Algebra 1 Review

​The Real Number System

Multiple Select

Select all sets that the number belongs to:

$$\frac{3}{5}$$  

• Irrational Number

• Rational Number

• Integer

• Whole Number

• Natural Number

Multiple Choice

Solve for a:

-3a + 8 = 14

• a = -2

• a = -7.5

• a = 2

• a = 6

Multiple Choice

Solve for a:

-8(-4+a) = - 3(2a+1) -19

• a = 27

• a = -27

• a = 3.86

• a = 1.67

Multiple Choice

Solve the equation. Check your solution.

• 80

• 45

• 180

• 5

Multiple Choice

• 19

• 9

• 2.5

• 5.96

​The cost of 7 cookies is $2.80, so 7x=2.80.

Also, x is $0.75 less than normal, so x=c-0.75

Putting it together, the equation is

7(c-0.75)=2.80

Multiple Choice

Speedy Boat Rental charges a $15 deposit fee plus $2 for each hour of use to rent a paddle boat. Write an equation for C, the total cost, to rent the boat for h hours.

• h = 2C + 15

• C = 15h + 2

• h = 15C + 2

• C = 2h + 15

Multiple Choice

The local service center advertises that it charges a flat fee of $50 plus $8 per mile to tow a vehicle. Write an equation that represents the total cost (C) of a service for m miles of towing.

• y = 8x + 50

• C = 50m +8

• y = 50x + 8

• C = 8m + 50

Multiple Choice

Solve for y:

5x - y = 16

• -y = 5x + 16

• y = 5x + 16

• x = 5y - 16

• y = 5x - 16

Multiple Choice

ax + c = R

(solve for x)

• ax = R + c

• ax = R - c

• x = a(R-c)

• x = (R-c) / a

Multiple Choice

-13t > 26

• t > -2

• t > 2

• t < 2

• t < -2

Multiple Choice

Select the inequality shown

• x > 5

• x ≥ 5

• x < 5

• x ≤ 5

Multiple Choice

Select the inequality shown

• x > 1

• x ≥ 1

• x < 1

• x ≤ 1

Multiple Choice

Which graph represents -5≤x≤5?

• Graph 1

• Graph 2

• Graph 3

• Graph 4

Multiple Choice

What inequality is graphed?

• 2 < x ≤ -3

• 2 < x < -3

• x > 2 or x ≤ -3

• x > 2 or x < -3

Multiple Choice

Find the slope

• -5/3

• -3/5

• 5/3

• 3/5

Multiple Choice

Find the slope of the line that passes through:

(6,7) and (4,2)

• 2/5

• -5/2

• 5/2

• -1/2

Multiple Choice

Use the given function or the graph to find the average rate of change

• 3

• -3

• 3/2

• -1/3

Multiple Choice

Which equation matches the graph?

• y= 2x + 5

• y= 2x

• y= -2x + 5

• y= -2x

Multiple Choice

Write the equation of the line.

• y = -1/3x - 2

• y = 1/3x - 2

• y = 3x - 2

• y = -3x - 2

Multiple Choice

For the equation

y + 1 = -3(x - 5),

the line contains the point (5, -1) and has a slope of?

• -1

• 1

• -3

• 5

Multiple Choice

For the equation

y - 3 = 2(x + 4),

the line has a slope of 2 and contains what point?

• (-4, 3)

• (3, -4)

• (-3, -4)

• (-4, -3)

Multiple Choice

Write the equation in point-slope form

for the line that contains the points

(3, -5) and (5, - 1)

• y - 5 = 2(x + 3)

• y + 5 = 2(x - 3)

• y - 3 = 2(x + 5)

• y + 3 = 2(x - 5)

Convert point-slope form to slope-intercept form:

SOLVE FOR Y!!

Multiple Choice

Solve for y:

5x + y = -10

• y = 5x + 10

• y = -5x - 10

• y = 2

• y = -5

Multiple Choice

Write the following equation in slope intercept form:

y - 3 = -2(x + 4)

• y=2x-5

• y=-2x+7

• y=-2x-5

• y=-2x +1

Multiple Choice

From the equation y = 3x + 18,  what is the value of the x-intercept?

• -6

• 6

• 18

• 3

Linear word problems

• Find the ONE TIME amount or STARTING VALUE and make it the y-intercept

• Find the amount that repeats and make it the slope (put it by the x!)

• Write the equation and solve!

Multiple Choice

The amusement park charges $20 to get in plus $1.50 per ride. Which linear equation below represents this relationship.

• y=1.5+20x

• y=1.5x + 20

• y = 20x + 1.5

• y= 21.5x

Multiple Choice

The total cost (y) at an amusement park can be modeled by y=1.5x+20 where x is the number of rides you ride. What is the price to ride one ride?

• 1.5

• 21.5

• 0

• 20

Solving systems of equations:

WHEN IN DOUBT, JUST USE DESMOS!!!!

