2z −6z 1. Simplify . Identify any z-values for which the expression is undefined. z −3z

a. 2z( z2 – 3z); z ≠ 3 or 0

8x y

3z

9xy z

4y

6x z 6x y z x y z 6x yz

5x 3x y 3y

9y

−6x +x−3 x +9 x +9

−6x −x−7 x +9

−6x −x−7 x +9

−6x +3x+1 x +9

−6x +3x+1 x +9

Name: ______________________ Class: _________________ Date: _________ ID: A

1

Probability and Statistics Summer Math    Multiple Choice Identify the choice that best completes the statement or answers the question.

____ 3 2

2

b. 2z; z ≠ 3 or 0 d. 2z; z ≠ 3

____ 2. Multiply 4 2

3 ⋅ 2 6    4 . Assume that all expressions are defined.

a. 5 3 c. 5 8 9

b. 3 2

3 2 d. 4 2

____ 3. Divide  3

2 25  9 . Assume that all expressions are defined.

a. 125x  10 c.  5 xy 8

b.  x 5y 8

d. 8 xy

 5

____ 4. Subtract 2

2 − −2x −4  2 . Identify any x-values for which the expression is undefined.

a.    b.

2

2  2

2

; The expression is undefined at x = ±3.    ; The expression is always defined.

c.    d.

2    2

2    2

; The expression is always defined.    ; The expression is undefined at x = ±3.

     c.    2z;  no  excluded  values  

÷  

−5 x−6 x−4 10

x −14x +14x+104

x −10x−26 x −10x−26

x −7x−18 x +x−2

Name: ______________________ ID: A

2

____ 5. Simplify  +

x+3 x−4

. Assume that all expressions are defined.

a.      b.

c.      d.

 x−56 10(x+3)!      2

¯!

____ 6. Solve the equation 2x 2 =

6x 2

.

a. b.

x = −2, x = 9, or x = 1 x = 0 or x = 13

c. d.

x = 0 or x = −13 x = 9 or x = 1

____ 7. Simplify the expression 256z 16 4 . Assume that all variables are positive.

a. 4

256 z 4 c. 4z 11

b. 4z 4 d. 4

256 z 11

____ 8. Write the expression 10 8 11 by using rational exponents.

a. 10 −3 c. 10 11 8

b. 10 8

11 d. 10 3

____ 9. Solve x+31 = x+1. a. No solution.

x+31 is not defined for x < −31. c. x =5

b. x = 5 or x = −6 d. x = –6

____ 10. Solve.    4 −y ≥ 1

a. b.

y ≤ 3 y ≥ 3

c. d.

y ≤ 0 or y ≥ 3 0 ≤ y ≤ 3

____ 11. Solve 7x+2 +1 = 8x+4 .

a. b.

−0.27 −26.27 and 0.27

c. d.

26.27 and −0.27 26.27

10(x2  –  x  –  12)  

10(x  +  3)   10(x2  -­‐  x  –  12)  

____ 12. (-2x 6 + 5x5 + 18x4 + 19x3 + 13x2 –x + 1) ÷ (−2x−3)!

x −4x −3x −5x +x−1 +

x −4x −3x −5x +x−1 −2

x −4x −3x −5x +x−1 −

x −4x −3x −5x +x−3

x −3x −9x+27 = 0 x −3x +9x = 0 x −9x +27x+8 = 0 x −3x +8x = 0

ID: A

3

Name: ______________________      Divide using long division. ¯!

a. 5 4 3 2  −2 −2x−3

5 4 3 2 −2  −2x−3

b. c.  d.

5 4 3 2      5 4 3 2

Find each f(c) using synthetic substitution.    5 4 3 2

a. b.

2,048 –1,840

c. d.

–628 –613.33

____ 14. Determine the equation whose roots are –3, –3, and 3.

a. b.

3 2

3 2 c. d.

3 2

3 2

____ 15. Jimmy invests $3000 in an account with a 5.5% interest rate, making no other deposits or withdrawals.  What will Jimmy’s account balance be after 10 years if the interest is compounded 6 times each year?

a. b.

$2,186.75 $3,286.63

c. d.

