4. Algebra 1: Formulas & Terms

Question 1

What is the formula for the Nth Term of an Arithmetic Sequence?

Answer 1

1. The formula for the nth term of an arithmetic sequence is given by f(n) = d(n - 1) + a of 1, where a of 1 is the first term in the sequence and d is the common difference.

Question 2

What is the formula for the Nth Term of an Arithmetic Sequence?

Answer 2

1. The formula for the nth term of an arithmetic sequence is given by f(n) = d(n - 1) + a of 1, where a of 1 is the first term in the sequence and d is the common difference.

Question 3

What is the formula for the Slope-Intercept Form of a Line?

Answer 3

1. y = mx + b, where m = slope of the line and b = y-intercept of the line (the place where the line crosses the y-axis

Question 4

What is the formula for the Point-Slope form?

Answer 4

1. y - y of 1 = m(x - x of 1), where the line passes through point (x of 1, y of 1) and has a slope of m

Question 5

What is the formula for the Pythagorean Theorem?

Answer 5

1. In any right triangle, the sum of the squares of the lengths of the legs equals the square of the length of the hypotenuse: a^2 + b^2 = c^2

Question 6

What is the formula for the Quadratic Formula?

Answer 6

1. x = (-b plus or minus the square root of b^2 - 4ac) / 2a

Question 7

What is the formula for the Vertex of a Parabola?

Answer 7

1. The vertex of a parabola is given by (a, b) if the equation is written in the form y = (x - a)^2 + b

Question 8

Abscissa

Answer 8

1. A number that shows where a point on a graph is located in relation to the x-axis

Question 9

Absolute Value

Answer 9

1. The number that tells you how far away a number is from zero

Question 10

Algebraic Expression

Answer 10

1. A combination of mathematical symbols that might include numbers, variables, and operation symbols

Question 11

Arithmetic Sequence

Answer 11

1. A sequence that is build term by term by adding the same number each time

Question 12

Binomial

Answer 12

1. An expression with two terms, such as x + 3 or n - 7

Question 13

Common Difference

Answer 13

1. In an arithmetic sequence, the amount by which you add each time you build a new term in the sequence

Question 14

Constant Term

Answer 14

1. The 3rd term of a trinomial that has no variable in it

Question 15

Degree of a Polynomial

Answer 15

1. The largest power in the polynomial

Question 16

Difference

Answer 16

1. The answer to a subtraction problem

Question 17

Difference of Two Squares

Answer 17

1. An equation that has one squared term subtracted from another term that is a square. There is no middle term in a difference of two squares

Question 18

Domain of a Function

Answer 18

1. The set of input values that we can plug into the function

Question 19

Dominant Term

Answer 19

1. The term in a polynomial that has the highest degree

Question 20

Equation

Answer 20

1. A mathematical sentence that uses or includes an equals sigh “=”

Question 21

Evaluate

Answer 21

1. Plug in numbers to determine the value of an expression

Question 22

Extraneous Solution

Answer 22

1. A number that appears to be a solution of a radical equation but is not

Question 23

First Difference

Answer 23

1. Another term for the common difference in an arithmetic sequence; the amount added to the previous term in a sequence to get the next term

Question 24

Function

Answer 24

1. A mathematical rule or relationship that assigns exactly one output value to each input value

Question 25

Geometric Sequence

Answer 25

1. A sequence that is build term by term by multiplying the same number each time

Question 26

Horizontal Asymptotes

Answer 26

1. Horizontal asymptotes for graphs of functions act like “borders” or “guides” for the graphs when the x-values are large, in either a positive or negative direction.

To find a horizontal asymptote, look at the dominant terms of the equation. If the exponents of the variables are the same, then the horizontal asymptote is the ratio of the two leading coefficients. If the exponent in the numerator is larger than the exponent in the denominator, then there is no horizontal asymptote. If the exponent in the numerator is smaller than the one in the donominator, the horizontal asymptote is y = 0

Question 27

Hypotenuse

Answer 27

1. The side of the triangle that is opposite the right angle. It is also the longest side of a right triangle

Question 28

Identity

Answer 28

1. An equation that is true for every possible value of the variable(s)

Question 29

Leading Coefficient

Answer 29

1. The coefficient (number) in front of the term that contains the larges power of x

Question 30

Legs of a Triangle

Answer 30

1. The other two sides of the triangle that are not the hypotenuse

Question 31

One-step Equation

Answer 31

1. An equation that only takes one step to solve

Question 32

Ordered Pair

Answer 32

1. Two numbers inside parentheses that are separated by a comma. The first number is the x-coordinate, or abscissa, and the second number is the y-coordinate, or ordinate, on a graph

Question 33

Ordinate

Answer 33

1. A number that shows where a point on a graph is located in relation to the y-axis

Question 34

Origin

Answer 34

1. The point at which the axes intersect in the Cartesian plane

Question 35

Parabola

Answer 35

A U-shape; the graphs of quadratic functions of the form y = ax^2 +bx + c are shaped like parabolas

Question 36

Perfect Square Trinomial

Answer 36

1. A trinomial (three terms) that can be written as the perfect square of a binomial (two terms)

Question 37

Polynomial

Answer 37

1. (in the variable x): an expression of the form a_0 + a_1x + a_2x^2 + … + a_nx^n where each of the a_0, a_1, a_2, …, a_n are numbers (which could be positive, negative, or zero) and the powers on all the x’s are positive integers. In other words, a polynomial is a number plus or minus a number with a variable plus or minus another number with a variable that has a positive exponent plus or minus another number witha variable that has a different positive exponent, and so on.

Question 38

Quadratic Equation

Answer 38

1. An equation that includes a variable raised to the second power (squared). Its typical form is y = ax^2 +bx + c

Question 39

Radical Equations

Answer 39

1. Equations that contain radical expressions

Question 40

Radical Expression

Answer 40

1. An expression with a radical (square root) symbol in it

Question 41

Range of a Function

Answer 41

1. The set of output values of the function

Question 42

Rational Expression

Answer 42

1. A “ratio” of two polynomials; one polynomial divided by another polynomial

Question 43

Second Difference

Answer 43

1. The difference of the first differences

Question 44

Sequence

Answer 44

1. A function whose domain is the set of natural numbers (or positive integers)

Question 45

Solution of an Equation

Answer 45

1. The value of the variable that makes the equation true

Question 46

Solution of the System

Answer 46

1. An ordered pair that makes all the equations in a system of equations true

Question 47

System of Linear Equations

Answer 47

1. A set of two or more linear equations

Question 48

Term

Answer 48

1. A number in a sequence

Question 49

Trinomial

Answer 49

1. An expression with three terms, such as x^2 - 5x +2

Question 50

Two-step Equation

Answer 50

1. An equation that takes two steps to solve

Question 51

Vertical Asymptote

Answer 51

1. If x = c is a vertical asymptote of the graph of a function, then as the values of x get really close to c, the values of the function grow “huge” (either going to +infinity or -infinity). In other words, the vertical asymptote is the line near which the graph makes a sharp turn. It is not actually on the graph

To find a vertical asymptote, look for those values of x where the denominator equals 0 after cancelling out anything that can be cancelled in the original expression

Question 52

Zeros of the Equation

Answer 52

1. Values of x that are solutions of a quadratic equation; they are the -intercepts of the graph ax^2 +bx +c. They can be any number, not just zero. However, when they are plugged into the quadratic equation, ax^2 + bx + c, the equation is true