MPT Best Practices 2

Question 1

When simplifying the expression (3x²)(4x³), what is the correct result?

Accepted Answer

12x⁵

Answer

Multiply coefficients (3×4=12) and add exponents (2+3=5) to get 12x⁵.

Question 2

What is the best first step when solving the equation 2(x + 5) = 18?

Accepted Answer

Distribute the 2 to get 2x + 10 = 18

Answer

Distributing first gives 2x + 10 = 18, which is easiest to solve by then subtracting 10.

Question 3

A student writes √(a² + b²) = a + b. This is incorrect because:

Accepted Answer

Square roots do not distribute over addition

Answer

√(a² + b²) ≠ a + b; the Pythagorean theorem shows the correct form is c = √(a² + b²).

Question 4

Which strategy is most efficient for finding the vertex of f(x) = x² − 6x + 8?

Accepted Answer

Complete the square or use x = −b/(2a)

Answer

Using the vertex formula x = −b/(2a) = 3 gives the x-coordinate of the vertex quickly.

Question 5

Before adding the fractions 2/x + 3/(x+1), the best practice is to:

Accepted Answer

Find a common denominator of x(x+1)

Answer

A common denominator x(x+1) allows the fractions to be rewritten before adding numerators.

(MPT) UCF Math Placement Test Practice Test