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Mr. GomezAlgebra 9th GradeName___________________________ Date______________________

Important Concepts, Procedures, and Vocabulary

January of 2011-2012 Midterm Exam Review

Unit 1: Expressions

Order of Operations:

List the order of the operations.

1. Parentheses

2. Exponents

3. Multiplication and division at the same time from left to right

4. Addition and subtraction at the same time from left to right

You will have to deal with sign numbers in the order of operations.

1. 2.

3. 4.

Mr. GomezAlgebra 9th Grade

Exponents:

List and describe the exponent rules—there are five.

1. Product Rule: if the bases are the same and they are being multiplied, add the exponents.

example: x 5 x 7 = x 5+7 = x 12

2. Quotient Rule: if the bases are the same and they are being divided, subtract the exponents.

example:

3. Power Rule: if an exponent is raised to a power, multiply the exponents.

example:

4. Zero Exponent rule: anything raised to the zero power is one.

example:

5. Negative exponent rule: if an exponent is negative, it is equivalent to the reciprocal raised to the same power, only positive

Example: or

Simplify the following expressions:


11. 12.

11. 12.

13. 14.

Expressions:

Absolute value is always positive. Understand that when we are looking for the absolute value is

the distance that number is from zero.

The square root of a number is what two identical numbers when you multiply them give you

that number. Know perfect squares up to 15.


Ex.

For non perfect square you need to you estimate which two perfect squares that number fall in

between.

Ex.

Evaluate the following using the order of operations.

5. Find 6. Find

7. Between which two whole numbers does the lies?

8. Between which two whole numbers does the lies?

9. What is the absolute value of 131? 10. What is the absolute value of -121?

Unit 2: Equations

Translate verbal phrases into equations

Translate verbal phrases into linear equations. (Use the table to identify what key word mean the arithmetic operation. Also, try and understand what your initial value is and what your rate of change is.)

Mr. GomezAlgebra 9th GradeCheck if a given value can be a solution to the given algebraic equation.

Use mental math to solve problems.

Solving Equations

What’s needed for something to be an equation? (I can think of four things…)

1. An equal sign

2. Variable

3. Number

4. OperationsSolve the equation.

1. Balance 2. Always do the inverse operation.3. Combine like terms if on the same side or on different sides.4. Make sure that you are following the rules of sign numbers.

When you’re solving equations, what do you look for in what order? Consider one or more of the following examples if that is helpful:

A.B.C.

D.

Solve the following equations and check your work. Show your work.

Mr. GomezAlgebra 9th Grade15. 16.

17. 18.

19. 20.

Mr. GomezAlgebra 9th Grade21. 22.

Find the ratio and write and solve proportion problems.

Find ratio Writing proportions make sure that you are consistent.Solve proportions using cross-product. Answer the following proportion problems. Show your work.

23

.

24.

25. 26.

Find the percent of a number.

Use formula to find the part, whole or percent.


Understand that the part is the piece and the whole is the entire thing.

Use cross product to solve the proportion.

27. What is 38% of 186? 28. 56 is 46% of what number?

29. 30.

Solve percents problems in the context of amounts of increase or decrease.

Use the formula

Determine if it’s an increase or a decrease from the original to the new. Then figure out the difference between the original and the new. Fill in what you know, and solve for the percent. Then write your answer as a sentence!

Mr. GomezAlgebra 9th Grade31. The average price of a new DVD in 1998 was $24. In 2003, the average price was 21. Find the percent of change?

32. In 2009 Playstation 3 cost $542 dollars. After that one year in 2010 the new price for the Playstation 3 is $3000 dollars. Find the percent of decreased?

Find the new amount:

Use the percent of change formula and fill in the information you have. Use cross product to find the missing value. Then either add or subtract depending on what you are looking for (increase or decrease)

33. Increase 14 by 45%. 34. Decrease 108 by 90%

35.Original Price: $48Discount: 20%Sales tax: 6.25%

36.Original Price: $268Discount: 35%Sales tax: 6.25%

Mr. GomezAlgebra 9th GradeUnit 3: Equations with more than one solution

Absolute Value

Once you have | | = #, break the equation into its two parts, the negative and the positive. And solve.

|x – 4| = 10

x – 4 = -10 x – 4 = 10 +4 +4 +4 +4x = -6 x = 14

x = -6 or 14

Absolute value equations have no solution when… they equal a negative number!

Solve the following absolute value equations.

37. 38.

39. 40.


Inequalities

Inequality Symbols and Graphs

1. < o (open circle to the left)

2. ≤ • (closed circle to the left)

3. ≥ • (closed circle to the right)

4. > o (open circle to the right)

Explain the difference between the Multiplication and Division Properties of Equality and the Multiplication and Division Properties of Inequality.

With the Multiplication and Division Properties of Inequality, you can only multiply and divide by POSTIIVE numbers.

When do you need to change the signs? Show an example.

You need to change the signs when the variable is negative.Example: -4x > 12 4x < -12 (changed all of the signs)

When do you need to flip the inequality over? Show an example.

You need to flip the inequality over when the variable is on the RIGHT.

Mr. GomezAlgebra 9th GradeExample: 18 < 6f 6f > 18 (make sure it is still opening towards

Solve and graph the following inequalities.

41. 42.

43. 44.

Solving compound inequalities

Mr. GomezAlgebra 9th GradeSolve each individual inequality and graph your solution according to the compound word connector “and” or “or”.

If the compound word connector is “and” then you graph what both solutions have in common (what is in between) on the number line.

Ex.

Ans:

If the compound word connector is “or” then you graph both solutions on the number line.

Ex.

Ans:

Solve the following compound inequalities

45. 46.

47. 48.


Solving absolute value inequalities

Make sure that the inequality is by itself.

You have to write two inequalities. When you write the second inequality you need to make sure that you change the inequality to its opposite and change the sign of the number after the inequality.

Use the connector word according to the initial inequality if it’s greater use “or” if it’s less than use “and”.

Graph both solutions according to the connector word.

Ex. Ex.

Solve the following absolute value inequalities and graph your solution set.

49. 50.


51. 52.

Solving inequality word problems.

Use the table to write the inequality

Symbol What it means

Similar words that


mean the same.

< Is less than Fewer than > Is greater

than More than

Is less than or equal to

At most, no more than

Is greater than or equal to

At least, no less than

Label your variable

Look for the initial value and the rate of change

Solve the inequality.

Graph your solution on a number line.

Write a complete sentence that answers the question.

Answer the following questions.

53. Keith has $500 in a savings account at the beginning of the summer. He wants to have at least $200 in the account by the end of the summer. He withdraws $25 each week for food, clothes and movie tickets. Write an inequality that represents Keith’s situation. How many weeks can Keith withdraw money from his account? Justify your answer.


54. Chris has $200 in a savings account at the beginning of the summer. He wants to have a no less $600 in the account by the end of the summer. He adds $20 each week from his allowance. Write an inequality that represents Chris’s situation. How many weeks will it take Chris to reach his goal? Justify your answer.

55. Keith withdraws $60 each week for food, clothing, clothes and movie tickets. He has $800 in a savings account at the beginning of the summer. He wants to have at least $330 in the account by the end of the summer. Write an inequality that represents Keith’s situation. How many weeks can Keith withdraw money from his account? Justify your answer.


Good luck and study!!!!!!!!

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