ALGEBRA 1 EOC REVIEW 4 EXPONENTS, FOIL, FACTORING, SYSTEMS

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ALGEBRA 1 EOC REVIEW 4 EXPONENTS, FOIL, FACTORING, SYSTEMS. SIMPLIFY:. 7 x 2 – 5 x – 3 + 2 x. 1). A) 7 x 2 + 3 x – 3. B) x 4. C) – 3. D) 7 x 2 – 3 x – 3. SIMPLIFY:. (- 3 c 3 d 4 )(5 c 5 d 2 ). 2). A) - 15 c 15 d 8. B) - 15 c 8 d. C) - 15 c 8 d 6. D) - 8 c 8 d 8.

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ALGEBRA 1

EOC REVIEW 4

EXPONENTS,

FOIL,

FACTORING,

SYSTEMS

SIMPLIFY:

7 x2 – 5 x – 3 + 2 x

1)

A) 7 x2 + 3 x – 3

B) x4

C) – 3

D) 7 x2 – 3 x – 3

SIMPLIFY:

(- 3 c3 d4)(5 c5 d2)

2)

A) - 15 c15 d8

B) - 15 c8 d

C) - 15 c8 d6

D) - 8 c8 d8

SIMPLIFY:

3)

B)

A)

- 15 x2 y3 z3

D)

C)

SIMPLIFY:

(6 b2 c3)2

4)

A) 12 b4 c6

B) 36 b4 c6

C) 12 b4 c5

D) 36 b4 c5

SIMPLIFY:

5)

B)

A)

D)

C)

SIMPLIFY:

6)

B)

A)

D)

C)

SIMPLIFY:

7)

B)

A)

D)

C)

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

SIMPLIFY:

14)

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

SIMPLIFY:

15)

A)

B)

C)

D)

SIMPLIFY:

16)

A)

B)

C)

D)

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

D) x – 1

C) x – 3

Given: 2 x – 3 y = 12

6 x + 2 y = 42

18)

What is x + y?

2(2 x – 3 y = 12)

4 x – 6 y = 24

3(6 x + 2 y = 42)

18 x + 6 y = 126

22 x = 150

x = 150/22 = 75/11

2(75/11) – 3 y = 12

x + y = 75/11 + 6/11

y = 6/11

150/11 – 3 y = 12

– 3 y = - 18/11

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?

x = cost of a hamburger

cost of a hamburger = \$ .38

y = cost of a hotdog

cost of a hotdog = \$ .995

270 x + 350 y = 450

550 x + 425 y = 630

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

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 fish

B = number of birds

F = 3(62.5) = 187.5

F = 3 B

F + B = 250

No solution since you cannot have a fraction of a bird or of a fish.

3 B + B = 250

4 B = 250

B = 62.5

Given: 4 x + 3 y = 60

x – y = 10

21)

x = y + 10

What is the value of x ?

4(y + 10) + 3 y = 60

4 y + 40 + 3 y = 60

7 y + 40 = 60

7 y = 20

y = 20/7 = 2 6/7 = 2.86

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

Given: 2 x + y = 15

5 x – 6 y = - 22

22)

y = - 2 x + 15

What is the value of x – y ?

5 x – 6(- 2 x + 15) = - 22

5 x + 12 x – 90 = - 22

17 x – 90 = - 22

y = - 2(4) + 15

y = 7

17 x = 68

y = - 8 + 15

x = 4

x – y = 4 – 7 = - 3

A) 11

B) 2

D) - 3

C) 3

Given: w = 1 – v

2 v + w = 4

23)

What is the value of w ?

2 v + 1 – v = 4

w = 1 – v = 1 – 3 = - 2

v + 1 = 4

v = 3

A) 3

B) 2

D) - 2

C) 1

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?

24)

limo: y = .05 x + 80

shuttle: y = .5 x + 60

.05 x + 80 = .5 x + 60

2000 = 45 x

5 x + 8000 = 50 x + 6000

44.4 = x

A) 24 miles

B) 34 miles

D) 54 miles

C) 44 miles

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?

25)

x = number of sodas

y = number of candy bars

6 x + 4 y = 18.50

x = \$ 2.25

y = \$ 1.25

8 x + 2 y = 20.50

A) \$ 1.25

B) \$ 2.25

D) \$ 2.15

C) \$ 1.65

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?

26)

(x – 6)(x + 1)

A) x – 6

B) x – 3

D) x – 1

C) x – 2

27)

Factor: x2 + 9 x + 18

(x + 6) (x + 3)

28)

Factor: x2 – 13 x y – 30 y2

(x – 3 y)(x – 10 y)

29)

Factor: w2 + 2 w – 15

(w + 5) (w – 3)

30)

Factor: x3 + 5 x2 + 6 x

x(x2 + 5 x + 6)

x(x + 2)(x + 3)

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?

31)

Constraints:

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

50 ≤ p ≤ 250

20 ≤ s ≤ 90

p + s ≥ 325

A) \$ 998.25

B) \$ 881.25

D) \$ 952.50

C) \$ 907.50

31)

x + y ≥ 325

P3(250, 90)

Corner points:

P1(235, 90)

y ≤ 90

P2(250, 75)

x > 50

y ≥ 50

x ≤ 250

P(235, 90) = 3(235) + 2.25(90) = \$ 672.50

P(250, 75) = 3(250) + 2.25(75) = \$ 918.75

HIGHEST PROFIT

P(250, 90) = 3(250) + 2.25(90) = \$ 952.50

SIMPLIFY:

32)

A)

B)

C)

D)

34)

Solve the following system of inequalities:

2 x + y < 3

x – 2 y ≤ 8

y < - 2 x + 3

y ≥ ½ x – 4

y = - 2 x + 3

y = ½ x – 4

34)

Solve the following system of inequalities:

3 y ≥ 6 x – 9

3 x + 4 y < 12

y ≥ 2 x – 3

y < - ¾ x + 3

y = - ¾ x + 3

y = 2 x – 3