MPT Best Practices 2 — Questions and Answers
Question 1: When simplifying the expression (3x²)(4x³), what is the correct result?
- 12x⁵ (Correct answer)
- 12x⁶
- 7x⁵
- 12x
Correct answer: 12x⁵
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?
- Distribute the 2 to get 2x + 10 = 18 (Correct answer)
- Divide both sides by 2 first
- Subtract 5 from both sides
- Square both sides
Correct answer: Distribute the 2 to get 2x + 10 = 18
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:
- Square roots do not distribute over addition (Correct answer)
- The formula is only valid for negative numbers
- You must square both sides first
- The result should be a² + b²
Correct answer: Square roots do not distribute over addition
√(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?
- Complete the square or use x = −b/(2a) (Correct answer)
- Plot many points and guess
- Set f(x) = 0 and solve
- Divide all terms by x
Correct answer: Complete the square or use x = −b/(2a)
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:
- Find a common denominator of x(x+1) (Correct answer)
- Cross-multiply both fractions
- Add the numerators and denominators separately
- Multiply the fractions instead
Correct answer: Find a common denominator of x(x+1)
A common denominator x(x+1) allows the fractions to be rewritten before adding numerators.
Question 6: When checking a solution to a radical equation like √(x+3) = x−1, you should always:
- Substitute the solution back into the original equation (Correct answer)
- Only check that the algebra steps were correct
- Accept both solutions if squaring was used
- Use a calculator to estimate the square root
Correct answer: Substitute the solution back into the original equation
Squaring can introduce extraneous solutions, so substituting back into the original equation is essential.
Question 7: When dividing both sides of an inequality by −3, you must:
- Reverse the inequality sign (Correct answer)
- Keep the inequality sign the same
- Add 3 to both sides instead
- Square both sides to remove the negative
Correct answer: Reverse the inequality sign
Dividing or multiplying an inequality by a negative number reverses the direction of the inequality.
MPT Best Practices 2
When simplifying the expression (3x²)(4x³), what is the correct result?