Algebra2 -- SemesterTest Copvriqht Notice: Many {or atl} af the questians were taken from Glencae Algebra 2 tertbaok and the assaciated resources.
No. of Questions: 17 {25 + 2 banus questions} Max Marks: 7A0{+ 4 bonus marks) Topicsfor this SemesterTest: ChapterL to Chapter4 of the textbook 1n$f.JctieQS; Givethe answer of each question next to it in the spaceprovided.
OuestionI Evalnate the expressionif e: 5, b : -1
{2 murks)
2lo- bl*la+ ebl
7 tl; -(-r)l+
Ita+-
,r r
>s: *dd) + tf
4H
tr.ffiJ * l-rl -
.*
Ouesticn_2 Solve the equatien. Checkyawr solutisns to see how many sctuat solutions are there. al ^i Zlc-21
-4c-20
( 2+ 1:3m*r ks)
2 c * l tr
+ lr* CA =,16- lo
Ouestion3 Sclve the follswing equation
242 - t--t-+-393
F:J*
*yi +* 3q lntl.
a)
*)
-5
&-w* drt
*,
d@.
3
\8+''-
L
**3
x J,
tur
.:}.."
(trl*+'il/
.!:
t
d{d#
.3 lTt' ' *t -4" -"")-,f=
1. . 4
n-. ,* g^L
ts"x
3
F
Ouestion4
-5;"ffi
Solve the inequality, Then graph your solufion on a real number line.
"'1*
4frtlrw -r" -+f v -18
Q + L:3 marks)
ab -+f 1-a4-Vf *7n '
f 7r
fr * A**--q?
s
F
g
(
7: 6 (A.5*8:4 marks)
Ouestion5
Translate the expressions in English below into equivalent Algetrraic expressions. NOTE: For parts e-h, you must trsnslste into sn sbsolute vslae fuequality. a) 7 times the sum ofanumber and I -r ,/ Z\
+(/ +E)
b) 2 more th'anthe qtfotientof 5 and a number
1 o+ -L-L ./-.
-productof a numberand 7 c) Sevenlessthan the
*7 +fr d) The sum of the square of a number and the cube of the samenumber .%9
X+X
e) All numbersbetween -1 and 1 including 1 and -1 ll
l*l
.
t All numberslessthan 4 a1d greaterthan -4
l-r I t* t < +' g) All minrbers greater than 5 or less than -5
z5 lxl h) All numbersbetween-3.5 and 3.5, excluding-3'5 ard 3.5
pr
Ouestion 6
(Total: ?ncarks)
{a} lVrife an equation for the line fhaf passesthrough (-4, 9} and $, A}
m #3 * * * R*
{",* r
( 2m ar k s )
Y- 1, * *
f-f) '* q:r'=^(*dn"$
* ,# 1
'u*
/
*,{*-*-*i1n",-ffii-'!fa graphaf )s :
{f u#,3
-+- 5 ? -*
.x*b .,
and ispara*er torhe
r -^&*x,)
u-ff' 4-*6F
*)
*"r
*r) $-"f,x
(/
43 H$-x -b)-t
*-t *{
4l
J
tu.=
6
i2 marks)
* t-(-&*d
+Jt $x
&*,
{c) Write an equation for the line that passesthrough-(2, -5} and is perpendicular to
ot,\ {t,n \ ') ilu'j
thegraphof ), - + * -+- 7 4
a v tz - h
3 -\tF
+
,. marks) (3
* /t' -# ,)
ulll-r)"'l(* * ? )
* ) '#u Us ' F r + K * ) Ouestisn7
*.-fr**S
(1+I+1+|+2:6 mtrks)
(a) Nametherypeof functionshownin thegrapharrove?dfu-"fd
f
{b} What is the value of y when x = -1? {t
k l "'ft r II
I
V
;- :
;t-'
'
r
W{o f^d-^
i '#
F
(c) What is the v*lue off(x) when x: 1?
rl Y{' \ r . f i UrL)
(d) What are tde possiblevalue(s) of x if f(9:2
?
X= ,2* n * h (e) \trhat is the domain & range of this function?
\ flh# 0rqn,,et te*^fu-'* flt**"o v dl (2 + 3:5 marks)
Ouestion8 Graph the following piece-wise functions:
f(x):
-3 -x*1
if x < 3 d x>3
{Total6 marks)
Ouestion9 (a) The graph of f{x): h{x):f(x-4}-6.
lxlis given below.In the same spacegraph '
(b) Give the domain and range of h{x}
|,rw,rr
Ait-'n-*&$"
de*#'
v v*6
{3 mwhs}
{2 madrs}
Ouestion10
(4 + 0.5+ 0.5 :5 marks)
fhe followiag system by graphing. TcII whefher fhe system is consisteaf? lolve Independent?
V'*2x-3 *Jrx-+ 2
2 x-!:3
u
x*2 y:Q
Ouestion11
( 4+1:5msr ks)
s_9lvethe system given in the last quesfion algebraically {substitution or elimination). Do you get atmost the same solution as inthe last question?