$74,519.31 $5,186.75

a. − 1 3

c. 1 3

b. −3 d. 3

Express each logarithm in terms of ln 3 and ln 5.

____ 17. ln      a.  b.

3125    9    5ln3 −2ln5  3ln2 −5ln5

c. d.

5ln5 −2ln3 5ln5 −3ln2

___16.    Evaluate  the  expression  log3  (1/27).  

ID: A

4

Name: ______________________      Solve each equation.

____ 18. 625 x−4 = 25 x+5

a. b.

14 13

c. d.

–13 –3

____ 19. If cotθ =  5 12

, find secθ.

a.  b.

secθ =  secθ =

8 5 13  5

c.  d.

secθ =  secθ =

6 7 7 6

____ 20. Find the values of the six trigonometric functions for angle θ, when AC = 10 and BC = 8.

a. sin θ = 5 3

, cos θ = 5 4

, csc θ = 3 5

, sec θ = 4 5

, tan θ = 3 4

, and cot θ = 4 3

.

b. sin θ = 4 5

, cos θ = 3 5

, csc θ = 5 4

, secθ = 5 3

, tan θ = 4 3

, and cot θ = 3 4

.

c. sin θ = 5 3

, cos θ = 3 4

, csc θ = 3 5

, sec θ = 4 5

, tan θ = 4 3

, and cot θ = 5 4

.

d. sin θ = 4 5

, cos θ = 3 5

, csc θ = 5 3

, secθ = 5 4

, tan θ = 4 3

, and cot θ = 4 3

.

ID: A

5

Name: ______________________    ____ 21. If g = 35.4 and F = 34°, find h. Round to the nearest tenth.

a. b.

h = 30.3 h = 32.3

c. d.

h = 28.3 h = 29.3

____ 22. Write 5π 30

in degrees

a. b.

300° 30°

c. d.

3° 30π°

____ 23. Write –2160° in radians.

a. 12π c. − 12 π

b. −12π d. −  π 12

____ 24. Solve ΔPQR.

Q = 54°, p = 12, q = 14 a. b.

P = 82°, R = 44°, r = 13.1 P = 44°, R = 82°, r = 17.1

c. d.

P = 82°, R = 44°, r = 17.1 P = 44°, R = 82°, r = 13.1

ID: A

6

Name: ______________________    ____ 25. Solve the system of equations using Gauss-Jordan elimination.  

 2x – 3y + z = –14  14x – 18y + 12z = –30  –15x + 21y – 9z = 81

a. b.

x = –3, y = 6, and z = 10 x = 5, y = 8, and z = 0

c. d.

x = –5, y = –3, and z = –1 no solution

2

a. b.

x = 4 or x = 15 x = −20 or x = −3

c. d.

x = −4 or x = −15 x = 20 or x = 3

2

a. b.

x = 3i or –3i x = –3 + 3i or –3 – 3i

c. d.

x = –3 + 3i x = –6 + 3i or –6 – 3i

 2

a. x ≤ 5 or x ≥ 9 c. 6 ≤ x ≤ 8 b. x ≤ 6 or x ≥ 8 d. 5 ≤ x ≤ 9

____  29.    Find  the  zeros  of  the  funcHon  f(x)  =  x2  +  6x  +  18  

____30.    x2  –  14x  +  45  ≤  -­‐3  by  using  algebra.  

_______26.%If%A%=%% 5!!!!!!!!!!!!!!!8−5!!!!!!!!!!!!5 %and%B%=%4!!!!!!!!!!!!!65!!!!!!!− 1 ,%find%AB.%

%%%a.%! −60!!!!!!!!!!− 22−5!!!!!!!!!!!!!!!!!!35 %%%%% % % c.%% 20!!!!!!!!!!!!!!48−25!!!!!!!!− 5 %%%%%%%%%%%%%%%%%b.%% 60!!!!!!!!!!!!225!!!!!!!!!− 35 %%%%%%%%%%%%%%% % % d.%%Not%Possible%

_____27.    Find  the  zeros  of  the  funcHon  h(x)  =  x2  +  23x  +  60  by  factoring.