1)

SIMPLIFY:

7 x2 – 5 x – 3 + 2 x

A) 7 x2 + 3 x – 3 B) x4

C) – 3

D) 7 x2 – 3 x – 3

2)

SIMPLIFY:

(- 3 c3 d4)(5 c5 d2)

A) - 15 c15 d8

B) - 15 c8 d

C) - 15 c8 d6

D) - 8 c8 d8

3)

SIMPLIFY:

A) B)

C) D)

zyx

zyx24

452

4

60

- 15 x2 y3 z32

4315

x

zy

2

4356

x

zy2

3315

x

zy

4)

SIMPLIFY:

(6 b2 c3)2

A) 12 b4 c6

B) 36 b4 c6

C) 12 b4 c5

D) 36 b4 c5

5)

SIMPLIFY: 0

1

528

t

tr

s

r

A) B)

C) D)

3

8 6t

65t 0

s

r8

6)

SIMPLIFY: 3

3

24

3

2

a

nb

A) B)

C) D)

9

612

27

8

a

nb6

57

27

8

a

nb

6

57

3

2

a

nb9

612

3

2

a

nb

7)

SIMPLIFY:

qp

qp6

23

A) B)

C) D)

q

p33

3

q

p

33

1

qp 2

3

q

p

8) Find the perimeter of a triangle whose sides are (3 x2 + 5); (5 x – 2); and (6 x2 + 5 x).

A) 9 x2 + 10 x + 3 B) 19 x2 + 3

C) 9 x4 + 10 x2 – 3 D) 7 x4 + 10 x – 3

9) Simplify: (2 x + 5) (2 x – 3)

A) 4 x2 – 15

B) 4 x2 – 4 x – 15

C) 4 x2 + 4 x – 15 D) 8 x – 15

10)

Simplify: (3 x2 + 5 x + 1) – (7 x2 – 2)

A) - 4 x2 + 5 x + 3 B) - 4 x2 + 5 x – 1 C) x2 – 1

D) x2 + 3

11)

Simplify: (x – 2) (3 x2 – x + 4)

A) 3 x3 – 7 x2 + 6 x – 8 B) 3 x3 – 6 x2 + 6 x + 4 C) 3 x3 + 7 x2 – 6 x – 8 D) 2 x3 – 8

12)

Find the perimeter of a rectangle if the width is (2 x – 4) and the length is (5 x + 1).

A) 7 x – 3

B) 7 x + 3

C) 14 x – 6

D) 14 x + 6

13)

Find the area of a triangle if the base is (2 x – 4) and the height is (x + 6).

A) x2 + 4 x – 12 B) 2 x2 + 8 x – 24 C) 2 x2 – 8 x – 24 D) 3 x + 2

14)

SIMPLIFY:

xy

yxxyxy

2

864 22

A) 2 x y – 3 + 4 x B) 2 y – 3 + 4 x

C) 2 y – 3 + 4 y

D) 2 x y – 3 + 4 x2

15)

SIMPLIFY:

4

3

x

A) B)

C) D)

x3 3 4x

4 3x 4 3x

16)

SIMPLIFY: 3

1

6 y

A) B)

C) D)

36 y 3 6 y

y36 32 y

17)

The area of a rectangle is given by the expression: x2 – 5 x – 6. The length and width have only integral coefficients. Which of the following could represent the length of the rectangle?

A) x – 6 B) x – 2

C) x – 3 D) x – 1

18)

Given: 2 x – 3 y = 12 6 x + 2 y = 42

What is x + y?

2(2 x – 3 y = 12)3(6 x + 2 y = 42)

4 x – 6 y = 24

18 x + 6 y = 126

22 x = 150x = 150/22 =

75/112(75/11) – 3 y = 12150/11 – 3 y = 12

– 3 y = - 18/11

y = 6/11

x + y = 75/11 + 6/11

x + y = 81/11 = 7.4

19)

A restaurant received 270 hamburger patties and 350 hotdogs on Monday for $ 450. On Friday the restaurant received 550 hamburger patties and 425 hotdogs for $ 630.a) How much did each hamburger

cost?

b) How much will 25 hamburgers and 50 hotdogs be?

x = cost of a hamburgery = cost of a hotdog270 x + 350 y =

450550 x + 425 y = 630

cost of a hamburger = $ .38cost of a hotdog = $ .995

25($.38) + 50($.995) = $ 59.25

20)

A local pet store has triple the amount of fish as birds and has a total of 250 fish and birds. Write a system of equations represents the number of fish and birds using the variables F and B.F = number of

fishB = number of birdsF = 3 BF + B = 2503 B + B = 2504 B = 250B = 62.5

F = 3(62.5) = 187.5No solution since you cannot have a fraction of a bird or of a fish.

