MCR 2014-2015 Semester 2...

MCR Semester 2 Review ** Only TI-108 calculator is allowed on exam!!**

Page 1 of 6 revised 6/2014

1. Find the degree of each polynomial. A. 4 3 75 12x x x− − + has degree ___. B. 23 5 1x yz xyz− + has degree ___. C. 2x has degree ___. D. x xy xyz+ + has degree ___.

2. Classify each polynomial according to the

number of terms (monomial, binomial, trinomial, polynomial):

A. xyxyyx 987 22 +− _______________

B. 52118325 edcba _______________

C. 56 −x _______________

D. 1536 22 −−− pqpqqp ______________

3. Match each letter with the correct Roman

numeral. You may use a number more than once.

A. 32x−

B. 32 x

C. 32x−

D. 3

2x −

⎛ ⎞⎜ ⎟⎝ ⎠

E. 18x−

F. 3

112x

−

−⎛ ⎞⎜ ⎟⎝ ⎠

4. Simplify each expression using no negative exponents. A. xxx •• 38 B. ( )( )43 35 xx

C. 03 )3( y

D. ( )475x−

E. 2

8

4515yy

F. 3

2 2

129xy zx yz

G. 26

2

84xx

⎛ ⎞⎜ ⎟⎝ ⎠

H. 2

7

45⎟⎟⎠

⎞⎜⎜⎝

⎛

pp

I. ( )312 −y

J. 2 3( 5 )xy−−

K. 2

5

4

3

−

⎟⎟⎠

⎞⎜⎜⎝

⎛

yx

L. 9

5

xxx •−

5. Find the sum or difference.

A. 3 2 3 2(9 8 1) (5 9 8)x x x x− + + − −

B. 2 2(6 9 8) (5 6 )x x x x− + − − +

I. 8x

II. 8x

III. 3

2x

IV. 3

8x



6. Find the product.

A. )2)(4( −+ xx B. (2 1)(8 5)x x− +

C. )12)(12( +− xx

D. 2)43( +x (Be careful here!)

E. 2)57( −x (Be careful here!)

F. )32)(6( 2 +−+ xxx

G. )245)(13( 2 −−− xxx 7. What is the greatest common factor of the terms

in the given polynomial?

A. 12 32x −

B. 2 3 26 18p m pm−

C. xxx 241812 23 −− 8. Factor each expression completely.

A. 43223 102515 xyyxyx +−

B. 2 4 60x x− −

C. 2 4 3x x− +

D. 2 10 25x x+ +

E. 310 2 −+ xx

F. 5136 2 −− xx

G. 4 3 212 20x x x− +

H. 3 230 26 4x x x− +

I. 2 9x −

J. 3 5x x−

K. 2223 +−− xxx

L. 3 23 15 2 10x x x− + − 9. Use factoring to solve each equation.

(Remember to get each equation in general form first!)

A. 2 5 6 0x x− − =

B. 2 25 0x − =

C. 432 += xx

D. 32 2 += xx

E. 214 33 5x x+ =

10. Determine the restrictions for the value of x for

each equation.

A. xxxf

65)( −

=

B. 5

4)(+

=xxxh

C. 42)( 2 −

+=xxxg (Factoring required here!)



11. Simplify each expression. Assume there are no zero denominators.

A. 33

7643

51510yx

yxyx +

B. 2

54335

992718

pqpqqpqp

−−−

C. 234

3

329xxx

xx−−

−

D. xxxx9966

2

24

+−

E. 11 76 6y y

+

F. 3 5 102 2x xx x− +

+

G. 3 6 67 7x xx x− −

− (Watch your signs!)

H. xx 35

42− (Think LCD!)

I. 5 1 23 6x xx x− +

−

J. 25

13

+−

+−+

xx

xx

K. 53

41

++

−−+

xx

xx

L. xy

yx

65

253

2

4

•

M. xy

yx32

812

2 •

N. 6 3xx y÷

O. yx

yx

34

98 2

7

5

÷

P. 4565

231

2

2

2

2

+−++

•++

−xxxx

xxx

Q. 822 22

23

−+÷

−−+

xxx

xxxx

(This factoring thing keeps coming up. It must be pretty important!)

