-------------------------Name: Math llA Midterm Classwork Review Sheet #1

1. Simplify:

2. Which of the following represents a one to one function(s)? HL..-T+ V LI (1)

L

....... v I'y

\ I

-"" \/ I ,.

(2) I[' ,!, (3) I'­

f\. I ,t-_._ ...._-o, d'/~0--'- ,""­\- ­/ - "5- - -I -! -1 1 ~ .01 .... :,X" -1

" x " -' ·3\.

" n ,) 3. The solution set for x2 + 7x + 12 = 0 is

(1) {3, -4} {-3, -4} (3) {-3, 4} (4) {3, 4}G t~r~)(~+-~)J )'=.. -"3 ,~- y

4. Sketch a quadratic function that has a one real root.

i

5. Simplify: (_2X 2y 4 z -3)4

Co 'v -\ 2. (\ '..9 ",7, ~'\,# ;e.-I - ) - \ G "'J4.'j -1!

. 2. ' 6+J2 .:: \ '"L t \,p rL +'-.\L (~6. Simplify: 2-J2 4 + ~fL-z.."'i: - r:r

-1.

7.

1

c

1-z.-.,c.. -3 :::. l.e ')<.t-Il.Q

lt ~ ::. , ~

'X :::-. :s.. 'u

. . ·72 I 109. Simplify: 1 .::..(.. -::::

10. For the polynomialf(x) graphed at the right a. State the real solutions.

X:;;. -2. ) X =: z... ) )( ~y

b. Write the equation off(x) in factored form .

.p (X) -=- &. -\- z) ll<. - i) (~ - ~) :; 6 -

11. Solve: 12x + 121 = 4x ~J... x-:;. (.,g.

Z')(."'" \1. -=- t.\~ '2.....,{. \-- n .. -=- -L\x ~=-~

\ \1.-I-It.\ ~ 1-'-i I.Hoo\"Z..\: - ~ \ !.. :.. -\.p'J...

\ ~~ 2.."1- \ ",!of \ ~ "..~ J \ ~\ :..-\{

1~ :'f--..l -2. =" ~ #-'%

12. Solve for x in simplest radical form: 5x2 +21 = -20x

5 ~ ~ l- '2..(:>)1. -,\-z..\ ::;.

_ 2-D t «"z..o)"% X-=- \'V

- 4(:5)(+- 2.1)

+- l')~ f5 -::;. - 20 - "

\~ 10

2

-------------------------Name: Math ttA Midterm Classwork Review #2

1. The solution(s) of the equation x2+ 7x + 11 = 0 are

(1) 1 real root (3) 2 imaginary roots

@ 2 real roots (4) 1 imaginary root

2. What is the value of g(2) for g(x) = x 3 - 2X2 + I?

J.3_2. ('-\) +

a - 8' + \

3. The graph ofj(x) is shown at the right.

Sketch the graph which represents f(x + 3) - 4? \-c.f'+- .3 d,o...oV'l ~

4. Solve for the following: 3x2 - 300 = 0

(1) { } (3) {-lOi, 10i}

@ {-10, lO} (4) {IOi}

5.

6. Factor completely: n3 + .5n2 - 9n - 45 v"l 2.C" + '5) -9 (1'1 +5)

b ~-4- a..,­

4'1 - ~ (,)U \)

L\~-'-\'--t

5

! I

I

y I I

I 1\ .\i,...-'

,

~ \ /' ,/

x

7. A model rocket is launched from ground level. Its height, h meters above ground, is a function of time, t seconds after launch, and is given by the equation h = -12x(x - 9) . a. How long till the rocket reaches the ground again rounded to the nearest tenth? b. What is the maximum height of the rocket rounded to the nearest whole number?

-;"'~I~':=' 0~ ,-=-- rz ,,()(. -ct) ')( ~= \0 y., ")V\ ~ I~ '- -=~ D

'1yV\.,,~ 0

't~-:' 300

'i 5c\ : !:JO

&L) '1 Sec ,

10) 2'+~ m~krs

8. For the function g(x) shown at the right, find

Domain: ~ ~ I - ~ ~ 'I... L 111 [- ~I Ltj xRange:1~ 1-5 L ~:: ~3 (-5) y]

g(2) '-\ g(-3) D

9.

