Best Practices Flashcards

Which of the following demonstrates proper use of the order of operations when evaluating 3 + 2 × 4²?

Answer: 3 + 2 × 16 = 3 + 32 = 35

PEMDAS: evaluate the exponent first (4²=16), then multiply (2×16=32), then add (3+32=35).

When solving a proportion like 3/5 = x/20, the most efficient method is:

Answer: Cross-multiply to get 5x = 60, then x = 12

Cross-multiplying gives 3 × 20 = 5x, so 60 = 5x and x = 12.

To avoid sign errors when subtracting polynomials (5x² + 3x) − (2x² − x), the best practice is to:

Answer: Distribute the negative sign first: 5x² + 3x − 2x² + x

Distributing the negative sign changes −(2x² − x) to −2x² + x, then combine like terms to get 3x² + 4x.

Which practice reduces errors when writing the equation of a line through (2, 3) with slope 4?

Answer: Use point-slope form y − 3 = 4(x − 2) then simplify

Point-slope form y − y₁ = m(x − x₁) directly uses the given information, minimizing algebra errors.

A student needs to evaluate log₂(32). Which best-practice thinking leads to the answer?

Answer: Ask: '2 to what power equals 32?' to get 5

Logarithms ask for the exponent: 2⁵ = 32, so log₂(32) = 5.

When simplifying a complex fraction like (1/2)/(3/4), the best practice is to:

Answer: Multiply by the reciprocal of the denominator: (1/2) × (4/3) = 2/3

Dividing by a fraction is equivalent to multiplying by its reciprocal, giving (1/2)(4/3) = 4/6 = 2/3.

To maximize success on the UCF Math Placement Test, which time-management strategy is most effective?

Answer: Answer questions you know first, then return to harder ones

Answering known questions first secures those points and leaves remaining time for harder problems.