August 2017 Algebra 2 Regents Flashcards

Questions and Answers

The function f(x) = x - 3/x² + 2x - 8 is undefined when x equals

2 or -4

Which expression is equivalent to (3k - 2i)², where i is the imaginary unit?

9k² - 12ki + 4 (correct)

9k² - 12ki - 4

The roots of the equation x² + 2x + 5 = 0 are

-1 + 2i and -1 - 2i

The solution set for the equation √x + 14 - √2x + 5 = 1 is

{2} Signup and view all the answers

As x increases from 0 to π/2, the graph of the equation y = 2 tan x will

increase without limit Signup and view all the answers

Which equation represents a parabola with the focus at (0, -1) and the directrix y = 1?

x² = -4y Signup and view all the answers

Which diagram represents an angle, α, measuring 13π/20 radians drawn in standard position, and its reference angle, θ?

Single line going counter-clockwise with θ near the x-axis Signup and view all the answers

What are the zeros of P(m) = (m² - 4)(m² + 1)?

2, -2, i, and -i Signup and view all the answers

What is the average decreasing rate of change per year of the value of the car from June 2012 to June 2014?

2450 Signup and view all the answers

What equation approximates the amount of Iridium-192 present after t days?

A = 100(0.990656)^t Signup and view all the answers

What proportion of the ball bearings will have a diameter less than 3.7 cm if the distribution is normal with a mean of 4 cm and a standard deviation of 0.2 cm?

0.0668 Signup and view all the answers

Which statements regarding the polynomial equation of degree three, p(x), with x-intercepts at -2, 10, and 14 could be true? (Select all that apply)

The maximum volume of the box is approximately 56 Signup and view all the answers

Which expression is equivalent to (4x³ + 9x - 5)/(2x - 1), where x ≠ 1/2?

2x² + x + 5 Signup and view all the answers

The inverse of the function f(x) = (x + 1)/(x - 2) is

f^-1(x) = (2x + 1)/(x - 1) Signup and view all the answers

Which expression has been rewritten correctly to form a true statement?

(x + 2)² + 2(x + 2) - 8 = (x + 6)x Signup and view all the answers

At a 95% confidence level, the proportion of New York City residents with hypertension and the margin of error are closest to

proportion ≈ 0.16; margin of error ≈ 0.02 Signup and view all the answers

Which scenario is best described as an observational study?

A social researcher wants to learn whether or not there is a link between attendance and grades. She gathers data from 15 school districts. Signup and view all the answers

Which sinusoid has the greatest amplitude?

y = -5sin(θ - 1) - 3 Signup and view all the answers

Study Notes

Function Undefined Points

The function f(x) = (x - 3) / (x² + 2x - 8) is undefined at x = 2 and x = -4.

Equivalent Expressions

The expression equivalent to (3k - 2i)² is 9k² - 12ki - 4.

Roots of Quadratic Equation

The roots of x² + 2x + 5 = 0 are -1 + 2i and -1 - 2i.

Solution Set

The solution set for √x + 14 - √(2x + 5) = 1 is {2}.

Graph Behavior

As x increases from 0 to π/2, the graph of y = 2 tan x increases without limit.

Parabola Equation

The equation representing a parabola with a focus at (0, -1) and directrix y = 1 is x² = -4y.

Angle Measurement

An angle measuring 13π/20 radians in standard position has a reference angle θ positioned near the x-axis.

Zeros of Polynomial

The zeros of P(m) = (m² - 4)(m² + 1) are 2, -2, i, and -i.

Car Depreciation Rate

The average decreasing rate of change in the car's value from June 2012 to June 2014 is approximately $2450 per year.

Half-Life of Isotope

After t days, the amount of Iridium-192 present, starting from 100 grams, is approximated by A = 100(0.990656)^t.

Normal Distribution Proportion

In a normal distribution of ball bearings, with a mean of 4 cm and standard deviation of 0.2 cm, approximately 6.68% will have a diameter less than 3.7 cm.

Polynomial Volume Model

For the polynomial p(x) with x-intercepts at -2, 10, and 14, true statements include:
- A.) The equation is p(x) = (x + 2)(x - 10)(x - 14).
- D.) The maximum volume of the box is approximately 56.

Correct Expression Rewrite

The correct rewriting of the expression is (x+2)² + 2(x+2) - 8 = (x + 6)x.

Proportion from Observational Study

In a 2004 study in NYC, 212 out of 1334 participants had hypertension, yielding a proportion of approximately 0.16 with a margin of error of approximately 0.02 at a 95% confidence level.

Observational Study Scenario

An observational study occurs when a researcher gathers data on a potential link between attendance and grades.

Sinusoid Amplitude

The sinusoid with the greatest amplitude is described by the equation y = -5sin(θ - 1) - 3.

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Description

Test your knowledge with our flashcards based on the August 2017 Algebra 2 Regents exam. Each card presents a question or equation followed by its answer, covering key concepts in algebra and functions. Perfect for revision and practice ahead of your exams!