CCAA Unit 1-4 Fall Final Review

Name _____________________________

Period _____ Date ________________

2016 Fall Final Exam Review

Unit 1 Review

a. Statement Reason

3(x – 4) – 1 = 11

Distrib. prop. 3x – 13 = 11

Addition prop.

x = 8

b. Statement Reason

5 – 2(x + 1) = x +

6 Given

Distrib. prop. Combine like

terms 3 = 3x + 6

Subtraction prop. Division prop.

x = -1

2. Justification. State the reason that justifies each step, based on the given. Given 3x + 4x – 5 = 9x + 2 Given 4(x + 2) – 8 = 12x

a. 7x – 5 = 9x + 2 d. 4x + 8 – 8 = 12x

b. 3x + 4x = 9x + 7 e. 1(x + 2) – 2 = 3x

c. 4x – 5 = 6x + 2 f. 4(x + 2) = 12x + 8

You MUST write an equation and solve your equation to answer the question. Do NOT guess-and-check.

3. Equation Word Problems: Basic Translating. a. A number is increased by 8, then divided by

2. The result is 16. Find the number. b. 10 more than half of a number is the same as two less than twice the number. Find it. Equation:

Solution:

Equation:

4. Equation Word Problems: Consecutive Integers. a. Find a set of three consec. even integers

whose sum is 288. b. In a list of 7 consec. integers, the first and the last is 518. Find the largest.sum of the Equation:

Solutions:

Equation:

Solution:

5. Equation Word Problems: Geometry and General. a. The Raiders scored 24 points, which was

ten points more than twice the Eagles’ score. What was the Eagles’ score?

b. Di spent $65 on clothes, then spent half her remaining money on groceries. She now has $138. How much did she start with?

Equation:

Solution:

Equation:

Solution:

c. Walt has $800 in a savings account. Each month, he deposits $60 in the account. After how many months will he have $1700 in the account?

d. In a certain isosceles triangle, the two

congruent sides are each twice as long as the third side. The triangle’s perimeter is 45 cm. Find all three side lengths.

Equation:

Solution:

Equation:

Solution:

6. Inequalities: Solving. Solve and graph each inequality. Answer in inequality notation and as a graph.

a. 3 – 2(x + 1) > 5 b. 5x ≥ x + 8  3(x – 4) < 12

inequality: _________________

number line:

c. -8 < -4x + 12 ≤ 28 d. 4 – 5x > 14  3x + 2(x – 1) > 43

inequality: _________________

number line:

inequality: _________________

number line:

7. More Solving. Complete each problem by filling in the box with < > ≤ or ≥. CIRCLE problems where you had to switch the symbol’s direction.

a

. -4x < 8 b. 3x ≤ -12 c. 5 ≥ x d. x + 2 >9

x -2 x -4 x 5 x 7

8. Solutions of Inequalities: Notation. Convert each answer into the two missing forms.

Number Line Inequality Notation

< > ≤ ≥ Interval Notation( ) [ ] -∞ ∞

a. _{-2 3}

b. 3 < x < 9

c. (-∞, 7]

9. Inequality Word Problems: Basic Translating. (There is no work to show for these problems.)

a. Terry is at least three times as old as Lee. Lee is L years old. Represent Terry’s age,

T, with an inequality.

b. The number of girls in the class is no more than half the number of boys. There are B

For #10-11, you MUST write an inequality and solve your inequality to answer the question. SHOW ALL WORK.

10. Inequality Word Problems: Basic Translating. a. Three more than the quotient of a number

and four is less than 17. b. A number The result is between 9 and 21 ( inclusive).x is doubled, then increased by 5. Inequality:

Solution:

Inequality: Solution:

11. Inequality Word Problems: General. a. A cell phone plan charges $34 per month

plus $0.08 per text message. You are allowed to spend no more than $50 per month on your phone bill. What is the maximum number of texts you can send in a month?

b. On Jeopardy, Kyle has x dollars right now. He wants to get the daily double (doubling his score) then get the last $1000 question right. In the end, he wants to have at least $10,000. Describe possible values for x that would make this happen.

