Name: ________________________________________________

Midterm Review 2017-2018 – Units 1, 2, 3, and 4 *Use notes, activities, quizzes, tests, and performance tasks to help remember how to solve problems*

Unit 1: Patterns Graphing

Extending? Connecting Points? Labeling and Scaling Axes

Tables Independent/Dependent Variables Extending Patterns

Verbal Descriptions Equations Describing Patterns Writing Explicit Rules

Getting information from a rule Using rule to solve for a term or for a term number

Writing Recursive Rules Getting information from a rule

Solving Equations Simplifying one side of the equation to get the dependent variable Arithmetic Sequences Geometric Sequences Simple and Compound Interest Order of Operations

2 23 vs 3

Simplifying by Combining Like Terms Dividing = Multiplying by the Reciprocal Distributive Property Unit 2: Equalities and Inequalities Expressions

Evaluating Expressions o Substituting with parentheses

Translating words to algebraic expressions Writing expressions/equations from word problems/stories

Equations Solving Equations

o 1-Step and 2-Step o Combining Like Terms/Dist Property o Variables on Both Sides Special Cases: Infinitely Many and No Solution

o Literal Checking solutions of equations with graphing calculator Inequalities

Translating to and from words Open vs. Closed Circle Flipping Inequality Symbol Number Lines Real World: possible solutions (points or arrow)?

Writing equations/inequalities from real world problems Properties: Commutative, Associative, and Distributive

Solving Equations Reminders

Simplify both sides, THEN solve If coefficient is a fraction, multiply by the reciprocal Eliminating Fractions

Unit 3: Functions Relation Function

Function Notation Table Mapping Diagram

o Input is mapped to >1 output Ordered Pairs

o x-coord. is repeated w/diff. y-coord. Graph – Vertical Line Test

Domain/Range Independent/Dependent Variable Input/Output Equations/Graph/Table Dependent Variable is a function of the Independent Variable Unit 4 (4.1-4.3): Linear Functions Linear Function Increasing/Decreasing Functions Rate of Change x-intercept/y-intercept Distance-Rate-Time Graphs Determining if a linear function – graph, table, or equation Slope Formula and Slope from a graphHorizontal and Vertical Lines Steepness of a line

3 Unit 1 Review 1.) Stages 0–2 of a triangular pattern are shown below. Use the pattern to answer the following questions.

a.) In the space above, draw stage 3 of the pattern. b.) Complete the table below comparing the stage number to the perimeter of the large triangle. c.) Make a graph showing the relationship between the stage number and the perimeter of the

triangle. Label and scale the axes appropriately.

Stage Number Perimeter 0 1 2 3 4 5

d.) Write a recursive rule to explain the pattern.

e.) Write an explicit rule for the perimeter of the pattern. Use n to represent the stage number and p to represent the perimeter.

f.) Use either rule to determine what the perimeter will be at stage 10. Show your work or explain your reasoning.

g.) Does the perimeter form an arithmetic sequence, geometric sequence, or neither? Explain. 2.) A fish store was breeding guppies. It started off with 3 pregnant fish. Each of the fish hatched 5 female

guppies. One month later, those fish hatched 5 guppies. The next month, those fish each had 5 female babies. Use this pattern to answer the following questions. a.) Complete the table below comparing the month number to the number of guppies born. b.) Make a graph showing the relationship between the number of months and the number of new

fish born that month.

4 # of months # of guppies

0 3 1 15 2 75 3 4 5

c.) Write a recursive rule to explain the pattern.

d.) Write an explicit rule to explain the pattern.

e.) If this pattern continues, how many fish will be in the tank after 6 months? Show all work.

f.) Does this pattern represent an arithmetic sequence, geometric sequence, or neither? Explain. 3.) The first three terms of a sequence are given in each problem below. Find the next 3 terms, circle if the

sequence is arithmetic or geometric, and give the explicit rule to find a term in the sequence. a.) 5, 3, 1, ________, ________, ________ arithmetic or geometric

Explicit Rule: __________________________________

b.) 2, 12, 72, ________, ________, ________ arithmetic or geometric

Explicit Rule: __________________________________

c.) 1, 2, 5, ________, ________, ________ arithmetic or geometric Explicit Rule: __________________________________

d.) 2, 9, 16, ________, ________, ________ arithmetic or geometric

Explicit Rule: __________________________________

5

e.) 2 2

2, , , ________, ________, ________3 9

arithmetic or geometric

Explicit Rule: __________________________________

4.) James wanted to invest $5000 in a savings account. He looked at two options.

Guilford Savings Bank (GSB) offers a 1.7% simple interest, which means that he will earn exactly the same amount of money (interest) each year. a.) Find 1.7% of $5000. This will be the amount of interest James will earn each year from GSB.

b.) Complete the following table. Round each amount to the nearest penny.

c.) What is a recursive rule for determining the amount of money in his savings account has each year?

d.) Does the pattern represent an arithmetic or geometric sequence? Explain your answer.

e.) Write an explicit rule for the amount of money, m, in this savings account after n years.

f.) Determine the amount of money that will be in his account after 8 years. Show your work or explain your reasoning.

