve: 𝒙𝟐 − 𝟏𝟔 = 𝟎
A. ±4
B. ±8
C. 4
D. -4
Answer: A
Rationale: Add 16 to both sides to get 𝑥 2 = 16, then take square roots.
10. What is the y-intercept of 𝒚 = 𝟑𝒙 − 𝟐?
A. 3
B. -2
C. 1
D. 2
Answer: B
Rationale: In slope-intercept form 𝑦 = 𝑚𝑥 + 𝑏, the y-intercept is 𝑏. Here, 𝑏 = −2.
𝟏
11. Find the domain of 𝒇(𝒙) =
𝒙−𝟐
A. All real numbers
B. 𝑥 ≠ 2
C. 𝑥 > 2
D. 𝑥 < 2
Answer: B
Rationale: The denominator cannot equal zero. Therefore, 𝑥 − 2 ≠ 0, so 𝑥 ≠ 2.
