ICET Mathematical Ability - Algebra 3

Question 1

If 2^x = 64, what is x?

Accepted Answer

6

Answer

64 = 2^6, so x = 6.

Question 2

The discriminant of x² + 4x + 5 = 0 is b² − 4ac. What does the discriminant indicate?

Accepted Answer

No real roots

Answer

Discriminant = 16 − 20 = −4 < 0, indicating the equation has no real roots.

Question 3

If x + 1/x = 5, what is x² + 1/x²?

Accepted Answer

23

Answer

(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)?

Accepted Answer

0

Answer

By the Remainder Theorem, substitute x = 1: 1 − 3 + 3 − 1 = 0.

Question 5

Solve for x: |2x − 3| = 7

Accepted Answer

x = 5 or x = −2

Answer

2x − 3 = 7 gives x = 5; 2x − 3 = −7 gives x = −2.

ICET - Integrated Common Entrance Test Practice Test