Algebra Unit

Question 1

What’s the order of operations?

Answer 1

1. Brackets / Parenthesis
2. Exponents
3. Division, Multiplication
4. Addition, Subtraction

Question 2

What are natural numbers (N)?

Answer 2

Counting numbers like 1, 2, 3, …

Question 3

What are whole numbers?

Answer 3

They are natural numbers including 0

Question 4

What are integers (Z)?

Answer 4

They are whole numbers, including negative whole numbers

Question 5

What are rational numbers?

Answer 5

Can be written as p/q where q is not 0

Question 6

What are irrational numbers

Answer 6

Cannot be written as p/q

Question 7

What’s a ratio in math?

Answer 7

A comparison of 2 numbers (E.g 2:3 ratio of girls to boys)

Question 8

What’s a proportion?

Answer 8

It’s when 2 ratios are equal

Question 9

What’s a radical?

Answer 9

It’s an expression w/ roots

Question 10

What’s an exponent?

Answer 10

It’s a power showing repeated multiplication

Question 11

What’s the absolute value?

Answer 11

It’s the distance from 0 along a real number line

Question 12

What’s a coefficient?

Answer 12

It’s the number in front of a variable

Question 13

What is the degree of a term or polynomial?

Answer 13

It’s the highest exponent

Question 14

What’s a polynomial?

Answer 14

An expression w/ non negative integer exponents. No variables in denominators, no roots.

Question 15

What’s a rational expression?

Answer 15

A fraction w/ polynomials in the numerator and denominator

Question 16

What’s a radical expression?

Answer 16

An expression w/ square roots or other roots

Question 17

How should you write a polynomial?

Answer 17

In standard form. Arrange its terms in descending order of their degrees.

Question 18

What are monomials, binomials, and trinomials?

Answer 18

They indicate the number of terms in a polynomial.

Question 19

What’s a constant term?

Answer 19

It’s the term w/ no variable

Question 20

What’s the leading term?

Answer 20

The term w/ the highest degree

Question 21

Difference of squares factoring formula?

Answer 21

a^2 - b^2 = (a - b)(a + b)

Question 22

Sum of cubes factoring formula?

Answer 22

a^3 + b^3 = (a + b)(a^2 - ab + b^2)

Question 23

Difference of cubes factoring formula?

Answer 23

a^3 - b^3 = (a - b)(a^2 + ab + b^2)

Question 24

How do you factor a simple trinomial? (x^2 + bx + c)

Answer 24

Find two numbers that multiply to c and add to b

Question 25

How do you factor a complex trinomial? (ax^2 + bx + c)

Answer 25

For example, 2x^2 + 7x + 3 = (2x + 1)(x + 3) because two numbers that create product of 6 and a sum of 7 are 6 and 1. Then you create two brackets with terms w/ the x variable, then make sure outer terms multiply to one of the numbers and the inner terms multiply to the other.

Question 26

How do you factor a perfect square trinomial (a^2 +- 2ab + b^2)

Answer 26

(a +- b)^2 For this to be possible, ensure the middle term = 2ab. If it's not equal, factor it as a complex trinomial.

Question 27

How do you factor by grouping?

Answer 27

Group terms together and factor them separately. Then factor again if needed.

Question 28

What does rationalizing the denominator mean?

Answer 28

Rewriting a fraction so that the denominator has no roots or irrational numbers. It's used to simplify expressions.

Question 29

There are 4 cases of when you need to rationalize the denominator. State them and the method.

Answer 29

Case 1: 1/√2 Multiply num and den by v2 Case 2: 3/2(√5) Multiply num and den by √5 Case 3: 1/(2+√3) Multiply num and den by the conjugate 2 - √3 Case 4: 1/∛2 Multiply num and den by 2^(2/3) to make the denominator rational

Question 30

What's a conjugate in math?

Answer 30

A related expression, usually a binomial, formed by changing the sign between its terms.

