ICET Mathematical Ability - Algebra 3 — Questions and Answers
Question 1: If 2^x = 64, what is x?
- 5
- 6 (Correct answer)
- 7
- 8
Correct answer: 6
64 = 2^6, so x = 6.
Question 2: The discriminant of x² + 4x + 5 = 0 is b² − 4ac. What does the discriminant indicate?
- Two distinct real roots
- One repeated real root
- No real roots (Correct answer)
- Two equal roots
Correct answer: No real roots
Discriminant = 16 − 20 = −4 < 0, indicating the equation has no real roots.
Question 3: If x + 1/x = 5, what is x² + 1/x²?
- 21
- 23 (Correct answer)
- 25
- 27
Correct answer: 23
(x + 1/x)² = x² + 2 + 1/x² = 25, so x² + 1/x² = 23.
Question 4: What is the remainder when x³ − 3x² + 3x − 1 is divided by (x − 1)?
- 0 (Correct answer)
- 1
- 2
- 3
Correct answer: 0
By the Remainder Theorem, substitute x = 1: 1 − 3 + 3 − 1 = 0.
Question 5: Solve for x: |2x − 3| = 7
- x = 5 or x = −2 (Correct answer)
- x = 5 or x = 2
- x = −5 or x = 2
- x = 5 or x = −5
Correct answer: x = 5 or x = −2
2x − 3 = 7 gives x = 5; 2x − 3 = −7 gives x = −2.
Question 6: Find S₅ of an AP where a = 2 and d = 3 using Sn = n/2 × (2a + (n−1)d).
- 35
- 40 (Correct answer)
- 45
- 50
Correct answer: 40
S₅ = 5/2 × (4 + 12) = 5/2 × 16 = 40.
ICET Mathematical Ability - Algebra 3
If 2^x = 64, what is x?