10. Simplify: (-2+J-16 )-(-S-J-49)

(-2 + ~ -.) - (-5 -- 71) 5 t- 1;

1 ~ + I I ~ I II. Solve by completing the square and express your answer in simplest a + bi form.

2

03x + 6x +5L=JL ~ ( ;-.. 2.. 'J"3 "3 ~ .3 ( )<. 1- I) = - "'"

z I ­X \--2.,,-+3 -:::'- c x +\ :: :t ";-2

..,'1. -\-'Z.:)<..~ -L ::. -3+ ~ r; +- .. '-1,.. L2: ::. - 1- IVz..

12. For the graph shown at the right, find

Domain: Lx )-5 LX ~ '-t} (-5,~ Range: 1!j I -L.\ ~'::) ! loT j (- L4 ",J

)

Is this a function? no

If yes, is it one-to-one? ~

Findj{-3) i( 1 - 3 . S j(4)_--->-i___

-~ ........ ......

"

-­

.,­

t-') i,...o- ~I""" ..­

....... I ,

~ ;~

""'" r-..... -f0-r-­

" /

c "'j

o

4

-----------------------------Name: Math llA Midterm Classwork Review Sheet #3

1.. Find the number of points of intersection of the following graphs: y = _x 2 + 2

® y=2

(2) o (3) 3 (4) 2

2. Simplify:

-2~ ~ G +-r:GS{'3 - z i \:-\ (3) -\- 1; (s rr) l

7i G_ ! i G +- 35\ {3 ~ 13­3. A function is defined by the equation y = .!..x3 + 2. Write the equation that defines the

4

inverse of this function? I 3

X ==41 lj +2 I ..3

x- 2.:' 4 j "1 ()(..~i) = ~ 3

~<~----~e~------~~~-----74. Solve and graph: ~7 - 2rl < 19 - \ () - to "b l3 Z:."J

/-z..r LICf'" (-l .. >-I'1 \ .. + Lv\ <...\ 0.. \ 1 \ L\9 \-, ~ '-w\ L'~ '- l. -r- L l 2. - 2 "(" "> -"'2. \.D

\"l,"1.\Ll,\ J \ -.3 a\ t-\~L 1.3

'F "3 3 ~ I '1 F~ - (., ~ X (.1 3}

5. The graph below shows the function fex).

ckwnL\

~

y

/ .......

~ x

r\oh~3 Which graph represents the function f tx -3) - 4 ?

3)

y

/ ...... / '"

x

2)

yv ....... v

V ,"",

x

y

V V

v, I'

4)

" I

N ...... '" I.....

I Y I

x

5

..;..... 2 + \\ ';' - \ + \C)\6. Simplify: (-2+ v'=l2l) -(1- J-l 00 ) r-.3 ~1.~ ~ }

7. Solve for x: x 2 - x - 6 2: 0 ~~'__".I-----:--'i.""=--"'''''''

eX.- 3)C)(..+Z.) ') 0 _ 5" - 2. 0 "3 5'

~ (X:' -2.) " (X ? 3')) 8. For the equation y = (x - 7)(x + 3), find 4

Roots: I J -:3 AOS: X::. Z ::. z... Vertex: (..(1 - Z. s) )<.=... ;)

9. Solve: 3x2 = 72 "3 3

10. Simplify: (4J6)( -2F2) (6+=3) - Lt~i 'f3L; ~ /-2. ~ ai }

II. For the equation y =(x- 2)2 -I a. State the shift from the parent graph f(x) = x 2

r i 'jht- Z ~o\'ci") '

b. Identify the vertex.

( L. ,-,) c. Graph the new equation.

X - I I D I I '2 3 y Js ~ ~ ,.3/ C t ·1 0 3/'&

12. For the equation, 8x -I 0 = x 2 -7x + 3 a. Describe the nat e of the roots.

(1) 1 real (2) 2 real (3) 1 imaginary (4) 2 imaginary

\:.f - ,-\ o..c.. = 2.1_S - 'i (1') l\?» ::: 2 z.. 'S - '52...

b. Solve for x in simplest form.

)(:: - b ~ ~ b'Z._L.\ o.c:.

~ ~~~-(o2 0

T ..

\

l

2.0...

6

Name: Math llA Midterm Classwork Review Sheet #4

1. A rocket is launched from the ground and follows a parabolic path represented by the equation y = _x2 + 5x At the same time, a flare is launched from a height of 4 feet and

follows a straight path represented by the equation y =-x + 4 Find the number of points of intersection before the flare hits the ground.