Question 31

Exponent law: (a^m)(a^n)

Answer 31

a^(m+n)

Question 32

Exponent law: a^m / a^n

Answer 32

a^(m-n)

Question 33

Exponent law: (a^m)^n

Answer 33

a^mn

Question 34

Exponent law: (ab)^m

Answer 34

(a^m)(b^m)

Question 35

Exponent law: a^0

Answer 35

1

Question 36

Exponent law: a^-m

Answer 36

1 / (a^m)

Question 37

Exponent law: a^(m/n)

Answer 37

n root of a^m or (n root of a)^m

Question 38

Exponent law extended: (a/b)^-m

Answer 38

(b/a)^m

Question 39

What's a system of equations?

Answer 39

Two or more equations w/ the same variables. A point (x,y) is a solution to the system if it makes each equation true. Graphically, a solution is a POI.

Question 40

What's a linear equation?

Answer 40

An algebraic equation where each term is a constant or a single variable (to the power of 1), forming a straight line when graphed

Question 41

Slope-intercept form equation and its best use?

Answer 41

y = mx + b Best for graphing

Question 42

Point-slope form equation and its best use?

Answer 42

y-y1 = m(x-x1) Best when you know a point and the slope

Question 43

Standard form equation and its best use?

Answer 43

Ax + By + C = 0 Best for solving a system of equations and finding intercepts

Question 44

Describe a consistent & independent linear system

Answer 44

Different slopes, one solution

Question 45

Describe a consistent & dependent linear system

Answer 45

Same slopes, same y-ints, infinite solutions

Question 46

Describe an inconsistent linear system

Answer 46

Same slopes, different y-ints, no solutions

Question 47

If an equation is a multiple of another, how many solutions does the linear system have?

Answer 47

Infinite solutions

Question 48

What are the 2 ways to solve a linear system?

Answer 48

Substitution and Elimination. Make sure to do a formal check of L.S = R.S

Question 49

What is a linear inequality and when do you use an open vs closed circle?

Answer 49

A mathematical statement comparing two expressions with an inequality sign. Use an open circle for > or < and a closed circle for >= or <=

Question 50

What are the type of linear system word problems?

Answer 50

1. Investing money 2. Mixing solutions 3. Driving distance 4. Speed, distance, time w/ current

Question 51

When you divide/multiply by a negative number in an inequality, what must you do?

Answer 51

Switch the direction of the inequality sign

Question 52

What is a rational expression?

Answer 52

An expression in the form p/q, where p & q are polynomials and q is not equal to 0. It is undefined when the denominator is 0

Question 53

What are restrictions?

Answer 53

Limitations on the possible input values (domain) for a function, often to prevent undefined operations like dividing by zero or taking the square root of a negative number

Question 54

What are the steps to simplify a rational expression?

Answer 54

1. Factor out the numerator & denominator completely 2. Cancel out common factors 3. State any restrictions

Question 55

What's a factor?

Answer 55

A number that divides another number evenly, leaving no remainder, or one of the numbers that are multiplied together to get a product

Question 56

What are the steps to multiply rational expressions?

Answer 56

1. Factor out num & den 2. Cancel out common factors 3. Multiply remaining num & den

Question 57

What are the steps to adding/subtracting rational expressions?

Answer 57

1. Factor out if needed 2. Find LCD & rewrite each fraction 3. Combine numerators 4. State restrictions

Question 58

What are the steps to solve rational equations?

Answer 58

1. Find restrictions 2. Use LCD 3. Solve 4. Check for extraneous roots

Question 59

What are extraneous roots?

Answer 59

A value that appears to solve an equation after algebraic manipulation but doesn't satisfy the original equation when substituted back in

Question 60

What's a prime number?

Answer 60

A positive integer greater than 1 that has exactly two divisors: 1 and itself. Examples: 2, 3, 5, 7, 11, 13...

Question 61

What is a composite number?

Answer 61

A positive integer greater than 1 that has more than two divisors (i.e., it's NOT prime). Examples: 4, 6, 8, 9, 10, 12...