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7/26/2019 Make the Grade - B Grade Algebra Answers
1/12
1 Simplify the following:
a) 24k6 4k4= c) (2y3)26y4=
6k
b) 8h45h2 h10=h4
h40= 5
6
d) 342 ab7ba3 73ba21=
4h5
(12)2 !"pand and #implify:
a) (y $2)(y $ 6) d) (" % 1) & (" ' 1)(" ' 1)
y +2
y y +2y
+6 +6y +12
= y + 2y + 6y + 12 = x - x x + 1
= y + 8y + 12 = x - 2x + 1
(3) (3)b) (" '3)(" $ 4) e) (2m $ n)(3m ' 2n)
x -3
x x -3x
+4 +4x -12
eltham omm*nity ollege +ea,ning -e#o*,ce#
x -1
x x -x
-1 -x +1
MAKE THE
GRADE
ALGEBRAANSWERS = 1
mark
7/26/2019 Make the Grade - B Grade Algebra Answers
2/12
= x - 3x + 4x - 12 = 6m + 3mn 4mn -2n= x + x 12 = 6m - mn 2n
(3) (4)
c) (p % 5)(p % 2)
p -5
p p -5p
-2 -2p
+10
= p - 5p 2p + 10= p - 7p + 10 (3)
3 Sol.e the following e/*ation#:
a) 2=6
p2+4
(3)
b) 2=6+3
y2
2)(6=y
(x3)12=2y
(-6)-4=3
y2
(3
c)2
m-4=
4
m4+5
12)(2
1=
12
6=m
(-10)6=12m
4m)+(16=12m+10
4m-16=8m+10
m)-4(4=)m4+5(2
(44 Sol.e the following pai,# of #im*ltaneo*# e/*ation#:
a) 3" $ y & 26 b) 4p % 2/ & 20
" $ y & 10 p % 2/ & 2
eltham omm*nity ollege +ea,ning -e#o*,ce#
2m +n
3m 6m +3mn
-2n
-4mn -2n
2)(4=p
(-4)8=2p
(x6)12=p2+4
7/26/2019 Make the Grade - B Grade Algebra Answers
3/12
-: 2x = 16 -: 3p = 18
x = 8 (2 p = 6 (3
!"# x=8 $n : 8 + y = 10 !"# p=6 $n : 6 2% = 2
y = 2 (-8 6 = 2 + 2% 4 = 2% (2 2 = %
" & 8 p &6
y & 2 / &2 (3) (3)
c) 5" $ y & 24 d) 3" % 3y & 24
2" $ 2y & 8 " % 2y &
x2: 10x + 2y = 48 x3: 3x 6y = 27
-
: 8x = 40 -
: 3y = -3 x = 5
(8 y = -1 (3
!"# x=5 $n : 25 + y = 24 !"# y=-1 $n
: x (2x-1 = &
y = -1 (- 25 x + 2 = & x = 7 (-2
" & 5 " & 7
y & -1 y & '1 (4) (4)
5 he g,aph of y&5" ' 4 i# #hown below:
eltham omm*nity ollege +ea,ning -e#o*,ce#
Check in : (3x8) + 2 = 26Check in
: (4x6) (2x2) = 20
Check in : (2x5) + (2x-1) = 8 Check in : (3x7) (3x-1) = 21+3=24
7/26/2019 Make the Grade - B Grade Algebra Answers
4/12
a) n the #ame a"e# d,aw the g,aph of " $ y & 5 (2)
b) #ing the g,aph# find the #ol*tion of the #im*ltaneo*# e/*ation#:y&5" % 4
" $ y & 5 (2)
6
#ing the e/*ation# of the g,aph# in the fo*, bo"e# gi.en abo.e:
a) 7,ite down two g,aph# that a,e pa,allel to each othe,A 'n ) (G*'$n, = 2
b) 7,ite down two g,aph# that c,o## the y'a"i# at the #ame point
'n ) (y=3
c) 7,ite down any g,aph# that go th,o*gh the point (210)A 'n D
d) 7,ite down any g,aph# that c,o## the "'a"i# at " & '3 ()A
ind the e/*ation of the line pa,allel to the line y & 4 $ 3" and pa##ing th,o*gh the point ('4'1)
eltham omm*nity ollege +ea,ning -e#o*,ce#
A
y = 2x + 6
B
y = 3 2x
C
2y = 4x + 6
D
y = 2 + 4x
x + y = 5
2
13= y
2
11=x
correct
line
label
7/26/2019 Make the Grade - B Grade Algebra Answers
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G*'$n, = 3
y = 3x + .
