Algebra 1 EOC Equations

Algebra 1 EOC Equations

by Darryl Padgett

FOIL Method

Algebra 2

Multiple Choice

What is the product of the following expression? 

$$\left(3x+6\right)^2$$  

• $$6x^2+12$$  

• $$9x^2+36$$  

• $$9x^2+18x+36$$  

• $$9x^2+36x+36$$  

Multiple Choice

Simplify the following expression by combining like terms:
3(2x - 4) + 6x - 1

• 12x - 13
• 12x - 5
• 11x - 2
• -x

Multiple Choice

Simplify:
4(8x + 1) - 6(1 - 8x)

• -80x - 2
• 80x + 2
• -80x + 2
• 80x - 2

Multiple Choice

In the diagram below, the dimensions of the large rectangle are (3x-1 ) by ( 3x+7) units. The dimensions of the cut-out rectangle are x by 2x+5 units. Which choice expresses the area of the shaded region, in square units? 

• $$x^2+23x-7$$  

• $$x^2+13x-7$$  

• $$7x^2+23x-7$$  

• $$7x^2+13x-7$$  

Multiple Choice

Add or Subtract to Simplify:
(5x + x² - 4) - (4x - x² + 6)

• 2x² + x + 2 
• x + 2
• 2x² + x - 10 
• x - 10 

Multiple Choice

There are 60 students going on a field trip to the chocolate factory. The students are from three different classes. Mrs. Hooper's class has 24 students and Mr. Gomez's class has 18 students. Which of the equalities correctly describes the students and could be used to solve for how many students are from Mr. Anderson's class? (Let A = the number of students in Mr. Anderson's class.) 

• A + 18 = 24

• A + A + A =60

• 60 - 18 = A - 24

• 24 + 18 + A = 60

Multiple Choice

Student council is renting a tent for $350 for an upcoming student fair. Each student attending the fair will pay $0.50. All other attendees will pay $2.25 each. If 200 students attend the fair, which inequality can be used to determine the number of "other" attendees, a, needed to cover the cost of the tent? 

• $$\left(0.50\right)\left(200\right)-\ 2.25a\ \ge350.00$$  

• $$(0.50)(200)+2.25a\ \ge\ 350.00$$  

• $$0.50a\ -\ \left(2.25\right)\left(200\right)\ \ge350.00$$  

• $$0.50a\ +\ \left(2.25\right)\left(200\right)\ge350.00$$  

Multiple Choice

Solve for x: 3(2x-1) - 10 = 8 + 5x

• -7

• -3

• 19

• 21

Multiple Choice

Solve for x: 4(x+5) = 3(x-2) - 2(x+2)

• x = -1

• x = -4

• x = -6

• x = -10

Multiple Choice

What is the value of x in the equation?

$$\frac{3}{4}x\ +2\ =\ \frac{5}{4}x\ -6$$  

• x = -16

• x = 16

• x = -4

• x = 5

Solving Inequalities

When solving inequalities the steps are the same as solving a regular equation, only difference is if you divide or multiply by a negative number the inequality sign flips directions.

Solving Inequality Steps

• Get rid of all Parentheses

• Combine like terms

• Move all x terms to the left hand side (LHS)

• Move all constants to the right hand side (RHS)

• Get rid of the x’s coefficient by doing the opposite operations (multiplication -> division or division -> multiplication)

• BE CAREFUL WHEN DIVIDING/MULTIPLYING BY A NEGATIVE

Example 1: Solving and inequality

- 8x + 2x - 16 < - 5x + 7x

Combine Like Terms and simplify: (-8x + 2x) - 16 < (-5x + 7x)

-6x - 16 < 2x

​Gather variables on LHS and numbers on the RHS side:

-6x - 16 - 2x < 2x - 2x

-8x - 16 < 0

-8x - 16 + 16 < 0 + 16

-8x < 16

​-8x < 16

-8 -8

dividing by a negative number implies that you have to flip the sign

x > -2

​

Multiple Choice

$$Solve:\ 5\left(2+2x\right)>90$$  

• $$x<8$$  

• $$x<-36$$  

• $$x>8$$  

• $$x>-31$$  

Multiple Choice

$$Solve\ for\ n:\ -7\left(n-6\right)<91$$  

• $$n<7$$  

• $$n>7$$  

• $$n<-7$$  

• $$n>-7$$  

Multiple Choice

$$Solve:\ -82>2\left(n-5\right)+7n$$  

• $$n>-25$$  

• $$n<-25$$  

• $$n<-8$$  

• $$n>-8$$  

Fill in the Blanks

Solve the following inequality for b, work carefully and completely. 

