Algebra and Trigonometry: Equations and Inequalities flashcards

Question 1

What is the distance formula between (x₁, y₁) and (x₂, y₂)?

Accepted Answer

d = √((x₂ − x₁)² + (y₂ − y₁)²)

Question 2

Which theorem is the distance formula derived from?

Accepted Answer

The Pythagorean Theorem

Question 3

How are the midpoint's coordinates of a segment found?

Accepted Answer

Divide the sum of the endpoints' x-coordinates by 2 and the sum of their y-coordinates by 2.

Question 4

What is the slope of the line through (x₁, y₁) and (x₂, y₂)?

Accepted Answer

m = (y₂ − y₁)/(x₂ − x₁)

Question 5

What is the point-slope equation of a line?

Accepted Answer

y − y₁ = m(x − x₁)

Question 6

What is the slope of a horizontal line?

Accepted Answer

Zero; it has the form y = c for a constant c.

Question 7

What is the slope of a vertical line?

Accepted Answer

Undefined; it has the form x = c for a constant c.

Question 8

How are the slopes of two parallel lines related?

Accepted Answer

They are equal (the lines have different y-intercepts).

Question 9

How are the slopes of perpendicular lines related, when neither is vertical?

Accepted Answer

They are negative reciprocals of each other.

Question 10

What is an x-intercept?

Accepted Answer

The point where a graph meets the x-axis; its y-coordinate is zero.

Question 11

What is a quadrant of the coordinate plane?

Accepted Answer

One of the four sections the axes divide the plane into

Question 12

What is an identity equation?

Accepted Answer

An equation that is true for every value of the variable

Question 13

What is a conditional equation?

Accepted Answer

An equation true for some values of the variable

Question 14

What are extraneous solutions?

Accepted Answer

Solutions that turn out not to work in the original equation

Question 15

What is the imaginary unit i?

Accepted Answer

The square root of −1: i = √−1

Question 16

What is the standard form of a complex number?

Accepted Answer

a + bi, where a is the real part

Question 17

In the complex plane, what does the vertical axis represent?

Accepted Answer

The imaginary part (the horizontal axis is the real part)

Question 18

What is (a + bi) + (c + di)?

Accepted Answer

(a + c) + (b + d)i

Question 19

What do you multiply by to divide by a complex number?

Accepted Answer

Multiply top and bottom by the conjugate of the denominator.

Question 20

How often do the powers of i repeat?

Accepted Answer

Every fourth power; they are cyclic.

Question 21

What is the quadratic formula for ax² + bx + c = 0?

Accepted Answer

x = (−b ± √(b² − 4ac)) / (2a)

Question 22

What is the discriminant of a quadratic equation?

Accepted Answer

b² − 4ac, the part under the square root in the quadratic formula

Question 23

What does the square root property say about x² = k?

Accepted Answer

x = ±√k

Question 24

How is |x| defined for x ≥ 0 and for x < 0?

Accepted Answer

|x| = x when x ≥ 0; |x| = −x when x < 0

Question 25

How else can a^(m/n) be written using a radical?

Accepted Answer

(ⁿ√a)ᵐ, or equivalently ⁿ√(aᵐ)

Question 26

If a < b and c < 0, how do ac and bc compare?

Accepted Answer

ac > bc

Question 27

What is a compound inequality?

Accepted Answer

A statement or problem that includes two inequalities

Algebra and Trigonometry: Equations and Inequalities flashcards

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