Unit 1 and Unit 2 Review

Unit 1 and Unit 2 Review

Interpret Graphs: Increasing, Decreasing, or Constant

Read a graph from left to right to determine if it is going up, going down, or constant (horizontal).

Multiple Choice

As the x-values increase, the y-values _____________ then ______________.

• increase, decrease

• decrease, increase

• increase, constant

• constant, decrease

Multiple Choice

The graph represents the distance a pilot is from the home airport during a period of time. Which describes the pilot’s distance in section II?

• constant

• increasing

• decreasing

• undefined

Converting Units

Converting one unit to another unit. Like 12 inches = 1 foot, 60 second = 1 minute.

Multiple Choice

Mia jogs 3 kilometers in 20 minutes. There are about 0.6 miles in a kilometer. What is Mia’s approximate speed in miles per minute?

• 0.09 mi/min

• 0.25 mi/min

• 1.8 mi/min

• 0.15 mi/min

Multiple Choice

Lola needs to sign 56 invitations. Using a stopwatch that measures time to tenths of a second, it takes Lola 3.5 seconds to sign her full name. Going by the accuracy of the stopwatch, which is the most accurate determination for the number of minutes Lola needs to sign all 56 invitations?

• 3.3 minutes

• 20.2 minutes

• 196 minutes

• 3.8 minutes

Parts of an Expression

Plug in variable for the solution to the question.

Multiple Choice

Simplify the expression shown.

What is the coefficient in the simplified expression?

3x + 2 – 3x + 7 + 5x

• 5

• 9

• 3x

• 5x

Multiple Choice

An electrician uses the expression 60 + 35h to determine the number of dollars to charge each customer. If h = 4, how much does the customer pay?

• $200

• $275

• $60

• $35

Multiple Choice

A plumber uses the expression 25 + 48h to determine the number of dollars to charge each customer. If h = 4, how much does the customer pay?

• $217

• $148

• $25

• $48

Simplifying Radicals

To simplify radicals, you must look for perfect square factors like 4, 9, 16, 25, 36, x^2 ...

Multiple Choice

Simplify

 $\sqrt{60x^8}$  

•  $2x^4\sqrt{15}$   

•  $3x^2\sqrt{30x^4}$  

•  $10x^8\sqrt{6}$  

•  $6\sqrt{10x^8}$  

Multiple Choice

Which radical is simplified correctly.

• neither

• both

Intro to Polynomials

The degree of the polynomial is simply the highest exponent. Terms are separating by plus and minus signs. Standard form is terms in descending order starting with the Degree.

Adding and Subtracting Polynomials

To Add polynomials, you just combine like terms.

To Subtract polynomials, you rewrite subtraction as addition, then combine like terms.

Multiplying Polynomials

Multiplying polynomials is like distributive property; whether you distribute once, twice, or three times.

After you distribute, combine like terms.

Multiple Choice

Which algebraic expression is a polynomial with a degree of 3?

• $4x^3-3x$

• $10x^{3\ }+\sqrt{x}$

• $8x^3-\frac{5}{x}+3$

• $6x^2-5x\ +\ 3$

Multiple Choice

What is the sum of the polynomials?

 $\left(7x^3-\ 4x^2\right)+\left(2x^3-4x^2\right)$  

•  $9x^3-8x^2$  
  

•  $9x^3$  
  

•  $5x^3-16x^2$  

•  $9x^6-8x^4$  

Multiple Choice

What is the difference of the polynomials?

 $\left(9x^2+8x\right)-\left(2x^2+\ 3x\right)$  

•  $7x^2+5x$  

•  $7x^4+\ 5x^2$  

•  $11x^2-5x$  

•  $7x^2+\ 11x$  

Multiple Choice

Find the perimeter of the shape. Figure not drawn to scale. Perimeter is adding all sides.

• 15x - 5

• $15x^2-5x$
  

• 20x

• 20x + 13

Multiple Choice

Using the rectangle, which expression represents the area (area = length times width)? 

•  $x^2-4x-12$  

•  $2x^2-12$  

•  $x^2+4x\ -12$  

•  $2x-4$  

Factoring with GCF (Greatest Common Factor)

Factor out the greatest number and the smallest variable that each have in common.