Year Amount in

Savings Account 0 $5000 1 2 3 4 5

6 5.) James also looked into putting his money in Connex Credit Union (CCU) which offers 1.4% interest

compounded annually. This means that he will get 1.4% each year based on all the money in his account at that time. The formula for compounded interest is:. t

A P 1 r

a.) Complete the following table. Round each

amount to the nearest penny.

b.) What is a recursive rule for determining the amount of money in his savings account has each year?

c.) Does the pattern represent an arithmetic or geometric sequence? Explain your answer.

d.) Write an explicit rule for the amount of money, m, in this savings account after n years.

e.) Determine the amount of money that will be in his account after 8 years. Show your work or explain your reasoning.

f.) If James wants to keep his money in the bank for 12 years, which bank should he use? Show your work or explain your reasoning.

Year Amount in

Savings Account 0 $5000 1 2 3 4 5

A=amount of money in account P=principal amount r=interest rate (as a decimal) t=number of years money is earning interest

7 6.) Better Banking offers a savings account that pays 2.7% simple interest each year. Mason decides to

deposit $15,000 into that account to gain interest. a.) Complete the following table. Round each amount to the nearest penny.

b.) Write a recursive rule to determine how much money is in his account each year.

c.) Is this sequence arithmetic, geometric, or neither? Explain your answer.

d.) Write an explicit rule for the money, M, he has in this account after y years.

7.) Better Banking offers a savings account that pays 2.5% interest compounded annually. Mason decides to deposit $15,000 into that account to gain interest. a.) Complete the following table. Round each amount to the nearest penny.

b.) Write a recursive rule to determine how much money is in his account each year.

Year Amount in

Savings Account 0 $15,000 1 2 3 4 5

Year Amount in

Savings Account 0 $15,000 1 2 3 4 5

8 c.) Is this sequence arithmetic, geometric, or neither? Explain your answer.

d.) Write an explicit rule for the money, M, he has in this account after y years.

8.) Simplify the following expressions. Show ALL work.

a.) 25 3 4 9

b.) 234 2 5 3

c.) 2 2 33 8 4 12 3

d.) 47 3 8 2

6 4 8

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9.) Evaluate the following expressions. a.) 24x 6x 4 x for x 5 b.) 26x 2x 9 for x 2

10.) Evaluate the following expressions for x 5 a.) 25x 2x 6 b.) 2

3 2x 3 4 x 7

11.) Simplify the following expressions. a.) 5 3x 12 3 x 2

b.) 6h 5 h 5

10 c.) 3 4 y 4 2y 6

d.) 8 5 x 7

Unit 2 Review 12.) Justin wants to rent a violin. The store has two rental options.

Option 1: Charges a $25 down payment to rent a violin, and then $8 per month. Option 2: $0 down, but $11 per month.

a.) Write an expression for the amount of money Justin will pay if he rents the violin for m months

on Option 1. b.) Write an expression for the amount of money Justin will pay if he rents the violin for m months

on Option 2. c.) If Justin rents the violin for 12 months, which store would be the best deal? Show your work and

explain your reasoning.

13.) Solve the following equations. Show ALL work.

a.) 18 4x 6

b.) 3x 9 24

11

c.) h

17 253

d.) 8 x 5 40

e.) 6y 4y 5 25

f.) 7 e 8 5 4e

g.) 2 5 3x 6x 10

h.) 11x 16 4x 19

12 i.) 3x 7 5x 2 4 2x 3 11

j.) 5 a 1 4 9

14.) The formula 1 2

1A b b h

2 is used to find the area of a trapezoid when given the two bases

1 2b and b and the height (h).

a.) Use the formula to find the area of a trapezoid with bases of length 7.5cm and 9.2cm, and a

height of 8.9cm.

b.) Use the formula to solve for the height, when the bases measure 8cm and 15cm, and the area is 126.5cm2.

c.) Solve the formula for h.

d.) Solve the formula for 1b .

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15.) The volume of a cone is found using the formula 21V r h

3 . Solve this formula for h.

16.) The equations for surface area of a cylinder is: S 2 r h r

a.) Find the surface area of a cylinder with a radius of 5 cm and a height of 12 cm.

b.) The surface area of a cylinder is 602.88 cm2 and the radius is 8 cm, what is the height?

c.) Solve the equation for h. 17.) Solve the equation for p: m 3n 7p 9

14 18.) Solve the equation for w: e 3 w z 5w

19.) Translate each real world situation in to an inequity using an appropriate inequality symbol. a.) In order to ride the rollercoaster, your height, h, must be at least 48 inches.

b.) To beat the high score in a video game you must get a score, s, of more than 205,800 points.

c.) To qualify for the skiing championship, you have to complete the course in less than 23.5 seconds.