@ (2) 0 (3) 3 (4) 2

2. Simplify: 6--.1-24 - 2--.1-54

o~ f4 ~ - Z-I'.,pf' {l; (p ~ (2U;) - 2i(3 n=) \z. i rrs; - La". -[l;

[l9i~l 3. Find the inverse of the equation:y =~x+4

~ . 3 X:= '3 'jtY

2­X~ ~ 3

~(K - lot)

4. Solve for x:

~ ~ I V"\\1

116 - pi >3 (t) (B ..>3 13 I C)\ ~ -f~3 0(. \lP-'P L - *0 ,S 2-0

-1(>'? -13 _+,,- -1'1 1\ \0 1 '> 3 \ \ to - \ 5"\'> :3 \\ l.,-zo\ 73

T I ?3 \_,-\\75f i-13 \J If'>'" I..\- '/3

T1(f L \ ~) '" ( fl '> \Cj)} f

5. For the graph shown at the right, draw the graph that represents the shift g(x - 2) - 5

n~\\ \-- .,.~

~)v;l \\ '5"

" f(x " y

I

x

'\.,

7

f ' \(

6. Simplify: (3 - 6i) - (8 +12i) \ ~ <4 ~J - b-\"L~_ - -.J - \ vl.J

7. Solve: x2 - 2x -15 < 0

(X-5)(X -\-3) '- \) t

to., $ 1"0

x.~ '5 'l( ::. - 3

T

8. For the following quadratic equation, g(x) = 4(x + 7)(x + 3)

-[0 Roots: -1

1- 3 AOS: X ': 1:" ~ -$"

9. Solve for x in simplest radical/orm: x2 + 6x = -\ 5" X,Z +- (O ~ 'f' 5:0

X. :- - lP :t -J 'IJ,~ -4(I)LtS'")

:;t

Vertex: (- 5 - I ~) \- / I

10. Simplify: 24J8 • ~.J5 ~ 4

t ~(\C ~ (,(LriO) ~ [f1.\Ic J ct~)

11. For the equation f = Ix + 11 + 3 ;;11If.:

/" 1". .I

a. State the shift from the parent graph f(x) = Ixl kft \ v-f a

b. Identify the vertex.

( - \) 3) c. Graph the new equation.

12. For the equation, 3x2 -I2x = -12

b?- ~ L\ c..c.... a. Describe the nature of the roots. I c\ "\ - 4 tJKtL.-) =-- D

o o

(2) 2 real (3) 2 imaginary (4) 1 imaginary ('I

o

b. Solve for x in simplest form. \2 t. r

""" -=- ~ - ::.@ 8

---------------------------Name: Math llA Midterm Classwork Review Sheet #5

1. The solution(s) of the equation _3y2 =6y-l0 are 3~1. t-(gJ -lO

OlP -~ (3)C-Io)(1) 1 real root (3) 2 imaginary roots

\ '5(q® 2 real roots (4) 1 imaginary root

2. What is the value ofg(-2) for g(x) = 3x2 -12x + 12 ?

[~i-z) . q~l

3. The graph off(x) is shown at the right.

Sketch the graph which represents f (x - 4) + 6 ?

rl Oj\\\- t4

Wf~ / \

J

" ~ ~

I,I'Y. J ~

, " " ,

IL,­

" ;;{

4. Solve for the following:

(1) { }

(2) {-6, 6}

3x2 + 108 = 0

C@-6i,6i}

(4) {6}

'3~2. = - \t)~ 2­

f -:.. - "3lc.

'f­ ::. ~ ~ -3 ;:

X=-tlo~

6. Factor completely:

;( X ( 10 ~4 - ,)

32x5 - 2x

N

::5

9

5.

o

A)<' ('-\ x z. +- \~ (4"~-I)

0,

t> <

,\.

" ~

I ~

~ , IL o

N. =>

1 o

7. A ball is thrown straight up. The height h of the ball, in feet, t seconds after it is thrown is given by the formula h(t) =_x 2 + 5x

a.

b.

8.

9.

10.

11.

12.

How many seconds after the ball is thrown wiD it return to the ground? Round to nearest hundredth.

What is the maximum height reached by the ball? Round to nearest hundredth.

)( (\'\i!') =­).. rY\0-¥. :.

)l.5d ':;., ~ V'<\ 1\"\ ::.