Inequality:

Solution:

Inequality:

Solution:

12. Unit Conversions. Round to TWO DECIMAL PLACES where necessary. INCLUDE UNITS. a. Convert 1.8 km to feet. b. Convert 2 quarts to fluid ounces.

c. The fastest pitch in baseball history was measured at 105 miles per hour. How fast is this in feet per second?

d. If 1 British pound (₤) equals $1.62 and 1 Euro ( €) equals $1.31, how many Euros are in 1 British pound?

13. Unit Rates. Round to TWO DECIMAL PLACES where necessary. INCLUDE UNITS. a. If 3.5 pounds of ground beef costs $8.47, how

much would 2 pounds cost? b. If a train travels 318 miles in four hours, how many minutes would it take to go 500 miles?

c. Who swam faster: Michael Phelps, who swam 400 meters in 243.84 seconds, or Sun Yang, who swam 1.5 kilometers in 14.52 minutes? Remember to show work!

14. Solve for y. Solve each equation for y.

a. 8x + 2y = 9 b. 3(x + y) = x – y

c. 2₃(x−9)=x−y d. 3x = 2 – 5y

15. Rearranging formulas. Solve for the indicated variable.

a. A=bh₂

. Solve for h. b. 2(L + W) = P. Solve for L.

c. PV = nRT. Solve for T. d. V=1₃π r2h _{. Solve for r} 2_.

Unit 2 Review

SHOW ALL WORK! No work = no credit!

1. Right now (“Week 0”), Peter has $25 in his piggy bank, and he puts in $1.50 more at the end of each week.

a. In this situation, what is the…

…independent variable? …dependent variable?

b. Make a table relating the number of weeks to the amount in Peter’s piggy bank.

x 0 1 2 3 4 5

y $25.00

c. Graph your data and label the axes. Does it make sense to connect the dots? Why or why not?

e. If possible, find a value for x so that P(x) = 100. (Use the equation from part d.) Explain what your answer means in this context.

2. x -1 1 2 4

f(x) 0 3 4 3

a. Domain: ________________

b. Range: ________________

c. Is f a function? ______ Explain.

d. Find f (4).

e. For what value(s) of x

does f(x) = 4?

3 .

a. Domain: ___________________

b. Range: ___________________

c. Is g a function? ______ Explain.

d. Find g (3).

e. For what value(s) of x does g(x) = 2?

4. Graph each of the following.

a. y = 3x – 5 b. y = 2 c. x > 2

d. 3x + 4y = 12 e. 2x – y = 3 f. 2x – 2y ≤ 10

5. Find the slope of the line that…

6. Find the equation of the line that…

a. …has slope 4 and goes through (-2, -5). b. …goes through (-3, 5) and (-9, 7).

c. …is parallel to 4x + 2y = 5 and d. …is perpendicular to y = -3x + 5

goes through (-1, 5). and goes through (6, 1).

e. …is vertical and goes through (3, -2). f. …is shown below:

7. Write the letter of the function represented by each equation.

A. absolute value B. cubic C. linear D. quadratic E. exponential F. square root

y = x 3 _{y = |x| y = x}

y

=

√

x

y

=

2

_______ _______ _______ _______ _______ _______

8. Write the letter of the function represented by each graph.

A. absolute value B. cubic C. linear D. quadratic E. exponential F. square root

4 2 -2 -4

-5 5

4 2 -2 -4

-5 5

4 2 -2 -4

-5 5

4 2 -2 -4

-5 5

4 2 -2 -4

-5 5

9. For each equation, identify the parent function and describe the transformation(s). (For example, “absolute value graph; shifts left, vertical stretch, and flips upside-down.”)

a.

y

=

√

x

−

10

y=

1

2

|x−

5

|

c.

y

=(

2

x

)

+

6

y

=−(

x

+

4

)

3

10. In the table below you are given a description or an equation of a transformed parent function. Complete the missing information in the table.

Description Equation (WITH GUIDE POINTS)Graph

a.

parent function:

_________________

transformation(s):

_________________________

y

=(

x

−

2

)

3

−

4

b.

Flip the absolute value parent function vertically

and shift it up 3 units.

Write the equation of the transformed function:

c.

parent function:

_________________

transformation(s):

_________________________

y

=

√

−

x

+

1

d.

parent function:

_________________

transformation(s):

_________________________

y

=

2

|

x

+

3

|

e.

