MIDTERM REVIEW

Algebra I and Honors Algebra I

Midterm Exams

◦Your midterm exam counts for ¼ or

25% of your first semester average.

◦Semester Average:

◦(Q1 avg + Q2 avg)/2 = QAVG

◦Sem avg = (QAVG + QAVG+QAVG +

midterm)/4

Example Calculations

◦Q1 = 75

◦Q2 = 75

◦Midterm = 40

◦Sem avg = (75 + 75 + 75 + 40) / 4

= 66 F average

Example Calculations

◦Q1 = 75

◦Q2 = 75

◦Midterm = 100

◦Sem avg = (75 + 75 + 75 + 100) / 4

= 81 C average

Example Calculations

◦Q1 = 65

◦Q2 = 65

◦Midterm = 83

◦Sem avg = (65 + 65 + 65 + 83) / 4

= 70 D average

Example Calculations

◦Q1 = 93

◦Q2 = 93

◦Midterm = 50

◦Sem avg = (93 + 93 + 93 + 50) / 4

= 82 C average

HOW I AM HELPING YOU

1. You are allowed to use a handwritten, 1-page “cheat sheet”…..you may write anything on it (except letter answers!)

2. You can earn 5 points extra credit for taking all notes and turning them on exam day. ALL OR NOTHING!

3. 5 additional extra credit points will be available later. (Stay tuned!)

HOW I AM HELPING YOU

◦You will get a detailed study guide this week.

◦There are other materials on my web site: http://hhsbrown.weebly.com/

◦I will spend at least 2-3 days reviewing for the midterm exam.

DO YOUR PART

◦Pay attention in class.

◦Take good notes.

◦Make a great “cheat sheet.”

◦Study by working problems and working

problems again.

NOTES

Notes Packet

◦ I am about to give you a stapled, 18-page

packet of notes. Bring this to class every day

until we take the exams.

◦Write all notes on these handouts.

◦ If you turn in these notes COMPLETELY filled out,

you will get +5 points added to your midterm

exam grade

NOTES PACKET

◦Write your name in ink on the top of

your packet.

◦DO NOT LOSE THIS! I do not have extra

copies.

POINT-SLOPE FORMULA &

TRANSFORMATIONSAt least 10 points of your test

Point-Slope Formula

◦Formula: 𝑦 − 𝑦1 = 𝑚 𝑥 − 𝑥1

Example (b)

◦Example: What is the equation of the line

through (-3, 5) with slope 4?

◦Formula: 𝑦 − 𝑦1 = 𝑚 𝑥 − 𝑥1◦m=4; 𝑥1= -3; 𝑦1= 5

Answer: 𝑦 − 𝟓 = 𝟒 𝑥 − (−𝟑)

Which reduces to 𝑦 − 𝟓 = 𝟒 𝑥 + 3

Your turn: Try (c)

◦What is the equation of the line

through (4, -6) with slope 2 in point-

slope form?

Your turn: Try (c)

◦What is the equation of the line through (4, -6) with slope 2 in point-slope form?

◦Formula: 𝑦 − 𝑦1 = 𝑚 𝑥 − 𝑥1◦m=2; 𝑥1= 4; 𝑦1= -6

Answer: 𝑦 − (−𝟔) = 𝟐 𝑥 − (𝟒) which simplifies to 𝑦 + 𝟔 = 𝟐 𝑥 − 𝟒

TRANSLATIONS

Translations

◦ If you have not been good at this by graphing

by hand, we can do these on your TI-NSPIRE!

Graph two functions!

◦Press the ON

button.

◦Press 1 for New

Document

◦Press the right

arrow key on the

NavPad and

select No. Press

Enter.

◦Press 2 to Add

Graphs

◦Type 2x for f1(x).

◦Press Enter

◦To graph the 2nd

function, press

Ctrl G

◦Type the 2nd

function for

f2(x)….so type 2x

+3

◦You now should

see both f1(x)=2x

and f2(x) = 2x + 3.

◦What took

place?

ANSWER

◦F(x) = 2x is

translated up 3

spaces to create

g(x) = 2x + 3.

YOUR TURN—the original function is f(x) = 2x

◦Try the next two problems on your

own!

