MPT Best Practices 3 — Questions and Answers
Question 1: Which approach best helps you avoid errors when evaluating f(−2) for f(x) = x² − 3x + 1?
- Replace every x with (−2) using parentheses (Correct answer)
- Substitute −2 only into the first term
- Change x to |x| before substituting
- Evaluate f(2) and negate the result
Correct answer: Replace every x with (−2) using parentheses
Using parentheses ensures signs are handled correctly: (−2)² − 3(−2) + 1 = 4 + 6 + 1 = 11.
Question 2: What is the recommended practice when solving a system of two linear equations?
- Check the solution in BOTH original equations (Correct answer)
- Check the solution in only one equation to save time
- Only verify that the x-values match
- Graph the equations without algebraic verification
Correct answer: Check the solution in BOTH original equations
Substituting the solution into both equations confirms it satisfies the entire system, not just one equation.
Question 3: To factor x² + 5x + 6 correctly, which pair of numbers should you look for?
- Two numbers that multiply to 6 and add to 5 (Correct answer)
- Two numbers that multiply to 5 and add to 6
- Two numbers that multiply to 6 and subtract to 5
- Two factors of the leading coefficient
Correct answer: Two numbers that multiply to 6 and add to 5
For x² + bx + c, find two numbers with product c and sum b; here 2 × 3 = 6 and 2 + 3 = 5.
Question 4: When applying the quadratic formula, which step should be done first?
- Rewrite the equation in standard form ax² + bx + c = 0 (Correct answer)
- Divide every term by a
- Compute the discriminant before identifying a, b, c
- Take the square root of both sides
Correct answer: Rewrite the equation in standard form ax² + bx + c = 0
The formula requires identifying a, b, and c from standard form, so rearranging first is essential.
Question 5: A best practice for estimating whether your answer to a word problem is reasonable is to:
- Check that the magnitude and units of the answer match the context (Correct answer)
- Only verify the arithmetic, not the setup
- Use the largest possible values in the problem
- Ignore units when comparing numerical results
Correct answer: Check that the magnitude and units of the answer match the context
Checking magnitude and units catches setup errors; for example, a negative length or impossibly large percentage signals a mistake.
Question 6: When reducing the rational expression (x²−4)/(x−2), the correct simplified form is:
- x + 2, with the restriction x ≠ 2 (Correct answer)
- x + 2 with no restrictions
- x − 2
- (x+2)/(x−2)
Correct answer: x + 2, with the restriction x ≠ 2
Factor the numerator as (x+2)(x−2), cancel (x−2), giving x+2, but x ≠ 2 must be stated.
Question 7: On the UCF Math Placement Test, if you are unsure about a question, the best strategy is to:
- Eliminate obviously wrong answers and make your best guess (Correct answer)
- Leave it blank to avoid any penalty
- Always choose the middle answer option
- Spend unlimited time on it before moving on
Correct answer: Eliminate obviously wrong answers and make your best guess
Process of elimination increases the probability of choosing correctly, and there is typically no penalty for guessing.
MPT Best Practices 3
Which approach best helps you avoid errors when evaluating f(−2) for f(x) = x² − 3x + 1?