Factoring Trinomials (a=1)

When factoring trinomials, look for factors that multiply to equal the last number (constant) and add to equal the middle number (coefficient of x) in the trinomial. Then write your two binomials using x as the first terms and your factors as the second terms.

Multiple Choice

What is the greatest common factor of 4xy and 20y?

• 4y

• 20xy

• 2y

• xy

Multiple Choice

Factor the following polynomial by the GCF.

 $25x^3-30x^2+5x^{ }$  

•  $5x\left(5x^2-6x+1\right)$  

•  $x\left(25x^2-30x+5\right)$  

•  $5x\left(\left(5x^2-6x\right)\right)$  

•  $5x^2\left(5x-6\right)$  

Multiple Choice

Factor the following trinomials:

 $x^2-10x+16$  

• (x - 2)(x - 8)

• (x + 2)(x + 8) 

• (x - 4)(x - 4)

• (x - 16)(x + 1)

Function or Not a Function

Remember...a function is a relationship where every input (x) only has ONE output (y). To determine if a graph is a function, use the vertical line test.

Multiple Choice

Which set of values is a function?

• (9,5) (10,5) (9,-5) (10,-5)

• (3,4) (4,-3) (7,4) (3, 8)

• (6,-5) (7, -3) (8, -1) (9, 1)

• (2, -2) (5, 9) (5, -7) (1, 4)

Multiple Choice

• It is a function

• It is not a function

Multiple Choice

• It is a function

• It is not a function

Domain and Range

Domain refers to the x's or the inputs. Range is the y's or the outputs.

Domain and Range

Domain refers to the x's or the inputs. Range is the y's or the outputs.

Multiple Choice

What is the range?

• {1, 2, 3, 4, 5, 6}

• {2, 4, 8}

• {0, 1, 2, 3, 4, 5, 6}

• {-1, 0, 1, 2, 3, 6}

Multiple Choice

What is the domain?

• {0, 1, 2, 15}

• {3, 7, 11, 15}

• (0, 1, 2, 3}

• {3, 7, 11, 3}

Multiple Choice

What is the domain of the function?

• all integers

• all real numbers

• all integers between -5 and 3

• all positive numbers only

Function Notation

f(x) is y the (output) and (x) is the input. Like f(3) = 5;

3 is the x (input) and

5 is the y (output).

Multiple Choice

The table represents a function. What is x when f(x) = 5?

• -8

• 3

• -1

• -4

Multiple Choice

Consider the function represented by the table. What is f(0)? *

• 4

• 5

• 6

• 7

Linear Functions

Linear functions have a constant rate (same rate) of change.

Linear Functions

Linear functions have a constant rate of change (same rise over run).

Slope of a Linear Function

Use the formula to find the slope of two points. (Important note: y's in the numerator and x's in the denominator)

 $\frac{y-y}{x-x}$  

Multiple Choice

What is the rate of change of the line?

• $-\frac{2}{3}$

• -4

• $-\frac{3}{2}$

• $\frac{2}{3}$

Multiple Choice

Calculate the rate of change.

• 6

• -6

• $-\frac{1}{6}$

• $\frac{1}{6}$

Multiple Choice

Find the slope of the line that passes through the points 

(2, 4) and (6, 12).

• $\frac{1}{2}$

• 2

• $-\frac{1}{2}$

• -2

Slope-Intercept Form of Linear functions

y = mx + b where m is the slope and b is the y-intercept of the line.

To graph a line, first plot the y-intercept on the y-axis, then count your slope with rise over run.

Multiple Choice

Write the equation of the line.

• $y=-\frac{2}{3}x+4$
  

• $y\ =\ \frac{2}{3}x+4$

• $y=-\frac{3}{2}x+4$

• $y=\frac{3}{2}x+4$

Multiple Choice

Write the equation of the line.

• $y=-\frac{1}{3}x-2$

• $y=\frac{1}{3}x-2$

• y = 3x - 2

• y = -3x - 2

Point-Slope Form

To plug into the Point Slope form, you need the slope and an ordered pair from the line. (Important note: The ordered pairs are opposite when plugged into the Point Slope form).

Multiple Choice

Write the equation of the line

in Point-Slope form that goes through

the point (10,5) and has a slope of -3.

