This document contains a multi-part advanced algebra test with questions involving solving systems of equations and inequalities, graphing lines and regions, matrix operations, and predicting trends from data. The test assesses skills like determining slopes of lines, writing equations in slope-intercept form, solving systems by elimination, substitution and graphing, performing matrix operations, interpreting scatter plots and finding linear regressions.

1. -# +r *-V
Advancetl Algebra
Calcrrlators Allorved
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75 ?#2,"rffi
SHOW ALL WORK!!!
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l. Determine the value of a so that a line through the points with coordinates (0, 3) and (5, a) has a
slopeofm=-5.
j - -;zD+b A._<- ,-5 x f +1
)+ Y - z9+7
J
-7-L ,/
2. Write an equation of the line in slope-intercept form that passes through (1, 7) and is parallel to
)
the graph of y - |x -3
5
,l -€ +h
J> 9;d+< ,/
+=b
3. Graph the following equations on space provided and write downpoint of intersection.
2x+6y =r) 6g -- - L?< + la
x-y=2 g-- - $X I Z :trtbxnqt
-3= -XtL (47
J:q<*L
4. Solve by elimination. Give exact answers. 5. Solve by substitution. Give exact
answers.
7x+2Y = {
5x+3y =l!,
3x-4Y=J 2x+ y =3
tLl>{+ *J *{ -Zd+7-/'
J--
+ n<-+3 -5 - 54+)(-74 +7)=l+
'*4 =#
l'l = 17 t-K -dd 4q = l$
--4--q-'l-
Z --
+ tzJ--+';lt'
?
U --1otV
2y-- -'T J l'l
l7 -_ l7
g-- -ffi
d:'fr
i -,A'-(1( 9=- '/ 'd =-{
J:,1?

2. Advaneed Algebra Unit One Test (A)
Calculators Allorved
6 Let ,=l: f] *r=[; 1]
*u ,=l!ri i] Perform the following operations. If
not possible then indicate as'1l{ot Possible" and explain. Give exact answer'
-*(r-::t)+
a. Fnd 2A+ B b.
" Find l-t
({-'*') -'
6* ?)
, (Y- ;*)+ (;' Z)
(? ;') -/ =l?* il /'-
=
a- F4 -t-- rt r
(t -;) (? q'',
What is the name ofthis matrix?
=(;D/
c-o loamrts J;r'l n
^-!c.l ,u/-& O
)b ,ru,mbr.
7. Solve the following system of inequalities by graphing. Clearly indicate solution region by
shading and proper labeling of axes.
x-y<5'_JS_X+5
l,l.+ ',l d -S
9t,
JM
"w6

3. Advnnced Algebra Unit One Test (A) Page 3
Calculators Allorved SHOW ALL WORK!!:
8. Solve the following system of inequalities by graphing. Clearly indicate solution regionlc4,,
shading and proper labeling of axes. br+Xl gS4*+( ./
y < 4x+6
x+4y<7 429-"1+r)
<7 t!- txr 4
2x+ y
x-6y <10
JL-ad+rl
-63 9 -d+ /0 I
a= 6"<-z
^a) t
I 7
/
a/
4
7/
7
,l
,/-9sto
7,,
/+b{rl
uI I 7
I
l,''#'
I
I
I
t
I
I
I
9. Solve this system of equations by any methld. Give exact answers only.
_#t -ffiy-+ l+y'-r'
x*z=-2ffi=V- _o
x*y=u
9--Z
I +Z-- -L
)t* z =2
a*z *9Z=
/
I
4-t /,
J=5o^,/
z*- -/
10. The sum of three numbers is 100. The last number is the sum of the frst two numbers. Twice the
first number is l0 less than the last number. (*Hint: Write the three equations and use matrices to
solve.*)
4+?tZ=ld .{+y+ ?>t 00
z --d+y -<,-.y+&-a
, ;/-
?.x
ZX=/-tb -10
?t;),) (il=(',f)
v'
& .?A (ii=
A :?,-A
q :50 !!i!},,t:)
Y E0,/ G

4. Unit One Test (A) Ptge 4
Advanced Algebra
SHOW ALL WORK!!!
Calculntors Allorved
At a firrn, there are three workers that are supposed to work a combined 110 hours per week.
ll.
Worker 1 is supposed to work 5 hours more than worker 2, and worker 2 is supposed to work 15
and
hours more than worker 3. How lo;rg should each one work? (*Hint: Write the three equations
Xi t + t '- i (b'
use matrices to solve.) ,/ .. r ---'"
/*2+7 =ito
X;_*z+tg -,a 4-1 =5-'
J+, /
J i,=1_'lf -/-'
ui !) (g):WL (*)-(,*:,
'i:)
<=ry 1;
J= 4 ?o
*=q t{
12. The table below shows-":[*/ number of people in the U.S. that are age 100 and over.
Source: U.S. Census Bureau
Draw and clearly label a scatter plot of the data to show the relationship. Let x represent the
^. years since 1990.
,/
ttJ, * he r
ud,
,{ ,0l}/
?* ogb Q$,
*4,
qq
6A
50
qrll0tttLl
b. Find a pr"ai"kftu"?", ,f,J*f*tr?* ,rl? fl{*e number orpeopre aged r00 and over
are related. Estimate values to two decimal places. Draw this on thg4raph.
c.
3= t A E 1.1+* - tzo37 ?Lf. s? -/
Predict the number of p9gple aged 100 and..over in the year 20A7 (Round your'answer to a
whole number). -/
t 274_ql
d. Predict the ygar in which approximately 129,000 people will be aged 100 years and over
(Round your answer to tfu-nearest year).
L00{ a

5. Advancctl Algebra Unit One Test (A) Pnge 5
Calculators Allorved SHOW ALL WORK!!!
13. Given triangle A(2,3), B(4, -1) and C(-1, -2).
(a) Show how triangle ABC can be translated 3 units righlg and one unit down using matrices. Write
lated righ-t
!,
down the coordinates of A'. B' and C'.
:L)r(3 l, :,) -/
7
-a"
(""
(s 'l L 'l
- z -z -7/ -/
A'" (7- , j) B'r(,-z) i=(U 4)
(b) Show how triangle ABC and be reflected across the y-axis using matrices. Write down the
coordinates of A', B' and C'.
Gffi(3 !, 1' )= r; t L
ch -r)
( l, -=,
tJ :) A,; (?t)'rt B,= t ,r,' il c' -- (2, -l)
BOIYUS [2 pointsJ
to football, there are two ways to score: by the run or by the pass' Team
,i*it* A
a sport
pass 21 times, and
scored 244 points,while Team B scored 273 points. Team A scored by the
r* il
times. Team B scored]tr'the pass 27 times, and by the run 6 times. How many
-6 by the
[r/rl";-?7;']"7tb "4t a'-*{{b -*&r!
plittt is each score worth? , -/
zqZ =-zrt )4tb <lq ,+6{ h = vtoT
/a
U9
r^. 'n" l{.t{
tl b:Z*q,ql
b;; r:a'; fiy /f 7
r u, n z?- ?
{*7 P*'ls*1eil€{ {
Useful Eouations
Ax* BY=( *-lz- lt
xz- xt
! =mx+b
(y-v")=*(*-*.)
rcM=1,
fa
1],,0.,
M-'=hl:, :)