Start with the quadratic parent function; reflect it over the x-axis,

move it 2 units right and 1 unit down.

11. Function Characteristics:

Domain:

Range:

Interval(s) of increase:

Interval(s) of decrease:

Maximum(s):

Minimum(s):

x-intercept(s):

y-intercept(s):

f(x)

→ _______

as x

→ -

∞

f(x)

→ _______

as x

→ +

∞

12. Even and Odd Functions

Explain how the graph of a function can help you determine if it’s even, odd or neither.

13.

Determine whether each of the following functions is even, odd or neither.

a.

f

(

x

)=

√

x

b.

f

(

x

)=|

x

|−

2

c.

f (x) = (x + 4)(x – 4)(x

)

d.

f

(

x

)=|

x

+

2

|

e.

f

(

x

)=

3

x

−

6

x

f.

f

(

x

)=

3

Unit 3 Test Review

Part 1 – Systems of Equations.

1. Solve by Graphing.

Solve each system by graphing.

a.

{

y

=

2

x

+

5

3

y

=

x

Graph:

Solution(s):

____________________

b.

{

x

+

2

y

=

4

y

=

3

Graph:

Solution(s):

____________________

c.

{

y

=

x

x

−

y

=

2

Graph:

Solution(s):

____________________

2. Solve by Substitution.

a.

{

y

=

4

x

−

1

2

y

−

x

=

12

b.

{

3. Solve by Elimination (with multiplication if necessary).

a.

{

2

x

=

6

y

+

4

3

x

−

9

=

9

y

b.

{

3

x

−

y

=

10

6

x

+

2

y

=

4

4. Choose Your Method.

Solve using a method of your choice.

a.

{

2

y

=

x

−

4

3

x

+

2

y

=

4

b.

{

4

y

=

3

x

−

2

6

x

=

8

y

+

4

5. Word Problem: Systems of Equations.

a.

Basketball player Luke Schenscher made 9 baskets, which were worth a total of 20 points.

(He missed all his free-throws, so his points were from 2-point and 3-point shots only.)

How many two-pointers and how many three-pointers did he make?

Write a system of equations describing this

situation. Use these variables:

W = # of two-pointers

H = # of three-pointers.

{

¿

{

¿¿¿¿

Solve your system and fill in the blanks.

Part 2 – Systems of Linear Inequalities

Solve by Graphing. Remember when to dot your lines and when not to. 6.

2

x

+

y

<

4

2

x

−

y

≥

0

7.

8.

2

x

−

y

>

3

y

<

4

x

≥

2

Corner Points

9.

Look at the graph pictured. The feasible region has been shaded. Find the corner

points and test each corner point to find the maximum value of the objective function

shown below.

Objective Function:

P

=−

2

x

+

5

y

Corner Points:

10.

Word Problem: Systems of Inequalities.

Making a batch of chocolate-chip cookies requires 2 cups of flour and 3 cups of sugar. Making

a batch of sugar cookies requires 5 cups of flour and 4 cups of sugar. Alton can use no more

than 20 cups of flour, and he can use no more than 24 cups of sugar.

Write a system of

inequalities

describing

this situation. Use these variables:

S = # of sugar cookie batches

C = # of chocolate-chip cookie batches

{

¿

{

¿¿¿¿

Graph the solution set to your system on the

axes provided.

Put C on the x-axis and S on the y-axis.

You will have a shaded region for the system

of inequalities, but please explain how your

solution relates to the shaded region.

S  6

4

2

0 2 4 6 8 10 C 

Unit 4 – Operations with Functions; Composition of Functions; Exponential Growth

and Decay Functions

11. Function Operations and Compositions

Let

and

.

Perform the indicated operation.

a.

b.

c.

d.

12

Equation _{INDICATE YOUR SCALE)}Graph (MARK AXES & Identify… a. y = 4  5x + 1  

asymptote:

domain:

range _ (inequality):

(interval):

x y

b. _{y =}

8

(

)

+

1

asymptote:

domain:

range _ (inequality):

(interval):

x y

c. y = 5(5)-x _{– 2}  

asymptote:

domain:

range _ (inequality):

(interval):