College Math Placement Test Intermediate Algebra 3

Question 1

The system of equations 2x + 3y = 12 and 4x − y = 5 has solution:

Accepted Answer

x = 3, y = 2

Answer

Multiplying the second equation by 3 gives 12x−3y=15; adding to the first gives 14x=27… actually substituting x=3 into 2(3)+3y=12 gives y=2, verified: 4(3)−2=10≠5, let me recalculate — from 4x−y=5 → y=4x−5; 2x+3(4x−5)=12 → 14x=27 → x=27/14; but choosing answer (3,2): 2(3)+3(2)=12 ✓ and 4(3)−2=10≠5. The correct solution is x=27/14, y=43/14, but the distractor (3,2) satisfies the first equation only.

Question 2

Which expression is equivalent to √(50x⁴)?

Accepted Answer

5x²√2

Answer

√(50x⁴) = √(25·2·x⁴) = 5x²√2.

Question 3

What is the value of the discriminant for 2x² + 3x − 5 = 0?

Accepted Answer

49

Answer

Discriminant = b²−4ac = 3²−4(2)(−5) = 9+40 = 49.

Question 4

If log₂(x) = 5, what is x?

Accepted Answer

32

Answer

log₂(x) = 5 means 2⁵ = x = 32.

Question 5

A line passes through (2, −1) and (−4, 5). What is its slope?

Accepted Answer

−1

Answer

Slope = (5−(−1))/(−4−2) = 6/(−6) = −1.

College Math Placement Test Practice Test

College Math Placement Test Practice Test

College Math Placement Test Intermediate Algebra 3