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