F(x) = 2x g(x) = 2x - 4

◦F(x) = 2x is

translated down

4 spaces to

create

g(x) = 2x - 4

F(x) = 2x g(x) = 2x + 2

◦F(x) = 2x is

translated up 2

spaces to create

g(x) = 2x + 2

REFLECTIONS

F(x) = 2x -2 g(x) = -2x - 2

◦Graph both lines on your graphing calculator if you are not very good at doing this by hand!

F(x) = 2x -2 g(x) = -2x - 2

◦Press the ON

button. Select 1

for New

Document

◦Arrow over to the

right and select

NO. Press Enter.

◦Select 2 for Add

Graphs.

◦Type 2x – 2 and

press enter.

◦Press Control G (for

graph) and you

can then type the

second equation.

◦Don’t use the subtraction key for the 1st -2.

◦Type

v2X-2 a

and Press enter!

◦If you get an error message, press Control G….then type

v2X-2 a

and Press enter!

Answer

◦F(x) = 2x -2 is reflected

in the y-axis to create

g(x) = -2x -2.

◦Remember: If you

change the x-term

from positive to

negative, you reflect

the line in the y-axis.

YOUR TURN: There is a typo!

Answer

◦F(x) = -3x + 1 is

reflected in the y-axis to create

g(x) = 3x +1

VOCABULARY20 PTS OF THE TEST

Vocabulary (20 points of exam)

◦The first ten questions of the midterm exam will require you to be able to recognize some definitions of key vocabulary words.

◦Throughout the exam, you also will need to be able to use three key formulas: slope-intercept form, slope formula, and point-slope formula.

Vocabulary Activity #1

◦You will get in groups of 2-4 people.

◦Each group will get a set of cards.

◦The words will be on white cardstock and the definitions will be on blue cardstock

◦Match the word with its definition.

◦You will be given ten (10) minutes to complete this activity.

Vocabulary Activity #2

◦Work with a partner to complete the crossword

puzzle on page 2-3.

◦You will be given ten (10) minutes to complete

this activity.

FORMULAS/RULES (PAGE 3)

Formulas/Rules to Know (p.3)

1. Interquartile Range = Q3 – Q1

2. Parallel lines have the same slope.

3. Perpendicular lines have opposite reciprocal slopes.

4. Point-slope formula:

𝑦 − 𝑦1 = 𝑚 𝑥 − 𝑥1

Formulas/Rules to Know (p.3)

5. Slope-Intercept formula: y=mx+b

6. Slope formula: 𝑚 =𝑦2−𝑦1

𝑥2−𝑥1

7. The y-intercept of f(x) = mx + b is b.

8. The slope of f(x) = mx + b is m.

VOCABULARY/FORMULAS PRACTICE

Vocabulary Practice (10 minutes)

◦Answer questions #1-10 on page 5.

◦If you finish early, begin the word search on page 4.

◦You probably will not have time to finish the word search now….You have plenty of time to complete it!

◦Answer questions #1-10 first on page 5!!

STATISTICS PROBLEMS #11-16

12 points of the midterm

PROBLEM #11: FIND THE MEDIAN

Two methods to solve this problem!

Median (Problem #11—page 5)

◦Method #1: To solve this by hand, put the

numbers in order and find the middle number.

Median: Problem #11

◦Cross out the first and last number.

◦Repeat until you are left with the middle #.

Method #2: Median

◦You can also solve this problem by

using your TI-Nspire!

Calculator: Median

◦Press the ON button.

◦Press 1 for New Document.

Calculator: Median

◦If you get this

message, select

NO and then press

ENTER.

Calculator: Median

◦Select 4 for Add

Lists and

Spreadsheets

Calculator: Median

◦Go to the top of

the first column

and type a name

for the data.

Calculator: Median

◦Enter the numbers

into the

spreadsheet:

7, 4, 28, 11, 48, 45, 37

Calculator: Median

◦Press the Menu button.

◦Press 4 for Statistics

◦Press 1 for Stat Calculations

Calculator: Median

◦Press 1 for One-Variable Statistics.

◦ (You go here to calculate the mean, median, Q1, Q3, interquartile range, and standard deviation.)

◦ You go to #3 if we were doing a line of best fit.

Calculator: Median

◦Press Enter.

◦Press the right arrow on the NavPad.

◦Press down on the NavPad to select data as your x1 list.

◦Press Enter.

◦Press Enter again

Calculator: Median

◦You see the mean, the sample standard deviation, and other stuff at first.

