In Mathematics, a Collection of Elements S Called a Set

Review For Exam 3 HOMEWORK: Chapter Test: Pg 356 - 358 # 11 – 22, 24 - 38 Chapter Test: Pg 421 # 1 – 23 Rest of ALEKS Pie! Study for Exam! Practice all types of problems again!

Factoring: (use Flow chart) *ALWAYS take out GCF first! * Ask how many terms - If binomial, check for forms a2 – b2 a3 – b3 a3 + b3 a2 + b2 - If trinomial, -Check for perfect square -use Trial & Error or A/C method -If a(something)2 + b(something) + c use a u-subst - If 4 or more terms Factor by grouping Reorder terms if this doesn’t work Try grouping differently (look for difference of squares or perfect squares)

** ALWAYS ASK “DOES IT FACTOR FARTHER?” If yes, keep going!

Review For Exam 3 Equations vs. Expressions

Expressions HAVE NO = SIGN. When simplifying, you will usually still have variables left.

When adding/subt. Fractions you must put EACH over the LCD. The final answer still has a denominator unless it cancels with something in the numerator in the last step.

When simplifying a complex fraction, simplify one step at a time and REWRITE EVERYTHING as you do it so you do not lose anything

If you want to do factoring off to the side, rewrite the step replacing it with the factored expression

Make sure expressions are factored completely!

Watch out for OPPOSITES!! a – b = - (b – a)

Remember, 1 is a factor of everything. If you cancel all other factors, you still have a 1!

You CAN NEVER cancel over addition/subtraction. Before you can cancel, you MUST have everything completely factored and written as products!

When dividing, rewrite as a multiplication by the reciprocal first BEFORE you cancel anything.

Review For Exam 3 Equations HAVE an = sign

NEVER drop the = sign. Recopy it each step!

When you solve with the zero property, you MUST have zero on one side and the other completely factored. Note: you cannot do the following x(x-1)=2 does NOT mean x=2 or x-1 = 2

You must get 0 on one side, distribute out, factor and then use the zero property.

If x2=4x, you CANNOT divide by x. If you do, you just divided by zero! You MUST get 0 on one side and factor!

Your final answer it typically a number/s or no solution.

When solving a rational EQUATION you MULTIPLE by the LCD (NOT put each fraction over the LCD.)

When solving literal equations, make sure you clear fractions; get the terms with the variable you want on one side and the terms without that variable on the other. Then if there is more than one term with the variable you want in it, you MUST FACTOR it out! Practice these from your TEXT!

Review For Exam 3 Domain: The set of all inputs

2x  5 Example: Find the domain of f (x)  . Give 6x 3  22x 2 8x your answer in interval notation.

Remember, the domain of an expression is the domain of the original expression BEFORE you canceled.

Review For Exam 3 Applications:

QUADRATICS: Geometry applications of quadratics Given Area and relationship between 3 sides, find the dimensions. (Like # 61 – 67, 75 in 4.8)

Rocket Launching problems (Like Example 11 in sec 4.8)

Number applications of quadratics Given the relationship between 2 numbers, find #’s. (Like # 53 – 59 in 4.8)

Pythagorean THM: (Like # 71 - 73 in 4.8)

RATIONAL EQUATIONS:

Proportions (Like # 27 – 40 & Skill practice problems in sec 5.6)

Distance/Rate Time (Like # 45 – 56 & Skill practice problems in sec 5.6)

Work applications: (Like #57 – 64 in sec 5.6) & ALEKS

Similar Triangles: (Like # 41 – 44 & Skill practice problems in sec 5.6)

Review For Exam 3 Problems From Quiz 5# 1 - 4: 2x 4 9 11x Quiz 5 #1) Solve   algebraically. x  3 x  3 x 2  9

Review For Exam 3 Quiz 5 #2) A rectangular pen is to contain 18 yd2 of area. If the width is 5 yds less than twice the length, find the dimensions of the pen.

Review For Exam 3 4 2  w  3 w  3 Quiz 5 #3) Simplify 17  w using METHOD I  2 9  w2

Review For Exam 3 x  y Quiz 5 #4) Solve  z for x. xy

Review For Exam 3 Additional Examples: 2x 2  5xy  2y 2 x 2  xy  2y 2 Sec 5.2 #28  4x 2  y 2 2x 2  xy  y 2

x  y Answer: x  y

Review For Exam 3 x 2 13x 18 x 1 Sec 5.3 # 48  x 2  9 x  3

2x  5 Answer: x  3

Review For Exam 3 The only way to master this material is to PRACTICE PRACTICE PRACTICE!

Make sure you can do all of the problems from the lecture notes BY YOURSELF without help.

After you have completed all of your topics in your chapter 5 pie, go to the review mode and have ALEKS make you some fresh practice problems for the topics that were most difficult for you.

Do the chapter test problems as a practice test. Make up a practice test with a study partner and take each others.

Make sure you can do all of the problems from the quizzes!

Go to the Review Session Monday night!