/n x = -4 y = -1: -1 = (3 x -4 + . -1 = -12 +. 11 = .
y = 3x + 11
(4
8 ind the e/*ation of the line that pa##e# th,o*gh the point# (1'1) and (33)
2=2
4=
13
)1(3=Gradient
y = 2x + .
/n x = 3 y = 3: 3 = (2 x 3 + . 3 = 6 + . -3 = .
y = 2x - 3
(5
9atch the e/*ation# with the co,,ect g,aph *#ing the li#t belowNote: You w!! "#$e to %&' # &* eu#to& #&' ,o!ete t"e .!#&/ *#"
eltham omm*nity ollege +ea,ning -e#o*,ce#
3-=+ x3-x=
3-x=yx
3=y
3
2
7/26/2019 Make the Grade - B Grade Algebra Answers
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!/*ation: y = x - 3 !/*ation: x + y = -3
!/*ation: y = -3 x !/*ation:x
3=y
!/*ation: y = x - 3 (6)
10. Sol.e 4" % 5 % 2"
6x 5 7 ( + 2x
6x 12 ( + 5
x 2 ( 6 (2
eltham omm*nity ollege +ea,ning -e#o*,ce#
7/26/2019 Make the Grade - B Grade Algebra Answers
7/12
Show yo*, an#we, on the n*mbe, line below:
(2
11 a) n the a"e# below ma,k the ,egion - that #ati#fie# the ine/*alitie#:
" 2 y ; 1 y < " $ 3 " $ y 4
(6
b) 7,ite down the $n,*co'o,dinate pai,# that lie within -
(-21 (-11 (01 (11 (12 (02 (-12 (03 (2)
12 a) omplete the table of .al*e# fo, y & "3$ 3"2% 3
= '3 '2 '1 0 1
y '3 1 '1 '3 1
eltham omm*nity ollege +ea,ning -e#o*,ce#
-4 -3 -2 -1 0 1 2 3 4 5
!btra"t #$r the re%i$n n$t &abe&&ed '
!btra"t #$r the &ine( n$t &abe&&ed
y=x+3
y=1
x=2
x+y=4
#$r 4 "$rre"t
a&& 8 "$rre"t
7/26/2019 Make the Grade - B Grade Algebra Answers
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(3)
b) >,aw the g,aph of y & "3$ 3"2% 3
(3
c) #ing yo*, g,aph o, othe,wi#e #ol.e:i) "3$ 3"2% 3 & 0
x = 1& ( 01 -13 ( 01 -25 ( 01
ii) "3$ 3"2% 3 & 4
x = 13 ( 01(4
13 9ake t the #*b?ect of the e/*ation in the following:
a) s+2
t=v
t=)(22
t=
(2
b)b
t=R
t=b'
b
t='
2
2
(2
14 acto,i#e completely:
eltham omm*nity ollege +ea,ning -e#o*,ce#
y&0
y&4
p$int( p&$tted
"$rre"t&y
m$$th "!r)e
7/26/2019 Make the Grade - B Grade Algebra Answers
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i) 3p/ $ 2p ii)4#t % 14t@
= p( 3% + 2p = 2,(2 7,
(15 acto,i#e completely:
i) " $ 5" $ 6 iv)p ' p $ 20
= (x + 3(x + 2 = (p 5(p 4
ii) " $ 2" % 8 v) t ' 4
= (x + 4(x - 2 = (, + 7(, - 7
iii) y ' y % 12
= (y - 4(y + 3
(15)
16 a) acto,i#e " - y
= (x + y(x - y!2)
b) Aence o, othe,wi#e" e.al*ate:
53 ' 4
= (53 + 47(53 - 47= (100(6
= 600(2)
1 Simplify:
eltham omm*nity ollege +ea,ning -e#o*,ce#
For each question
for correct
variables and
format (x (x
for one correct