~M~-='

y. sd -=..

",,_~____-,---_ __, _ --/- ( __. . , ...L-_____ ___+1 ~~<.~___

For the functionf(x) shown at the right, find

Domain: 1X IQ =-X ::. '1\ [1> ,~ Range.: 1!j \1..\ ~ ~ ~ '2.\ 10\ \ \ 'Z..J

Findj(2) % f(3.5}_\_"2._ _ _

Simplify: (12+.J=4)-(7+~-25) I Z. +1.1

- 5" ; . 5 - I

Solve by comp eting the square and express your answer in simplest radical form. ~ 4x2

- 40x - 12 =..Q..-zr -cr t:f hi z.

X -(DX. -.3 "':.. 0

XZ.-I D~

(Y- - -:;Y ~ 2. <a

+-!.i:~ 3+ 1..5

For the graph shown at the right, fmd Domain: \ Y- \ C) ::. X~ 5t>1 [ 01 St>]

~ ,00 IOU

Range: \ ~ l ~ 0 :. j ~q oitJ [1,0 ; lDo]

Is this a function? If yes, is it one-to-one? ,;0 0

Findj(10) '80 Findj(50) 9 S

v I::" _ + c.r=-;;:-z.,, - ~ - - "'- ,,

Ix ~ 5 ± 2r7]

10

90 I

'" ~ 7 "3 '"iii ~ 50

10 20 30 40 Time (minutes)

Name: Math IIA Midterm Classwork Review Sheet #6

1. Simplify:

2. a. Which graph(s) represents a function?

A)'8 ~\

b. Which Waph(s) is one-to-one? '''---­AI D - -+-----1--+--!-t-+-~-+--+ +++j

J I-H+ -+----+-+-+--+--_-t-----<

>--­c. Which graph(s) is onto? cA A

2 2 2­3. Solve: -x + 42 =0 >< ~ -u3

3 )<. =. !.. ~ 2. z.

3 ~ :::. -4 ~ IX::! "3'I..[7J 2)<.. "2- -:. - I Z. to

4. Describe the "nature of the roots" if the graph

a) lies entirely above or below the x- aXis_~2",-----,i,-,-m.:....!a""'-"'\'5\C!..n......(L"",j'--",lot-L--_________

b) touches the x-axis on ly once._----'-I---'..G"-fOQ...,""""'-"L--_______________

c) passes through the x-axis two times._-';(=-C'-'e'-'~=-,_____________

11. _-z. -'-t IZ­

!) 'X. ~ ;?~ X4

.5 -I .;:;;l

J3-i f3-~ rf - k(3 -.-A.G -\- ~... ':2 -2i (£6. Simplify: -- C ' - ­

J3+i \3-.J,.... {if- ...d3 +-)J~ -.A.,""£. t1 -:;:;.. (-I ) .,.,

1 ,,£:,.3 +, \ ~ ~

~ - 2. \ ::.:: -~{~

1 1

5.

--~-------~-- - -­

7. Find the inverse of y =3x - 2 .

X =3~ - L.

~ +- ::t :::. '3'1

Pf "')i"~ S~ +IS -:. ~)(. +38.

1 1~:x J

.34 • 2. I9. Simplify: 1 =~ :. ­II 10

10. For the polynomialf(x) graphed at the right a. State the real solutions.

-.; ­

b. Write the equationf(x) in factored form.

-2

-8 -9 -10 -11 -12 -13

11. Solve: i~ y+4i = 6 Ch~ 1 i ~ ~~ I =: (P

C-h 't:: y~ ~ +L\ -=- iD ~ ~ ~4 ~ -Co \ 2 p·. l -=- l,--i ") :: 1... :i ':) ::. - I0

'~\ ~ fo \ ~ -:. 'i L , ) :;. - ;)0 I T

12_ Using the given set, h(x) = {(-3, 1), (-2, -4), (2, -I)} Find the

domain: 1-3,-2.,1.3 range: 7 \ j -'1, -I

t: ~ write the inverse 1 ( C- 3) ( -y, I - 2.) ( -I \2)3 is the original a function?--l'i'-e..s=-__________

is the original] - 1?--1'1-""-(.'-.......)'------------- ­

is it onto?___,\. e.-=-"---,___________ _ _+ ~

-1-+

/- I \) t-I-J } =- '" I - <D\~~

lJ,:.",1

T

1 2

4