IM 1 Final Exam Review (Fall)

Integer Operations and Simplifying Expressions:

100

-36/6

-6

200

Define the phrase, "like terms."

Terms that contain the same variable which is raised to the same power. (In algebraic like terms, only the numerical coefficients can vary). Constant terms are also like terms. 

300

-6+ (-9)=

 -15

400

Define the term, "coefficient."

A numerical or constant quantity placed before and multiplying the variable in an algebraic expression (e.g. 5 in 5x).

500

Identify the like terms, coefficients, and variables in the following expression:

3a+4-11+17a-b+6-13b

Coefficients: 3, 17, -1, -13

Variables: a, b

Like Terms: 3a - 17a; -b - 13b; 4 - 11 + 6

Solving Equations (one-step, multi step, variable on both sides, and types of solutions)

100

Solve for the variable: 

c-6=18

24

200

Solve for the variable: 4s=48

s=12

300

Solve for the variable: 4a-7=21

a=7

400

Solve for the variable: 

1/6 (18x + 24) = 12 - 4 (x-4)

What is: -8/7

500

Write the number of solutions for each problem:

(1) 3y+9=-12y+39
(2) 13k-5k+14=8k+7+9-2
(3) 8x+19=8x-2

problem 1 has 1 solution, problem 2 has infinite solutions, and problem 3 has no solutions.

Simplify the expressions: Combine Like Terms and use Distributive Property

100

What is the difference between problems that ask you to simplify versus problems that ask you to solve? 

Simplifying means to combine like terms by distributing and following PEMDAS-- you simplify expressions by making them smaller and doing all possible operations. 

Solving: you solve equations by doing inverse operations on both sides to get a variable by itself. 

200

Simplify the expression: 

4-(a+3b)+12-4a     

-3b+16-5a

300

Simplify the Expression

-4(6-9x+w)-4w+11

-13+36x-8w

400

-4(10-6x+w)-4w+3

 -37+24x-8w

500

-1/4(8x+16)-6x

 -8x-4

Inequalities:

100

When do you flip the sign when solving inequalities?

What is, multiplying or dividing by a negative?

200

Create an inequality from the following phrase: Three times a number is at least 27

What is, 3x is greater than or equal to 27

300

Identify whether the following include or exclude values:

(Parenthesis), [Brackets], open circle coordinate, closed circle coordinate, < , >, greater than or equal to, less than or equal to

Include:[Brackets], closed circle coordinate, greater than or equal to, less than or equal to

Exclude: (Parenthesis), open circle coordinate, < , >

400

Write the inequality that matches the word problem.

Cristiano Ronaldo has bet Lional Messi to see how can run the farthest. Ronaldo has already finished 8.75 miles and is running at a rate of .25 miles per minute. In order to win, Ronaldo must run at least 10 miles.

What is, 8.75+.25x is greater than or equal to 10

500

Solve the following inequality, write it in words, graph it, and provide the interval notation:

-4x+6 is less than or equal to 18

What is:

x is greater than or equal to -3

graph must show a closed circle plotted at -3 with an arrow pointing to the greater values 

[-3, infinity symbol)

Exponents

100

Rewrite 4³ (exponential form) in expanded form and simplified form.

Expanded: 4 x 4 x 4

Simplified: 64

200

Simplify where the exponent is positive 

(−2)⁻⁸ / (−2)⁻¹

1/ 2⁹

300

(6a^-1)^-2

a²/36

400

1. Find the equivalent values of 4⁶

4 Options:  

(1/4)^-6       4⁴ · 4²    (4·4)(4·4)(4·4)    4^12./4²

(1/4)^-6       4⁴ · 4²    (4·4)(4·4)(4·4)

500

Write a value in standard form and then re-write it in scientific notation. An extra 200 points will be awarded if you can also indicate which types of exponents lead to bigger numbers vs smaller numbers when writing values in scientific notation.

Student generated responses.

Bonus: When using scientific notation form, negative exponents lead to smaller (decimal) values and positive exponents lead to larger (whole number) values.