Download Cumulative Review 1

ALGEBRA I
FIRST TERM REVIEW
I.
1.
State the property, axiom, or definition in each example. Assume all variables represent real numbers.
2
2  1 
( x  12  y )  z  ( x  12  y )  z
  16     
2.
3
3  16 
d (0)  0
3.
rs (t )  (t )rs
5.
If x  y  z  a  b and a  b  m  n , then x  y  z  m  n
6.
If x  y  z  a  b and
7.
d (1)  d
9.
If  2  x  y   3  4w  3v , then 4w  3v   2  x  y   3
10.
x  ( x)  z  0  z
11.
m  (n  p)  t   (m  n)  p  t 
12.
2
2
2
2
 w   v   z  (w  v  z )
5
5
5
5
13.
d (1)  d
14.
a b
  1
b a
15.
(rs)t  r ( st )
16.
If x  9 and 9  y then x  y
17.
x  (9)  (9)  x
18.
If w 2  7 and 7  5  2 , then w 2  5  2
19.
x  y  ( z )   x  y  z 
II.
Simplify and show all work on a separate sheet of paper.
1.
35  2(4  9  3)  23
3.
2 4  (6) 
5.
7.
4.
y  z  r , then x  r  a  b
8.
1
(3 z )  1
3z
2.
4(6)  48  (6)  (2)
4.
 3
36      6
 4
5  2  2 5 4
    
9  3  9 3 9
6.

(6)(12)  (9)(2)  (32)
8.
4  6(3  8  2  2)
1
18
3
7  19
(22 )
9.
4 2(a  3b)  (b  3a)  2(4a  6b)
11,
5
2 
4
5 
3
1
12  x3  x 2  x   27  x 2  x  x 3 
6
3 
3
9 
4
9
12.
3 2a  b  2(b  3a)  b  4(a  2b)
10.
13.
 1
48  (12)      4
 6
2
1
3
12a  3b  6c   10b  8a  16c   16c  4a) 
3
2
4
Evaluate if a  2, b  3, and c  4
3 abc  3a  2 b  ac
14.
4b  2a  12  c(5a  4c)
15.
16.
2a 2  c 2  4b  1
17.
10a  3b  7c
19.
(c  b)(c  2b)
2 a
18.
a  b
a b
2
2
  b2  4 
III.
Solve over the Real numbers
1.
2  6x  3x 16
2.
w  6  3
3.
5(2a  3)  3a  2(4a  1)  13
4.
2
3  ( y  9)  1
3
5.
6 x  4
6.
3 c  3 1  c   2   8c  5  2(2c  2)
7.
3x  7
4 4
2
8.
Solve for x : 4 y  2 x  8
9.
Solve for T: E  am(T  t )
10.
10  (2  x )  2
11.
3
13  ( x  4)  10
2
12.
2(b  2)  3(1  3b)  26
13.
  t  6  2t  9
14.
3( x  2)  2 x   5x  6
15.