4b - 12 - 5b < 9b + 8

Multiple Choice

Which graph represents the solution set of the inequality  $$3x-4y\le24$$ ?

Multiple Choice

Which graph best represents the solution to this system of inequalities? $$\left\{2x\ge y-1\ \ and\ 2x-5y\ \le10\right\}$$  

A Literal equation is easy if you know your basic operations and how to apply them to equations.

By now you know the basics,

but let us review.

Why do we even need this?

Some common literal equations involve converting temperature from celsius to fahrenheit or vice versa. There are also lots of literal equations in geometry. They will save you time.

Maybe you should try a few yourself.

Use paper and pencil if needed.

Multiple Choice

Solve for m in:      $$y=mx+b$$  

• $$m=x+b-y$$

• $$m=y-b-x$$

• $$m=\frac{x-b}{y}$$

• $$m=\frac{y-b}{x}$$

Multiple Choice

Solve the equation for 'a'. $$u=b-ka$$  

• $$a=ku-kb$$  

• $$a=\frac{-u-b}{k}$$  

• $$a=\frac{-u+b}{k}$$  

• $$a=\frac{k}{-u+b}$$  

Multiple Choice

Solve the equation for 'a'. $$\frac{a}{c}=\frac{d}{r}$$  

• $$a=-\frac{r}{cd}$$  

• $$a=cd+r$$  

• $$a=-\frac{cd}{r}$$  

• $$a=\frac{cd}{r}$$  

Multiple Choice

Solve the equation for 'x'.

$$z=-5mx-4yx$$  

• $$x=\frac{z}{5m+4y}$$  

• $$x=\frac{z}{-5m-4y}$$  

• $$x=-\frac{z}{-5m+4y}$$  

• $$x=-\frac{z}{-5m-4y}$$  

Multiple Choice

Bruce bought two books. One book costs $4.00 more than three times the other. Together, the two books cost him $72. Choose the equation that represents this scenario.

• 3+4x=72

• 3x+4+x=72

• 5x-72=4

• 3+x+5x=72

Lets take a look!

One Solution looks like..

​

​

​ x = 4 and y = 5

Multiple Choice

The system 5y = 8x + 8 and 7y = -8x + 16 is graphed as shown. Which choice is the point of intersection? 

• $$\left(\frac{1}{2},\ 2\right)$$  

• $$\left(\frac{1}{3},\ 2\right)$$  

• $$\left(\frac{1}{4},\ 2\right)$$  

• $$\left(\frac{3}{4},\ 2\right)$$  

Multiple Choice

These two lines intersect at _____.

• (4, -2)
• (4, 2)
• (-2, 4) 
• No solution

Multiple Choice

This system has _____ solutions

• no
• 1
• 2
• Infinitely many

Multiple Choice

Solve the system of equations by graphing.

• (-1, 4)

• (1, 0)

• No Solution

• (0, 2)

Multiple Choice

Solve the system of equations by graphing.

• No Solution

• Infinitely Many Solutions

• (-1, 1)

• (-2, -2)

Multiple Choice

Sandy has a total of 35 coins in her money jar. If Sandy's jar contains only nickels and dimes and the value of all the coins is $2.50, how many nickels does Sandy have? 

• 5

• 15

• 20

• 30

Multiple Choice

The enrollment at High School R has been increasing by 20 students per year. Currently High School R has 200 students attending. High School T currently has 400 students, but its enrollment is decreasing in size by an average of 30 students per year. If the two schools continue their current enrollment trends over the next few years, how many years will it take the schools to have the same enrollment? 

• 4 years

• 5 years

• 10 years

• 20 years

What is a system of equations?

• two or more equations solved simultaneously to see if they have a common solution

• can be the same type of function (as in both linear) or a combination of types of functions (as in linear and quadratic seen in the image)

Multiple Select

At which point do the two equations 3x + 5 = y +4x and y = x² intersect? Select all that apply.

Hint simplify the two equations and graph the solutions or simply look at the graphs.

• (1.8, 3.2)

• (-2.8, 7.8)

• (0, 5)

• No solutions