20.) Solve the inequality, check your solution, graph the solution on the number line. a.) 8 2x 16

b.) x

11 74

15 c.) 7x 3 4x 15

d.) 3 2x 4 27

21.) Sam wanted to sell buttons for a student council fundraiser. The button machine costs $85 to buy and each button costs $0.15 to make. He plans on selling the buttons for $0.75. Sam wants to make sure that he makes a profit so wants to know how many buttons he needs to sell before his income is more than his expenses. a.) Define the variable. b.) Write an inequality. c.) Solve, check, and graph the inequality.

16 d.) State your answer in a complete sentence.

Unit 3: Functions 22.) For each relation, determine if it is a function. Explain why it is or why it is not.

a.) 1,0 , 3,5 , 4,5 , 5,7

b.) 5,2 , 3, 2 , 4, 8 , 3, 10

c.)

d.)

e.)

x y –3 5 –1 2 0 5 2 –4

17 23.) This table compares the height of ten apple trees at Bishop’s

Orchards with the pounds of apples harvested from each tree. a.) What is the independent variable?

b.) What is the dependent variable?

c.) Is this relation a function? Explain.

d.) Using just this table of values, what is the domain?

e.) Using just this table of values, what is the range?

f.) About how many pounds of apples would you expect from a tree that is 4 feet tall? Explain.

g.) If a tree produced 100 pounds of apples, approximately what height would you expect the tree to be? Explain.

24.) Determine if each of the situations below illustrate a function. Explain your reasoning. a.) Monica has sold Girl Scout cookies for the past 6 years. Is the amount of cookies sold a function

of the year? Explain.

Tree Height (feet)

Apples Harvested (pounds)

3 38 4 47 4 49 5 46 7 102 9 128 9 148 11 150 12 175

18 b.) Is the year a function of the number of cookies sold? Explain c.) Justin measured the height of his grass every Saturday morning during the summer. Is the week a

function of the grass height? Explain. d.) Is the grass height a function of the week? Explain.

25.) The Silvia family decided they wanted to join the Soundview YMCA. There is a one-time, $100 joining

fee, and then it costs $79 per month for the family to be members. Write a function to represent the situation where m represents the number of months and c represents the total cost.

a.) Write an equation in function notation that represents the given situation.

b.) Use the equation to find c(4).

c.) If the total cost came to $653, use the equation to find the number of months paid.

19

Mo

ney

in a

cco

unt

in d

olla

rs

Months since bank account 1 2 3 4 5 6 7 8 9 10

10

20

30

40

50

60

70

80

90

100

0 x

y

d.) If the Silvias wanted to join for 1.5 months, how much would it cost? 26.) Tommy decided to open a bank account on the first day of the month. The graph below shows how

much money was in Tommy’s bank account on the first day of each month. a.) State the domain of the function. b.) State the range of the function. c.) What is amount of money at 7 months? d.) What does the point (3, 30) mean in the context of this problem?

27.) Is the number of points scored a function of

the players? Explain. 28.) Is the number of flowers in bloom a function

of the day? Explain.

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Plot the points from the given tables. State whether the graph represents a linear function. Use the rate of change to explain your reasoning. 29.) 30.)

31.) On the first day of the school year, Lara put $22 on her lunch card. She buys lunch every day for $2.75. a.) Make a table and a graph of the given situation. Label axes.

x y –2 3 –1 3.5 0 5 1 7.5 2 11

x y –2 3 –1 3.5 2 5 7 7.5 8 8

Days of school Money remaining on lunch card

0 22 1 2 3 4

21

a.) Does the line represent and increasing or decreasing function? Explain.

b.) What is the meaning of the point (4, 11)?

c.) What is the y-intercept? What is the meaning of this coordinate?

d.) What is the x-intercept? What is the meaning of this coordinate? 32.) Jimmy and his family went for a drive while on vacation in New Hampshire to look for moose. They

left their campsite and drove slowly for the first 20 minutes looking out their window in hopes of seeing a moose. At 20 minutes they thought they saw a moose in a lake, so they immediately stopped the car and got out. They stayed there for 5 minutes, but realized that what they had seen was just a fallen log. They got back in their car and continued their journey. This time, they drove even slower for the next 10 minutes until Jimmy’s little sister yelled out that she saw something in the forest. They again stopped the car and a moose came out of the woods! They were overjoyed and spent the next 15 minutes taking pictures and celebrating. Finally the moose ran away. Jimmy and his family got back into the car and drove quickly back to their campsite to enjoy s’mores. Make a graph that represents this situation.

Time in Minutes

Dist

ance

fro

m c

amps

ite in

mile

s

10 20 30 40 50 60

2

4

6

8

10

12

14

16

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33.) Use the graph below to answer the following questions.

a.) What is the slope of the line?

b.) What is the y-intercept of the line? c.) What is the x-intercept of the line?

34.) Graph each line on the coordinate plane provided and then find the slope. a.) y 8

Slope: ____________

b.) x 4

Slope: ______________

35.) Using the formula, what is the slope of the line that contains the coordinates 4,12 and 6, 4 ?

36.) Write an equation that is parallel to the equation in #27 and goes through the point 5, 9 .

37.) Write an equation that is perpendicular to the equation in #27 and goes through the point 5, 9 .

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-10-9-8-7-6-5-4-3-2-1

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