Pre-calculus Summer Math Packet 2017 Multiple Choice Page 1A

Pre-calculus Summer Math Packet 2017 ? Multiple Choice

Page 1A

Complete all work on separate loose-leaf or graph paper. Solve problems without using a calculator. Write the answers to multiple choice questions on the attached answer sheet.

1. Evaluate: 1 + 1 + 1 =

2 3 4

2.

Simplify completely:

22-50 2-10+25

A)

13 12

B)

1 24

C)

1 9

D)

19 18

A)

2(-5)2 (+5)2

B)

- 2-2

10

C)

2(-5) +5

D)

2(+5) -5

3. In , = 90?. If = 5 and = 4, which statement is NOT true?

A) cos = 4

5

B) tan = 5

3

C) sin = 4

5

D) tan = 3

5

4. The hypotenuse of right is 10 and the = 60?, what is the measure of the leg opposite angle A?

A) 5 B) 103

C) 52 D) 53

5. Which cubic polynomial best describes the data?

x -3 -2 -1 0

1

2

3

4

y -12 0 0 -6 -12 -12 0 30

A) = 3 + 62-7x-6 B) = 3 - 7 + 6

C) = 3 - 7 - 6 D) = -3 - 7 + 6

6. The graph of a polynomial function has the following x-intercepts: 0, 1, 3, 6. Which of these expressions represents such a function?

A) ( - 1)( - 3)( - 6) C) ( + 1)( + 3)( + 6) B) 2( - 1)( - 3)( - 6) D) ( + 1)(3 + 1)(6 + 1)

7. The base angle of an isosceles triangle measures 30?, and the length of one of the legs is 12. What is the length of the altitude drawn to the base of the triangle?

8. Divide, using either polynomial long or synthetic division: 24+73+82+8+8:

+2

A) 23 + 2 + 3 + 2 C) 23 + 32 + 2 + 8

A) 6

C) 63

B) 23 + 2 + 3 + 4 D) 23 + 32 + 2 + 4

B) 12

D) 9

9. The side of a square is 8 units. What is the length of its diagonal?

A) 83 B) 82

C) 42 D) 162

10. The graph of a quadratic function = ( + 1)2 - 3 is reflected across the y-axis and then translated 2 units down. Which are the coordinates of the vertex of the new graph?

A) (-1,1) B) (1, -1)

C) (1, -5) D) (-1, -5)

11. If () = 2 - , find (2+)-(2).

A) 3 + B) 6 +

C) 1 + D) 5 +

Precalc Summer Math Packet 2017 ? Multiple Choice Page 2A

12. With respect to which line is the graph of the equation () = 4 - 32 + 6 symmetric?

A) = 0 B) = 0

C) = 6 D) =

13. Which of the following is NOT an asymptote of the function () = ||((22-+--66)):

A) = 3 B) = 1

C) = 0 D) = -1

14. The table below shows several corresponding values of x

and y in a continuous polynomial relation. Based on the table,

within which interval is there a zero of the polynomial?

x -3

-1

1

3

5

7

y 4.24 -10.18 -16.60 -15.02 -5.44 6.35

A) -1 < < 1 B) 1 < < 3

C) 3 < < 5 D) 5 < < 7

15. Combine to a single rational expression: -5 -

+3 +2 +7

A)

-3-41 2+10+21

B)

-2-31 2+10+21

C)

3-41 2+10 +21

D)

2-31 2+10+21

16. The SUM of the two real solutions to + 4 = 13 + 30 is:

A) 10 B) 9

C) 5 D) 6

17.

Simplify

the

rational

expression:

22-7-15 42+10+6

A) +3

2+2

B)

-5 2+2

C) +5

2+6

D)

+3 2+1

18. A number c is a multiple zero of a polynomial P(x) if P(x) has a factor in the form ( - ) when 2 (multiplicity).

How many numbers are multiple zeros of the polynomial () = (6 - 1)( - 1) - (3 - 1)(2 - 1)?

A) 0 B) 1

C) 2 D) 4

19. If () = 2 + 4 and () = 1 - . What is the value of ((-3))?

20. Solve; check for extraneous solutions: 6 = 24 + 12

A) 23 B) 2

C) 8 D) 13

A)

=

2 3

B) = -1

C)

= 1 and

-2

3

D)

= - 1

3

and

2

Precalc Summer Math Packet 2017 - Multiple Choice Page 3A

21. Solve the inequality for x:

+2 2-1

>

5.