• y - 5 = -3(x - 10)

• y= -3x + 35

• y + 5= -3(x + 10)

• y= -3x - 35

Multiple Choice

Write the equation in point-slope form

of the line that passes through the point

(4, -7) and has a slope of -1/4.

• y + 7 = -1/4(x - 4)

• y - 4 = -1/4(x + 7)

• y + 7 = 4(x - 4)

• y - 7 = -1/4(x - 4)

Solving Linear Equations and Inequalities

First: Use the distributive property to simplify, if necessary. 

Second: Combine like terms on either side of the equals sign. 

Third: If variables are on both sides of the equation, move one the variables by using the subtraction or addition property of equality.

Third: Isolate the variable using the properties of equality. (Important note: When dividing or multiplying by a negative coefficient, you must change the direction of the inequality sign.)

Fourth: Check the solution.

Multiple Choice

Solve.

5x + 8 - 3x = -10

• -9

• -1

• 1

• 9

Multiple Choice

Solve.

4x + 6 = 2 - x + 4

• -2

• 0

• 4

• 6

Multiple Choice

Solve.

12x + 1 = 3(4x + 1) - 2

• infinite solutions

• no solutions

• x = 0

• x = 12

Multiple Choice

Solve.

3(x + 4) + 5 = 3x - 10

• One solution: x = 7

• No solution

• One solution: x = 10

• Infinite solutions

Multiple Choice

Solve.

6x + 8 - 4x = 10

• 1

• 2

• 9

• 0

Multiple Choice

Solve:

2(2t - 3) = 6(t + 2)

• 9

• -9

• 4

• -3

Multiple Choice

Solve the inequality.

-3n + 8 < 26

• n < - 6

• n > - 6

• n ≤ -10

• n > - 8

Multiple Choice

Solve the inequality.

28 − k ≥ 7(k − 4)

• k ≥ -7

• k ≤ -7

• k ≥ 7

• k ≤ 7

Multiple Choice

Solve the inequality.

7(x + 3) < 5x + 13

• x > -4

• x < -4

• x < 17

• x > -17

Multiple Choice

S = 3F - 25 Solve for F

•  $F\ =\ \frac{\left(S+25\right)}{3}$ 

•  $F=3S+25$ 

•  $F=\frac{S}{3}+25$ 

•  $F=3\left(S+25\right)$ 

Multiple Choice

Solve:

12x - 4y = 20 , for y

• y = 3x - 5

• y = -3x - 5

• y = -3x + 5

• y = 3x + 5

Solutions to Systems of Linear Equations 

Possible solutions:

Linear equations can cross at one solution (x, y).

Linear equations can be parallel (no solution).

Linear equations can be the same line (infinite solutions).

How to Solve Systems of Linear Equations: Graphing

First: Rewrite in Slope-Intercept Form: y = mx + b.

Second: Graph the first line. 

Third: Graph the second line. 

Fourth: Locate the intersection point (x, y). 

Fifth: Check the solution.

Multiple Choice

What is the solution to the system of linear equations? *

• (2, 0)

• (–3, 3)

• (0, 2)

• (3, 1)

How to Solve Systems of Linear Equations: Substitution

First: Plug in the isolated variable into the other equation. 

Second: Solve for the unknown variable.

Third: Plug in the solved variable to any original equation to find the other unknown variable and solve.  

Fourth: Check the solution. 

Multiple Choice

What is the solution to the system of equations?

y = –3x – 2

5x + 2y = 15

• (-40, 19)

• (-19, 55)

• (19, -40)

• (55, -19)

Multiple Choice

What is the solution to the system of equations?

y = 4x – 10

y = 2x

• (5, 10)

• (10, 5)

• -5, -10)

• (-10, -5)

How to Solve Systems of Linear Equations: Elimination

First: Create coefficients that are additive inverses on one of the variables. 

Second: Add the equations to eliminate the x-terms.

Third: Solve the new equation for y.  

Fourth: Substitute back into either original equation to find the value of x.

Fifth: Check the solution. 

Multiple Choice

What is the solution to this system of linear equations?

2x + 3y = 3

7x - 3y = 24

• (2, 7)

• (3, -21)

• (3, -1)

• (9, 0)

Multiple Choice

What is the solution to this system of linear equations?

3x + 6y = 45

2x - 2y = -12

• (-27, 6)

• (-1, 7)

• (1, 7)

• (27, -6)