12. Solve each rational equation.

A. 743

=x

B. 325

=x

C. 1 2 15 9

xx−

=

D. 39

24

+=

− xx

E. 752=+xx

F. 1442

3=+xx

G. 10123

=+xx

H. 731

45

−=+xx



13. Simplify each square root expression. No decimal answers!

A. 416x

B. 162

C. 364x

D. 527x

E. 5 48

F. 2718 •

G. 188 •

H. 2 3 6 6•

I. 114

J. 108

K. 16 9− +

L. 3 5 45+

M. 6 12 3−

N. 3 4 27 12− +

O. ( )( )5754 ++

P. ( )( )3232 +−

Q. ( )254 −

R. 21

3−

S. 21

5+

14. Solve each square root equation.

A. 63 =x

B. 105 =x

C. 10733 =+−x

D. 145 −=+x

E. 11713 −=+ xx 15. What is the length of the diagonal of a non-

regulation tennis court with length 20 feet and width 15 feet?

16. A 25-foot ladder leans against a wall. The base

of the ladder is 15 feet from the bottom of the wall. How far up the wall does the top of the ladder reach?

17. What is the length of the diagonal of a square

with perimeter 12 m? Express the answer as a simplified square root.

18. Solve each equation using the square root

method.

A. 22 24x = B. 1012 =−x

C. 2( 1) 9x+ =

D. 24( 3) 20x + =



19. Solve each equation using the Quadratic Formula. Express each answer as a simplified square root. (Formula is provided on exam.)

For 02 =++ cbxax , a

acbbx2

42 −±−= .

A. 2 3 2 0x x− − =

B. 0173 2 =−− xx

20. What is the number of x-intercepts for the graph

of each quadratic equation?

A. 2832 −+= xxy

B. 25102 ++= xxy

C. 1742 +−= xxy

21. What is the vertex of the graph of each quadratic equation? (The formula to find the vertex is NOT given on the exam!)

A. 382 2 −−= xxy

B. 1123 2 ++= xxy

22. Which direction does the parabola with the

given equation open?

A. 534 2 −+−= xxy

B. 972 −−= xxy

23. The graph of 32)( 2 −+= xxxf is provided below. What are the solution(s) of the equation

0322 =−+ xx ?

−4 −3 −2 −1 1 2 3 4 5

−4

−3

−2

−1

1

2

3

4

x

y

24. The graph of 32)( 2 −−= xxxf is provided

below. What are the solution(s) of the equation 0322 =−− xx ?

−4 −3 −2 −1 1 2 3 4 5

−4

−3

−2

−1

1

2

3

4

x

y

25. What is the equation of a quadratic function

with vertex (3,-1) and y-intercept (0,8)? (Choose the correct answer below.) A. 862 +−= xxy

B. 832 +−= xxy

C. 1622 −+= xxy

D. 132 −+= xxy 26. What is the equation of a quadratic function

with vertex (-3,1) and y-intercept (0,-8)? (Choose the correct answer below.) A. 862 +−−= xxy

B. 862 ++= xxy

C. 862 −−= xxy

D. 862 −−−= xxy



27. Which is the equation of a quadratic function with x-intercepts (8, 0) and (4, 0)? A. 2( ) 12 32f x x x= − + B. 2( ) 12 32f x x x= + − C. 2( ) 12 32f x x x= + + D. 2( ) 8 4f x x x= + +

28. What is the equation of a quadratic function

with x-intercepts (-5,0) and (1,0)? A. 54)( 2 −−= xxxf

B. 54)( 2 +−= xxxf

C. 54)( 2 −+= xxxf

D. 54)( 2 ++= xxxf 29. What is the solution of the inequality

0)3)(4( ≥+− xx ? A. 4−≤x or 3≥x B. 3−≤x or 4≥x C. 34 ≤≤− x D. 43 ≤≤− x

30. Graph the solution to problem #29 on the

number line below.

31. What is the solution of the inequality

01892 ≤+− xx ? A. 6−≤x or 3−≥x B. 3≤x or 6≥x C. 36 −≤≤− x D. 63 ≤≤ x

32. Graph the solution to problem #31 on the

number line below.

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MCR 2014-2015 Semester 2...

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