◦Arrow down to find the median.

Calculator: Median

◦The median is 28.

◦You can do this

either way on

the exam….your

choice!!!!!

Your Turn (Daily Grade #1)

◦I will now pass out a bubble sheet and a

pink “daily grade” handout

◦Please do not write on the pink handout.

◦Try problems #1-11 now.

◦Bubble your answers on your bubble sheet.

◦Stop at question #11.

#12: RANGE

Example #12 (page 6 Notes)

◦Range = Max – Min

Max = 593 Min = 115

Range = 593 – 115 = 478

YOUR TURN (Daily Grade #1)

◦Try #12 on your daily grade and

bubble sheet.

INTERQUARTILE RANGE

EXAMPLE #13 (page 6 notes)

◦We have only done this problem on a

calculator. Create a new document on

your TI-Nspire and enter the data.

◦After you do

Menu, Statistics,

1-var Stats, and

select your data,

you will find Q3

and Q1

Interquartile Range = Q3 – Q1

◦IQR = Q3 – Q1

◦IQR = 10 – 4 = 6

◦IQR = 6

YOUR TURN! (Daily Grade #1)

◦Try #13 on your bubble sheet.

#14: LINE OF BEST FIT(PAGE 6 NOTES)

CALCULATOR: LINE OF BEST FIT

◦You must enter the x numbers in one

column and the y numbers in another

column.

◦Name the columns, too!

LINE OF BEST FIT INSTRUCTIONS

◦Press the On

Button.

◦Select 1 to get a

new document

LINE OF BEST FIT

◦Select No and

Press the enter

button.

LINE OF BEST FIT

◦Select 4 for Add Lists and Spreadsheet.

◦Name the columns (xc, yc)

◦Enter the data

Name columns; Enter data

◦Name the first columns something like xc.

◦Enter the x-coordinates in the first column.

◦Do the same for the y-coordinates (yc).

Line of Best Fit

◦Press the Menu button.

◦Select 4 for Statistics.

◦Select 1 for Stat Calculations.

Line of Best Fit

◦Select 3 for Linear

Regression (mx

+b).

Line of Best Fit

◦You now have to

tell the calculator

your variable

names for the x-

list and y-list.

Line of Best Fit

◦Press the right arrow on the NavPad.

◦Press the down arrow to select xc.

◦Press Enter

◦Press TAB to get to the Y list.

◦You should be on the y List line.

◦Right arrow.

◦Down arrow

◦Select yc.

◦Press Enter twice.

Line of Best Fit

◦The line of best fit is provided.

◦Slope = m

◦Y-int = b

◦Use y = mx + b

◦The answer to this

example problem

is B since m=1.17

and b=16.4

Your TUrn

◦Try #14 on your daily

grade…Bubble your answer on

your bubble sheet.

#15: SAMPLE STANDARD DEVIATION

Example for #15 (page 6 Notes)

◦To find the standard deviation, type

these numbers into a list on your

calculator like we did for median and

IQR.

◦Remember to name

your column at the top.

◦Type in all the numbers:

55, 18, 40, 22,

20, 42, 55

Standard Deviation

◦Press Menu, Statistics, Stat Calculations, 1-var Statistics, Enter, and Enter again.

◦You will see this screen.

◦Right arrow over,

then down arrow

to select Score.

◦Press enter.

◦Press enter again.

Sample Standard Deviation

◦ 𝑥 is the mean.

◦sx is the sample

standard

deviation…..this is

the number you

want!

◦The sample

standard deviation

is 16.1

YOUR TURN!

◦Try #15 on your daily grade/bubble

sheet.

MEAN: #16(NOTES PAGE 6)

Mean (Arithmetic Average)

◦We could do this on a calculator….but

the quickest way is to add up the

numbers and divide by 9.

Oh NO! We get a fraction!

◦To avoid getting

a fraction, type

516/9.

◦(Put a decimal

point after the 9)

Mean: Decimal Answer

◦Type 516, division

symbol, 9, and

then a decimal

point.

◦Press Enter

YOUR TURN!

◦Try #16 on your bubble sheet!

◦Turn in your bubble sheet and daily

grade handout when you are finished.