21)

Given: 4 x + 3 y = 60 x – y = 10

What is the value of x ?

x = y + 10

4(y + 10) + 3 y = 604 y + 40 + 3 y = 607 y + 40 = 607 y = 20y = 20/7 = 2 6/7 = 2.86

x = 2 6/7 + 10 = 12 6/7 = 12.86

22)

Given: 2 x + y = 15 5 x – 6 y = - 22

What is the value of x – y ?

A) 11 B) 2

C) 3 D) - 3

y = - 2 x + 15

5 x – 6(- 2 x + 15) = - 225 x + 12 x – 90 = - 2217 x – 90 = - 2217 x = 68x = 4

y = - 2(4) + 15y = - 8 + 15

y = 7x – y = 4 – 7 = - 3

23)

Given: w = 1 – v 2 v + w = 4

What is the value of w ?

A) 3

B) 2

C) 1 D) - 2

2 v + 1 – v = 4v + 1 = 4v = 3

w = 1 – v = 1 – 3 = - 2

24)

A limosine company charges a flat-fee of $ 80 plus $.05 per mile. A shuttle van company charges a flat-fee of $ 60 plus $.50 per mile. Approximately what mileage will yield the same fare for both?

A) 24 miles

B) 34 miles

C) 44 miles

D) 54 miles

limo: y = .05 x + 80shuttle: y = .5 x + 60.05 x + 80 = .5 x

+ 605 x + 8000 = 50 x + 6000

2000 = 45 x44.4 = x

25)

The price of six sodas and four candy bars is $ 18.50. The price of two candy bars and eight sodas is $ 20.50. What is the price of a candy bar?

A) $ 1.25

B) $ 2.25

C) $ 1.65

D) $ 2.15

x = number of sodasy = number of candy bars

6 x + 4 y = 18.508 x + 2 y = 20.50

x = $ 2.25y = $ 1.25

26)

The area of a rectangle is given by the expression: x2 – 5 x – 6. The length and width only have integral coefficients. Which of the following could represent the length of the rectangle?

A) x – 6

B) x – 3

C) x – 2

D) x – 1

(x – 6)(x + 1)

27)

Factor: x2 + 9 x + 18

28)

Factor: x2 – 13 x y – 30 y2

(x + 6) (x + 3)

(x – 3 y)(x – 10 y)

29)

Factor: w2 + 2 w – 15

30)

Factor: x3 + 5 x2 + 6 x

(w + 5) (w – 3)

x(x2 + 5 x + 6) x(x + 2)(x + 3)

31)

A restaurant makes at least 50 pizzas a night, but no more than 250 pizzas. The restaurant makes at least 20 salads but no more than 90 salads. A total of no less than 325 pizzas and salads are made each night. Each pizza makes a profit of $ 3.00. Each salad makes a profit of $ 2.25. What is the maximum profit the restaurant can make in a night?

A) $ 998.25

B) $ 881.25 C) $

907.50 D) $ 952.50

Constraints: 50 ≤ p ≤ 250 20 ≤ s ≤ 90

P(x, y) = 3 p + 2.25 s

p + s ≥ 325

31)

0 25 50 75 100 125 150 175 200 225 250 275 300 325010203040506070809010011 0120130140150160170180190200210220230240250260270280290300310320330340

x

y

x > 50

x ≤ 250

y ≤ 90

y ≥ 50

x + y ≥ 325

Corner points:

P1(235, 90) P2(250,

75)

P3(250, 90)

P(235, 90) = 3(235) + 2.25(90) = $ 672.50 P(250, 75) = 3(250) + 2.25(75) = $ 918.75 P(250, 90) = 3(250) + 2.25(90) = $ 952.50

HIGHEST PROFIT

32)

SIMPLIFY: 3

4

32

y

x

A) B)

C) D)

12

98

y

x

9

12

8x

y

9

12

6x

y

6

7

6x

y

9

12

93

129

12

3

82

2

x

y

x

y

y

x

33)

SIMPLIFY: 2

2

3

6

4 24

c

ab

c

ba

4

62

6

4 44

c

ba

c

ba

2

7616

c

ba

34)

Solve the following system of inequalities: 2 x + y

< 3x – 2 y ≤

8y < - 2 x + 3

y = - 2 x + 3

y ≥ ½ x – 4

y = ½ x – 4

34)

Solve the following system of inequalities: 3 y ≥ 6 x –

9 3 x + 4 y <

12y ≥ 2 x – 3

y = 2 x – 3

y < - ¾ x + 3

y = - ¾ x + 3