SAT Prep

A.) Vocabulary Monomials – Any number or variable or product of number(s) and variable(s) Ex. Evaluate when a = -4 and b = 0.5.

B.) Simplifying Polynomials !!**ADD OR SUBTRACT LIKE TERMS ONLY **!! Like terms – same variable(s) and same exponent(s). Ex. Simplify Binomials – 2 monos separated by +/- Trinomials – 3 monos separated by +/-

Multiplying Monomials - Mult. Coeffecients and add exponents of like bases Ex. Simplify the following:

Dividing Monomials- Div. coeff. And subtract exponents of like bases Ex. Simplify the following:

C.) Factoring and Expanding FOIL – First Outer Inner Last Ex. Expand the following:

Three important binomial products

Ex. If (a – b) = 17.5 and (a + b) = 10, what does a 2 – b 2 =? Ex. If x 2 + y 2 = 36 and (x + y) 2 = 64 what is xy?

D.) MORE FACTORING GCF, Common Monomials, and Product/sum table Ex. Find all real solutions of FACTORS (-6)SUM (-1)

Ex. Find an equivalent expression for Ex. Find the sum of reciprocals of

A.) Single Equations Ex. Solve the following for x:

Ex. If a = b(c + d), solve for d in terms of a, b, and c. Ex. If, then x = ?

Ex. If 2x – 5 = 98, then 2x + 5 = ? Ex. For what value of x is ?

Ex. If, solve for x. Ex. If, then x = ?

Ex. Find the largest value of x that satisfies. Ex. If, what is w?

B.) Systems of Equations/Inequalities Use appropriate method Substitution, elimination, graphing, matrices Ex. Solve for x and y if x + y = 10 and x – y = 2.

Ex. If 3a + 5b = 10 and 5a + 3b = 30, what is the average of a and b?

READ, READ, READ, READ, and READ AGAIN!!! A.) Strategies 1.) Substitution i.e., “Plugging it in” Why??? - Numbers make more sense than letters. - Choose numbers easy to work with, but not 0 and ,3,5, etc. are good choices for algebra problems. - Multiples of 100 for percent problems. - Multiples of 60 for time problems.

When??? -You have NO idea how to do the problem -There is a variable in the question and the answers are all numbers -The problem is about “some number” and you have no clue as to what that number is.

B.) Examples Ex. The price of an item in a store is d dollars. If the sales tax on the item is s%, what is the total cost of x such items, including tax? a.) b.) c.) d.) e.)

Let’s choose some numbers for d, s, and x. The total price for 1 item = The total price for 10 items = Which choice gives us $105.00? – Start with A Obviously, B.) is out

C.) D.) E.)

Ex. Vehicle A travels at x miles per hour for x hours. Vehicle B travels a miles faster than Vehicle A, and travels b hours longer than Vehicle A. Vehicle B travels how much farther than Vehicle A, in miles? a.) b.) c.) d.) e.)

Let’s choose some numbers for x, a, and b. Vehicle A = Vehicle B = Vehicle B – Vehicle A = By substitution – A.)