FUNCTION/GRAPHINGREVIEW (P. 7 NOTES)

◦-1 is x; 2 is y

◦Substitute -1 into x and 2 into y and

see if the inequality is true or false

◦Parallel lines have what type of

slope? Perpendicular?

◦You can also check perpendicular lines by multiplying the slopes…if you get -1, they are perpendicular!

#4 Slope-int form (page 7 notes)

◦It asks for the equation in slope-intercept form….so I know that B and D are automatically incorrect!!!! What form are they written in?????

Word Problem using y = mx + b

◦To see if it is a function, see if any x-

values appear more than once.

Domain: x Range: y

#7 Domain of a linear function

◦Domain:x

◦The graph goes left forever on the x-axis and right forever on the y-axis.

◦This means that the domain is ALL REAL NUMBERS.

◦Answer: B

#8 Domain/Range (page 7 notes)

◦Domain: x

◦Range: y

#8 on page 7 notes

◦(a) is incorrect---Don’t write down 2 twice!

#9 Function Notation (page 7)

◦F(-4.2) means that x is -4.2

◦Substitute -4.2 into x and calculate y.

#10 Vertical Line Test

#11 and #12 Slope Formula

◦Write (x1,y1) and (x2,y2) underneath the

ordered pairs.

◦Write the slope formula.

◦Write boxes or parenthesis where the

numbers go….substitute the numbers into

the equation.

#11 (page 8—Notes)

#12 (page 8—Notes)

#13 Notes----(page 8)

◦I know that (B) and (D) are wrong since the

slope is m=-3….(B) and (D) has 3 for the slope

#14—page 8 NOTES

◦Read this problem carefully……they gave

you the slope (m) and the y-intercept (b)

◦There is no work to do!!!!

#14 Use y=mx+b

#15 y-intercept (p. 8 notes)

◦The y-intercept is where the graph

crosses the y-axis…..

#15

◦The y-intercept is where the graph

crosses the y-axis and is a y-value!

Checkpoint----62%

◦I have now gone over 62% of the

test…If you can do these problems,

you are on your way to passing this

midterm exam!

MIDTERM DAILY GRADE

◦You will be given a green

handout…Please do not write on this

handout!

◦Bubble your answers on the bubble sheet.

◦Turn the green handout and the bubble

sheet in when you are done!

Graphing/Shading: page 9

◦Is this a dotted or

solid line?

◦What is the y-

intercept?

◦What is the slope?

#16 (page 9)

◦The y-intercept is

1.

◦The y-intercept is

on the y-axis

#16

◦Starting at the y-intercept 1, go down 2 and run over 1 to the right.

◦Then, draw a dotted line through the points!

#16

◦Use a checkpoint like (0,0).

◦ If you get a true statement, shade below the line where (0,0) is located….if not, shade above where (0,0) is not located

◦A and C

cannot be

correct

because

the slope is

increasing/

positive.

◦Answer: B

#17 (page10)This is a slope formula problem

Vocabulary (page10)

◦Complete the Word Jumble on page

10 by unscrambling each word. Then,

write the letters in the correct number

so that you can get the phrase at the

bottom of the page.

◦Finish the word search on page 4.

GRAPHING FUNCTIONS ON A

CALCULATOR

#1 on page 11 (Notes)

◦Type the

equation

into your

calculator.

◦Press the ON

button on your

calculator.

◦Arrow over to No

and then press

ENTER (if needed)

◦Press 2 to Add

Graphs

◦Type Xq+12X·

◦Oh..no! This does

not look like a u-

shaped

parabola!!!!!

◦Press Menu

◦Select 4 for

Window/Zoom

◦Arrow down to A:

Zoom-Fit

◦From this view, we

can tell the answer

is (A) because of

how it passes

through the origin.

◦After Christmas,

we will learn

this….Press Menu,

Select 5 for Trace,

and then 1 for

Graph Trace

Answer: A

◦You can arrow left and right to move the cursor on the parabola by pressing the left and right key on the NavPad.

Your Turn: Try #2 on page 12

◦Press On….Do a new document.

◦Graph the function….by selecting New Graph.

Answer: D (Look at the x-intercepts)

MIDTERM STUDY GUIDE

Midterm Study Guide

◦I will go over a page of the Midterm Study guide in your notes….Write down everything I write down.

◦I will then give you time to try some of these on your own…..on a separate practice test.

◦We will start with #36 on the review….and go over #1-35 again later.