Make the Grade - B Grade Algebra Answers

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


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


2m +n

3m 6m +3mn

-2n

-4mn -2n

2)(4=p

(-4)8=2p

(x6)12=p2+4


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:


Check in : (3x8) + 2 = 26Check in

: (4x6) (2x2) = 20

Check in : (2x5) + (2x-1) = 8 Check in : (3x7) (3x-1) = 21+3=24


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)


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


5/12

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 .!#&/ *#"


3-=+ x3-x=

3-x=yx

3=y

3

2


6/12

!/*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



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


-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


8/12

(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:


y&0

y&4

p$int( p&$tted

"$rre"t&y

m$$th "!r)e


9/12

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:


For each question

for correct

variables and

format (x (x

for one correct

number

for the other

correct number


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


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(/


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

#

#

#


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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Make the Grade - B Grade Algebra Answers