Multiple Choice

Solve for x and y

3x + 2y = 16

7x + y = 19

• (-2,5)

• (-2,-5)

• (2,-5)

• (2,5)

Multiple Choice

Solve for x and y

2x − 3y = −1

y = x − 1

• (-2,-3)

• (0,-1)

• (3,4)

• (4,3)

Multiple Choice

The school that Stefan goes to is selling tickets to a choral performance. On the first day of ticket sales the school sold 3 senior citizen tickets and 1 child ticket for a total of $38. The school took in $52 on the second day by selling 3 senior citizen tickets and 2 child tickets. Which equations represents the system that could be used?

• 1s + 3c = 38

  2s + 3c = 52

• 3s + 1c = 38

  3s + 2c = 52

• s + c = 38

  s + c = 52

• 3s + 3c = 38

  1s + 2c = 52

Graphing Linear Inequalities:

DESMOS WILL DO THIS FOR YOU!

Multiple Choice

Which point is a solution?

• (0, 6)

• (-3, 4)

• (1, 0)

• (-4, 3)

Multiple Choice

• Function

• Not a Function

Multiple Choice

• Function

• Not a Function

Multiple Choice

Is y a function of x?

• function

• not a function

Multiple Choice

What is the range of the graph?

• y≥1

• x≥1

• All real numbers

• none of these

Multiple Choice

What is the domain of the graph?

• y≥1

• x ≥ 1

• All real numbers

• none of these

Multiple Choice

f(x) is the same thing as ______.

• y

• x

• input

• an equation

Multiple Choice

Evaluate f(-2) if f(x) = x²+ 3

***Desmos will evaluate functions for you! Type in the original function as f(x), then type in f(-2) on a new line!

• -1

• 1

• 7

• -7

Multiple Choice

What is x if
f(x) = -2?

• 4

• 0

• 3

• 8

How to find a linear regression equation:

• Enter the table of values into desmos

• On the next line, type EXACTLY this: y_1~mx_1+b

• Desmos will tell the value of m and b!

Multiple Choice

A restaurant sells pizza for the prices in the data table. Calculate the linear regression equation of the data.

• y = 1.5x + 12

• y = 12x + 1.5

• y = 0.67x - 8

• y = -8x + 0.67

Correlation Coefficient

• Desmos also gives you another number: r. This is the correlation coefficient.

• A positive r value is a positive correlation.

• A negative r value is a negative correlation.

• |r|=1 is a perfect correlation

• r=0 is no correlation at all

• Closer to 1 or -1 means STRONG

• Closer to 0 means WEAK

Multiple Choice

Simplify the expression: $$\frac{x^8}{x^2}$$  

• $$x^6$$  

• $$x^2$$  

• $$x^4$$  

• $$4x$$  

Multiple Choice

Simplify 6^-4

• 6⁴

• 1/6⁴

• 1/6

• 6²

Multiple Choice

Simplify (3x)⁰

• (3x)¹

• 0¹

• 1

• 3x

Multiple Choice

(3xy)²

• 9x²y²

• 6x²y²

• 3xy²

• 3x²y²

Multiple Choice

x⁵ * x⁴

• x⁹

• x²⁰

• 2x⁹

• 9x

Multiple Choice

Simplify the expression: $$\frac{12x^9y^4z^2}{24x^3y^4z^6}$$  

• $$2x^3z^3$$  

• $$\frac{x^6}{2z^4}$$  

• $$\frac{x^3}{2z^3}$$  

• $$\frac{2x^6}{x^4}$$  

Exponential Functions:

The initial value (y-intercept) happens when x=0, so it's 2.​

Notice the y values are multiplying by 3 every time, so the multiplier is 3.

Therefore the equation is y=2(3)^x

Multiple Choice

The equation for this table is:

x y

0 50

1 150

3 450

4 1350

• y = 3x + 50

• y = 50^x

• y = 3^x

• y = 50(3^x)

Multiple Choice

Which of the following functions shows an initial amount of $15 and an increase of 35% each year?

• y = 15(35)^x

• y = 15(1.35)^x

• y = 15(0.35)^x

• y = 35(1.15)^x

Multiple Choice

Suppose a culture of bacteria begins with 5000 cells and dies by 30% each year. Write an equation that represents this situation.

• y=5000(0.7)^x

• y=30(5000)^x

• y=5000(1.3)^x

• y=5000x^x

Multiple Choice

Write the explicit rule for this situation.

• f(n) = 35 + 3(n − 1)

• f(n) = 35 −3(n − 1)

• f(n) = 3 + 35(n − 1)

• f(n) = −3 + 35(n − 1)

Multiple Choice

Write an explicit rule for the general term of the sequence 5, 15, 45, . . . ?

• a_n = a_n-1 x 3

• a_n = 5(3)^n-1

• a_n = 3(5)^n-1

• a_n = 5 + (n-1)3

Multiple Choice

Does the following table represent a geometric sequence or an arithmetic sequence?

• geometric

• neither

• arithmetic