2x-!:3
(-) I (- -r 2v :4.
?r*#* 3 Jx r- 5+ f" 5 *I 4â&#x201A;Ź
,{il. #
Ouestion12
*b
{4 + 2:6 mnrks)
Solve the following system of inequalities by grnphing. Confirm your solution by picking a point inside the solution and checking if it satisfies the system of inequalities.
y<x-1 .
a;-\*u
-x{3
F*b Ouestion13
{Total 19 marks)
Given
* :l 'o - l b J ' Lr
r:[o
l-z
Il cf,
tr r |
t' I
-t
- -t' v-t'>
t9
L-
-3
ol
o a
t
*r1
r l'
z : l f o1
-7
1l
ol
L-l
3
0J
Find each of the following:
{a) W- X
{2 marks)
? f::1 1 b-t) L3
{b} wx
? fa^o*#q*J, d"{f 'enr*J Y da l r r o *f e - a &{t-+u *J L 'g
{2 marks}
:rrJ
{c} XW
s{o+j.rt"f -Oftr^+{.rT dJ' [*uu + d rf *f,xo+&q
(d) Is 'WX: XW ? t
fVn
ffi. PJ(2marks) {1 mafk}
{e} detffi?
Amarks)
w"UfJ,&tfrJ" d"il;*fo ^
$) YZ
{2 marks}
f-5 2o -l I
' l-s t+ -yl es -eY [-a
(t Y-'
(2 marks)
[-*.ul O o,lo3 I
f-thq # Tnl
y -u, ot ' |= l, *,f l- LhI I-,,t){l7 -l),oVJ Ul,w &
-ii,tgJ
fo,o5 {e}YY-r
A marks)
f1* 0r"1 t lo 3*q fo, # LJ (h) Z7;t
(2 marks)
fL s mJ "f, qf f* #
(*
l*
U
"'i;:"-*.ffir"r)"'.,;#*' h (/# *r#-fril* t*-tt\;i#Akd
Ouestion14
{Tatal 17 marks}
The fcllorving is a system of three equations in three variatrles:
2x +- 3v - z : A x -2Y -42:t4 3x -+v -82:17 {a} Solve the follorving system of equations in three variatrles using substitution and/ or elimination methods. Note yau CANNOT use matrices to solve this part and yau must show your work to get marks. {8 marks)
',.*f^:.,'fl'
l,t 'kj\-btr:
]'i - . Itt*t r*u*---'r .!fr . l# S* r1ln-%$ 7
f x+3 q * nsI{r 'p
r'l
,
-dJ6*ffi
g(o -t''J-\V r I+-)
t lu U
nlr{I-T;.:!A :4dil-r-#{j.#--
71*
** '{}
b('td
*?$ * 77 V V+ ?< V -:.."' 1 u .."J
L)*f
4A '$ j
--15
-s
S: ,ry--:* 5*u,* 14 _ff; -dl1,, JS #ffis (rffiffim e-:*fit;
",ltz
s*'<-etd*-^"
'
&m) il-#' #
+- ( x ) 5-.*l * -L
3r{+ $* *'k'= 0
!ft)' r "p 2t.- Il-,-r; 2r+s[4)
'' -*l
5,L&;,L Y"",/F v3t*J* *\ j {{,
{tr} Now give the augmented matrix of the system of equati beginning of this question
s given at the {4 marks}
The sum sf three numbers is six. The third number is the sum af the {irst and seccnd number. The frrst number is one more than the third number. Find the number:s by setting up a system of equations and then sclving the system of eqtations. You nay use 3ny method to solve the system of equations.
Y- +# +0E * 6
nuy + & #.{ fnY g 6*
I+
x
X â&#x201A;ŹLTV
f L L
f 1* J-
p
V
0
*.\"
ct
{l -t-| L t
wMN#d;L {o-L l
fj
ttJ*Ailh*,
q-1
lJ,*q
L
o0
J *f f i #
ffi d4t*dffi--&-w Bonus Ouestions
*-
#
#"# 6*
4
(2 marks)
Oaestionl6
Solvethe following equation. You may not use the calculatcr for this question and you must show all your stepsin detail t) 9
ro
; { s a- 2 ) : - - q *
+*Vâ&#x201A;Źl* -kV+Lt'* # -g n ) +ry"r Wv 4;
4 + .11 -q,*_.1 lo r
+
lo
{2 marks)
Ouestion17
A nateboak and a pencil together cost $9.00.If the pencil costs$2.5 lessthan the notebook find the cost ofeach.
Adth e'l -t; r rr
ft
/fl*" 1,5 + A,
n* A,5
P;
ff{
ir
f
{+h
fu mJM* ,.#fue
+
n
yl : l 4
tt f
{.h s. lf'?
*1*;;h
( T l, 5 ' t ?
'";9 ,e6 -.."-"
I
&utNtr rl i|f
EI
s"#
$ x'#q
'-d6fud ${,?F
*