Algebra

Question 1

a^2 - b^2 =

Answer 1

(a-b)(a+b)

9x^2 - 4y^2 = (3x)^2 - (2y)^2 = (3x-2y)(3x+2y)

Question 2

ax^2 + bx + c factors into

Answer 2

x^2 - 6x + 8 = (x - 4)(x - 2)
x^2 - 3x - 18 = (x + 3)(x - 6)

The first two terms need to multiply to align to the first term of the trinomial

The last two terms need to multiply to align to the last term of the trinomial

The sum of the products of the inner and outer terms must equal the second term in the trinomial

Question 3

Trinomials of the form a^2 + 2ab + b^2 factor into two identical binomials

Answer 3

The first term is the square root of the first term in the trinomial and the second term is the square root of the last term in the trinomial

Question 4

If xy = 0

Answer 4

Then x or y = 0 or both x and y = 0

Question 5

To solve an equation that = 0

Answer 5

Set each factor = 0 and solve each mini equation

Question 6

Quadratic equations

Answer 6

Is one in which variables are squared:

1. Put the equation in standard form of ax^2 + bx + c = 0
2. Factor the equation into linear terms
3. Set each linear factor equal to 0 and solve

Question 7

Dividing By 0

Answer 7

When solving quadratic or linear equations - make sure the solutions don’t result in a situation where we are dividing by 0

Question 8

Taking the square root of two sides of an equation

Answer 8

Need to make it + or - the square root of the result

Question 9

Simultaneous Equations

Answer 9

You can solve for these in two ways:

1. Substitution - Solve for one of the variables and plug it into the other equation. Use that to solve for one of the variables and then plug it into the other equation
2. Addition - you can add the two equations to each other to cancel out the terms

Question 10

When multiplying or dividing by negative numbers within inequalities you need to

Answer 10

Reverse the direction of the sign

Question 11

When solving for inequalities that include quadratic equations —

Answer 11

There is always two potential answers

Question 12

If x

Answer 12

x

Question 13

If a

Answer 13

a+x

Question 14

If x

Answer 14

1/x > 1/y

Question 15

To solve word problems follow the following steps

Answer 15

1. determine what is being asked for
2. determine all of the givens
3. sketch the relationships presented
4. decide which formulas are relevant
5. set up algebraic equations
6. solve and make sure your solution makes sense

Question 16

Distance =

Answer 16

Rate x Time

Question 17

Rate =

Answer 17

Distance / Time

Question 18

Time =

Answer 18

Distance / Rate

Question 19

Work problems where people work at the same rate

Answer 19

Inversely related proportions because the more workers the less time it will take to get the job done

Align common terms on same side of the equal sign

Question 20

Work Problems where the workers work independently but at different rates

Answer 20

Determine the rate per hour for each person and then add the two rates together to get the rate per hour for the team combined.

The rate * time to do the job = 1 job

Question 21

Set Problems

Answer 21

• Draw relationship diagrams

Question 22

Set Problems - Combinations

Answer 22

IF you are asked for the number of combinations then multiple the elements

Ex - 3 Sets of funny teeth, 6 pairs of unusual eyes, and 9 wigs - 3 x 6 x 9 = 162 possible combinations