MCR3U – Unit Test #2 Name: _________________

Instructions: 1. Read each question carefully before answering. 2. Express all fractions in lowest terms. 3. Do not change fractions to decimals unless exact! 4. Calculators can be used but cannot be shared. Your phone is not a calculator! 5. Good Luck !!

1. Determine whether each pair of functions is equivalent:

a) and

b) and

c) and

EF1 /9 EF2 /18 EF3 /15 EF4 /8 EF5 /20 Total /70

EF1 We are learning to determine whether algebraic expressions are Equivalent. /9

EA

:)=*×)(×+2)

fW=×3+×2.z×941=3×3-31

fkttglx )bCD=§±+i)(3ttD( 3++1 )

=§t2t6ttD( 3++1 ) : .bH)=Ht)

=27t3t 27+2+9++1

f(x)=xI6× . x?xt4 +2×3+1

flx )= 2×2-7×+5

glx ) . 4×2.7×-3 -2×2+81×1=2×2-7×+59

fwjtgk )

2. Simplify the following expressions a) � � � � � �235423 222 ������� xxxxx (3 marks) b) )()( xgxf � , where xxxf 37)( 2 � and 12)( 2 �� xxg (3 marks) 3. Expand and simplify. (6 marks)

a)

b) 4. A cylinder with a top and bottom has radius and height . Write

a simplified expression for its a) volume, where (3 marks) b) surface area, where (3 marks)

EF2 We are learning to add, subtract, and multiply polynomials. /18

*= 3×2+2×-4 - Xhtx +5+3×2+2

= 5×2+3×+3

a= 75 . 3x . (-2×2+1)

= 7×2 - 3×+2×2-1= 9×2 -3×+1

= 155-25×-12×+20 - (2×-3×2×3)= 155 - 37×+20 - (4×2.6×-6×+9),

1 5×2- 37×+20 - 4×2+6 x +6×-9

= 11×2 - 25×+11

=8x3y3+iox4y2 . Rniy"

. lsnij= 10×46-7×3 y

'. Riiy

: as 27 (2×+1×2×+1)

a) V=I (2×+1)/2×+1 ) (2*1)

+2tG*#⇒V=t (4×2+4×+1) (2×-1)Sa=2t§*D#)tf#¥V=I( 8×3+4×2 . 2×-1 ) sat'TE4I+4xtD'#xiD]sA=2H(8x2t4x]

EF3 We are learning to factor polynomials. /15 5. Factor fully. a) 10112 �� xx b) 22 70063 xy � c) 3311217 ��� yxxy d) 2 2 4 4p q p� � � e) f) EF4 We are learning to simplify rational expressions /8 6. Simplify and state and restrictions on the variable. (4 marks)

����������� ������������������ !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~��������������������������������� ¡¢£¤¥¦§¨©ª«¬­®¯°±²³´µ¶·¸¹º»¼½¾¿ÀÁÂÃÄÅÆÇÈÉÊËÌÍÎÏÐÑÒÓÔÕÖ×ØÙÚÛÜÝÞßàáâãäåæçèéêëìíîïðñòóôõö÷øùúûüýþÿ2����������� ������������������ !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~��������������������������������� ¡¢£¤¥¦§¨©ª«¬­®¯°±²³´µ¶·¸¹º»¼½¾¿ÀÁÂÃÄÅÆÇÈÉÊËÌÍÎÏÐÑÒÓÔÕÖ×ØÙÚÛÜÝÞßàáâãäåæçèéêëìíîïðñòóôõö÷øùúûüýþÿ

=(x .io#=7(9yHo0x2 )@

����������� ������������������ !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~��������������������������������� ¡¢£¤¥¦§¨©ª«¬­®¯°±²³´µ¶·¸¹º»¼½¾¿ÀÁÂÃÄÅÆÇÈÉÊËÌÍÎÏÐÑÒÓÔÕÖ×ØÙÚÛÜÝÞßàáâãäåæçèéêëìíîïðñòóôõö÷øùúûüýþÿ2����������� ������������������ !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~��������������������������������� ¡¢£¤¥¦§¨©ª«¬­®¯°±²³´µ¶·¸¹º»¼½¾¿ÀÁÂÃÄÅÆÇÈÉÊËÌÍÎÏÐÑÒÓÔÕÖ×ØÙÚÛÜÝÞßàáâãäåæçèéêëìíîïðñòóôõö÷øùúûüýþÿ =7(3ytloxX3ytoD-7xCyff.uly.D@H.4ptlD.q

'

Kkuxyid I&¥IEskd30=[24+7×247]

3%0%5566×-3=5×(2×+1)

- 3( 2×+1 )= (5×-3×2×+1)

MTHO= Mt3 mtdM¥+7 mhto

M¥-7= # Mt -753

7. An isosceles triangle has two sides of length . The perimeter of the triangle is . Determine the ratio of the base to the perimeter, in simplified form. State the restriction on . (4 marks) EF5 We are learning to add, subtract, multiply, and divide rational expressions. /20 8. Simplify each rational expression (remember to state restrictions) (8 marks)

a) yxyx

yxyx

3

53

25

42

4216

3512

y b) 127

29

322 ��

��

� xxx

x

915,9×+3 18×+6

pb.sk/+4bb=(39tkf- (18×+6)

3¥ b= -30×+10-18×-6TREIB b=l2×t4

bg.gs/s;3xYxtE9x=t ↳

x=: to

=*¥sxTyx¥÷ITy.

= Estate'¥Et's

= .fi#YIIxxItEIKYTIy2Tx8y7=3lx-4)tlx2Xxt3)

(¥6→Xf4)=%×3y-

2=3×-12+5+-1-6

attn= It 4×-18

FEET ) 5*734

9. Simplify and state restrictions: (12 marks)

a) 472232

32186

2

2

2

2

2

2

���

y����

u���

xxxx

xxxx

xxx

b)

2 2 2 2

2 2 2 2

2 2

2 2

5 6 2 35 6 2 3

4 32

a ab b a ab ba ab b a ab b

a ab ba ab b

� � � �y

� � � �� �� �

. ¥¥E¥t×¥¥¥t5¥¥¥* ,

i¥*¥2Ix¥¥**xe¥¥⇒. .tk#IgDxdIgIsxti4i2s' ii 's '

¥¥÷¥#¥t¥s¥x¥**→=@+2§(atb#+3ha a- b)

59¥34 . bbepb