number
for the other
correct number
7/26/2019 Make the Grade - B Grade Algebra Answers
10/12
a)1+x
)1+x!3 2& 3(x + 1 b)
1+x
4+x5+x2
=1+x
)1+x)(4+x(& x + 4
(1) (3)
18 Sol.e " $ 13" $ 12 & 0
(x + 12( x + 1 = 0
x + 12 = 0 * x + 1 = 0 x = -12 * x = -1
(4)
1
a) 7,ite down an e"p,e##ion fo, the a,ea B of the ,ectangle in te,m# of "
( x + 5 (x 2
(2b) Cf B & 18cm find the longe#t #ide of the ,ectangle
( x + 5 (x 2 = 18
x + 5x 2x 10 = 18
x + 3x 28 = 0
(x + 7( x 4 = 0
x + 7 = 0 * x 4 = 0
x = -7 (n, p$# * x = 4eltham omm*nity ollege +ea,ning -e#o*,ce#
" '2
" $ 5
7/26/2019 Make the Grade - B Grade Algebra Answers
11/12
9n, $ = x + 5 = 4 + 5 = &.m
(5
!id "ou #$ake the %rade&'
*ippee++ - , %$t a&& the !e(ti$n( "$rre"t.
, made mi(take( and need t$ pra"ti(e thi( t$pi" m$re.
,# y$!r ("$re i(/
eltham omm*nity ollege +ea,ning -e#o*,ce#
Skill !
, "an (imp&i#y in)$&)in% indi"e( expre((i$n( 1
, "an expand t$ &inear bra"ket( 2
, "an expand and (imp&i#y t$ &inear bra"ket( 2
, "an ($&)e &inear e!ati$n( in)$&)in% #ra"ti$n( 3
, "an ($&)e (imp&e (im!&tane$!( e!ati$n( a&%ebrai"a&&y 4ab
, "an ($&)e m$re "$mp&ex (im!&tane$!( e!ati$n( a&%ebrai"a&&y 4"d
, "an dra the %raph $# a &inear e!ati$n 5a 11a
, "an ($&)e (im!&tane$!( e!ati$n( %raphi"a&&y 5b
, "an interpret the e!ati$n $# a (trai%ht &ine y=mx+" 6
, "an #ind the e!ati$n $# a (trai%ht &ine y=mx+" 78
, "an identi#y &inear !adrati" "!bi" and re"ipr$"a& %raph(
, "an ($&)e ine!a&itie( ith !nkn$n( $n b$th (ide( 10
, "an ($&)e ine!a&itie( %raphi"a&&y 11
, "an "$mp&ete tab&e( $# )a&!e( and dra %raph( $# "!bi"( 12ab
, "an ($&)e "!bi" e!ati$n( %raphi"a&&y 12"
, "an "han%e the (!be"t $# harder #$m!&ae 13
, "an #a"t$ri(e (imp&e expre((i$n( 14
, "an #a"t$ri(e !adrati"( 15i - i)
, "an identi#y #a"t$ri(e and !(e the di##eren"e $# t$ (!are( 15) 16ab
, "an !(e #a"t$riin% t$ (imp&i#y a&%ebrai" #ra"ti$n 17
, "an ($&)e !adrati" e!ati$n( 18
, "an #$rm and ($&)e !adrati" e!ati$n( 1
$p 3 t$pi"( , need t$ re)i(e are
#
#
#
7/26/2019 Make the Grade - B Grade Algebra Answers
12/12
100 - 144 - e&& d$ne. *$! are $rkin% at %rade ith y$!r a&%ebra (ki&&(.
50 - - 9r$mi(in% $rk : make (!re y$! a(k #$r he&p and re)i(e the t$pi"( that y$! had
di##i"!&ty ith. *$! "an (ti&& %et that
0 : 4 - eri$!( re)i(i$n and he&p i( needed i# y$! are %$in% t$ %et
that . $rt it $!t n$. ;$n
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