The solution

set for x is (Hint: Don't forget to consider any

vertical asymptote):

A)

<

17

29

<

B) < 2

C)

1 < < 2

2

D) 1 < < 7

2

9

22. Find the inverse of = 72 - 3; 0

A) = +3

7

B) = +3

7

C) 2 = -3

7

D) = -3

7

23. Rationalize the denominator of the expression: 33-+66; simplify completely.

A) -1-218

3

B)

-3-218 9

C) -3 + 22 D) 9 - 218

24. Use the quadratic formula to solve the equation: 52 + 9 - 2 = 0

A)

= 2 , -4

5

B)

= 1 , -2

5

C)

= 56 , -13

5

D)

= - 1 , 2

5

25. Simplify -175 using imaginary number i.

A) 175 B) 57

C) 5-7 D) -57

26. Simplify the expression (2 + 5)(-1 + 5)

A) -27 + 5 B) 23 + 5

C) -2 + 25 D) -2 + 5

27. Factor the expression: 3 - 512

A) -( - 8)(2 + 8 + 64) B) ( - 8)(2 + 8 + 64)

C) ( + 8)(2 + 8 + 64) D) ( - 8)(2 - 8 - 64)

28.

Divide;

state

all

restrictions

on

the

variables:

2-16 2+5+6

?

2+5+4 2-2-8

A)

(-4)2 ; -3, -1

(+3)(+1)

B)

(+4)2(+1) (+2)2(+3)

;

-3,

-2,

4

C)

(-4)2 ; -4, -3, -2, -1, 4

(+3)(+1)

D)

1 (+3)(+1)

;

-4,

-3,

-2, -1,

4

Precalc Summer Math Packet 2017 ? Multiple Choice Page 4A

29. Simplify 3128136; assume all variables are positive.

A) 242(34) B) 44(3)

C) 24(38) D) 442(32)

30. Find the missing value to "complete the square" of 2 + 6 + .

A)

3 2

B) 9

4

C) 9 D) 36

31. Factor the expression: 4 - 202 + 64

A) ( - 2)2( + 4)2 B) ( - 2)( - 4)(2) C) ( - 2)( + 2)( - 4)( + 4) D) No solution

4

33.

Simplify

the

complex

fraction:

+3

1+3

A)

12+4 2+3

B) 4

3+9

C)

4 32+10+3

D) None of these

32. Simplify the complex fraction:

(49- 2)1/2 +9 2(49- 2)-1/2

49-2

A)

49+82 (49- 2 )3/2

B)

49+112 (49- 2 )3/2

C)

582 (49- 2 )3/2

D) None of these

34. Solve the equation and check your solution:

2-36

+

2 -6

=

1 +6

A) = -6 B) = -9

C) = -9, -6 D) = 6

35.

Let

()

=

1 42-5

and

()

=

-

3.

Find (()) and (()).

A)

(()) = 1 ;

4-3-5

(()) = 422--45

B) (()) = 1 ;

4-14

(()) = 349-2-124

C) (()) = 1612-8; (()) = 42 - 14

D)

(()) = 1 ;

4-17

(()) = 244-23-52

36. A water tower is located 410 feet from a building. From a window in the building, the angel of elevation measured to the top of the tower is 42? and the angle of depression to the bottom to the tower is 25?. Approximately how tall is the tower?

A) 191 feet B) 369 feet

C) 448 feet D) 560 feet

42

25

Precalc Summer Math Packet 2017 ? Free Response Questions

Page 5A

1. Factor by grouping: 34 + 83 - 15 - 40

2. Find the domain of the

function:

=

2-3-28 2-6-27

3. Find the domain of the function: = - 36

4. Find the zeros of the polynomial m(x) and factor the polynomial into linear factors: () = 3 + 42 + - 6

5. The length of the hypotenuse of a right triangle is 13 mm. The length of the shorter leg is 7 mm less than the length of the longer leg. Find the length of the shorter leg (MUST show ALL algebra work or NO credit).

6. The expression () = -162 + 1800 models the height of an object t seconds after it has been dropped from a height of 1800 feet. Find the height of the object after falling for 4.8 seconds.

7. In right triangle , = 18.3, = 11.2, and = 90? What is the measure of angle A to the nearest tenth of a degree?

8. The height h in meters of a rock thrown straight up at t seconds is described by the equation () = 2 + 20 - 4.92. Find and interpret the average rate of change of the change in the height of the rock over the first two seconds of flight.

9. A company's total revenue, R(x) (in millions of dollars), is related to its expenses by the equation () = 43 - 162 + 12, where x is the amount of expenses (in tens of thousands of dollars). What values of x will produce zero revenue?

10. On a single sheet of graph paper: (a) Draw the graph of the equation = 2 - 4 + 4, including all values of x from = -1 to = 5.

Label the graph a.

(b) On the same set of axes, draw the image of the graph drawn in part (a) after a translation that maps (, ) ( - 2, + 3). Label the image b.

(c) On the same set of axes, draw the image of the graph drawn in part (b) after a reflection across the x-

axis. Label the image c.

(d) Which equation could represent the graph drawn in part (c)? 1) = -2 + 4 + 4 2) = 2 - 3 3) = -2 - 3 4) = -2 + 3

11. Graph the function 12. Graph the function

= + 3

= -3 + 42 - 5

13. Graph the function 2 - 4 - 12

= 22 - 8

14. Graph the solutions to the system of inequalities.

{2

-

2 5

+ <

3 20

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