Best Practices Flashcards

Which of the following is a valid algebraic identity useful on placement tests?

Answer: (a + b)² = a² + 2ab + b²

The perfect square trinomial identity (a+b)² = a² + 2ab + b² is fundamental and frequently tested.

To solve |2x − 4| = 6, the best practice is to set up:

Answer: 2x − 4 = 6 and 2x − 4 = −6

Absolute value equations require two cases: the expression equals the positive value and the negative value.

When graphing a line using slope-intercept form y = mx + b, the best starting point is:

Answer: Plot the y-intercept (0, b), then use slope to find the next point

The y-intercept is immediately readable from the equation, making it the most efficient starting point.

Which technique is most efficient for solving 3x/4 = 9?

Answer: Multiply both sides by 4/3

Multiplying both sides by the reciprocal 4/3 isolates x in one step: x = 12.

A common error when expanding −(x − 5) is writing −x − 5. The correct expansion is:

Answer: −x + 5

Distributing the negative sign changes every sign inside: −(x − 5) = −x + 5.

For the placement test, recognizing that 0.25 = 1/4 = 25% is an example of which best practice?

Answer: Knowing equivalent forms of common fractions, decimals, and percents

Fluency in converting between fractions, decimals, and percents speeds up computation on timed assessments.

When asked to find the domain of f(x) = √(2x − 6), what is the correct procedure?

Answer: Set 2x − 6 ≥ 0 and solve for x

The radicand must be non-negative, so 2x − 6 ≥ 0 gives x ≥ 3 as the domain.