16.
 1 
2 1  x   12
 2 
17.
4v  21  19  v
18.
3
 y  5  2  y  3  10
5
7w
 14
6
IV.
Solve and graph the solution set.
1.
8 2y
 3
4
2.
2 y  17  4( y  3)  5
3.
3( z  2)  25  2( z  3)  z
4.
14  4k  2  6
5.
8  2w  2w or 5w 1  2w 14
6.
6t 12  12t and 13  4t  1
7.
3  3x  7
8.
3a  7  2
9.
1  2  x  1  7
10.
2 k  4  3  11
11.
5  3 4  2k  7
12.
4  2  1  x   8  20
13.
8 1  z   1   2 z  5
14.
5 
15.
x  7  4 1
16.
19  4 2  5x  11
1
t 1  1
2
V.
Word Problems
1.
In triangle ABC, the degree measure of angle A is 15 more than that of angle B. The degree measure of
angle C is three that of angle B. Find the measure of the largest angle in ABC.
2.
One number is 12 greater than a second number. If three times the lesser number is subtracted from 5
times the greater number, the difference is 66. Find the greater number.
3.
At 8:00 PM Mrs. Stan left a campground driving at 48 mph. Twenty minutes later, Mr. Cheek left the
same campground and followed the same route, driving at 60 mph. At what time will Mr. Cheek
overtake Mrs. Stan?
4.
Jason’s father is 4 times as old as Jason. Twenty-two years from now he will be twice as old as Jason
will be. What is his father’s age now?
5.
Peggy has 4 times as many dimes as quarters and 6 more nickels than quarters. If her nickels, dimes,
and quarters total $4.50, how many6 dimes does she have?
6.
Kim hiked up a hill at 4 km/h and back down at 6 km/h. Her total hiking time was 5 hours. How long
did the trip up the hill take Kim?
7.
The sum of an even integer and twice the next greater even integer is eight more than four times the
greater integer. Find the lesser integer.
8.
Find the measure of an angle if the sum of the measure of its supplement and twice the measure of its
complement is 207 .
9.
Zach is 4 years older than Josh. In 6 years the sum of their ages will be 46. What are their ages now?
10.
Two planes start from Chicago at the same time and fly in opposite directions, one traveling a speed of
40 mph more than the other. If they are 2000 miles apart after 5 hours, find their speeds.
11.
Janice will need 64m of fence to enclose her rectangular garden. If the length of the garden is four
meters more than the width, what are the dimensions of the garden?
12.
If each base of an isosceles triangle measures twenty degrees less than twice the measure of the vertex
angle, find the measure of each angle.
13.
The difference of two numbers is fifteen. If twice the lesser number is subtracted from four times the
greater number, the difference is 36. Find the greater number.
14.
Find four consecutive odd integers whose sum is 213 more than the greatest of these integers.
15.
The base of a triangle has the same length as the side of the square. A second side of the triangle is one
centimeter longer than the base, and the third side is five centimeters shorter than three times the base.
If the perimeter of the triangle equals that of the square, find the length of the longest side of the
triangle.
16.
James and Thomas are in two cities which are 186 miles apart and travel toward each other. James’s
average rate was 32 mph and Thomas’s average rate was 36 mph. If James started at 9:00 a.m. and
Thomas started at 9:30 a.m., at what time did they meet?
VI.
Multiple Choice
1) 3 + (-8 + x) = 3 + (x + (-8)) is an illustration of which property?
a)
b)
c)
d)
e)
Associative property for addition
Associative property for multiplication
Commutative property for addition
Commutative property for multiplication
Distributive property
2) If x represents an even integer which of the following expressions represents another even integer?
a) x – 2
b) x + 1
c) x 2  1
d) 2x + 1
e) none of these
a) 6
3) Find the value of b – a(b + c) when a = 4, b = -2, and c = 1.
b) 2
c) -6
d) 10
k k
 1
3 4
8
b) { }
11
e) none of these
4) Solve for k:
a) {
11
}
8
c) {
7
}
12
d) {
12
}
7
e) {
1
}
7
5) If 7m = 3m – 20, then m + 7 =
a) 0
b) 2
c) 5
d) 12
e) 17
6)
If 2x - 3 = 2 , what is the value of x b) 2
a) 2
a)
1
2
1
?
2
d) 4
c) 3
1
2
e) 5
1
2
7)
An airplane travels m miles at the rate of h miles per hour. How many hours does the trip take?
m
b) h+m
c) -m+h
d)
e) m  h
h
8)
Which of the following signs inserted in the parentheses will make the statement below correct?
6
9 3
  
14
21 7
h
m
c) x
d) 
b) y+ax
c) ax-y
d)
a) {-7}
Solve 29 – 3k = 1 + k.
b) {-4}
c) {4}
d) {7}
11)
a) x + 12
Kippy is x years old and Judy is seven years younger. How old will Judy be in five years?
b) 2
c) 2x – 2
d) x – 2
e) none of these
a) +
b) 9)
If ax+b-y=0, then b=
a) y-ax
10)
e) =
y
dx
e)
ax y
y dx
e) none of these
12) Jessica bicycles to the beach at 20 km/h and returns by car at 60 km/h. If the car trip is two
hours shorter than the bicycle trip, how far did she bicycle?
a) 20 km
b) 40 km
c) 60 km
d) 80 km
e) none of these
13) A pile of nickels and quarters is worth $4.40. There are two more quarters than nickels. How
many coins are there?
a) 13
b) 15
c) 28
d) 32
e) 36
14)
3n  1 2n  4

1
5
3
b) -2
c) 38
Solve for n:
a) 2
15) Solve the formula F = 1.8C + 32 for C.
F
F  32
F  32
 32
a) C 
b) C 
c) C 
1.8
1.8
1.8
16)
d) -38
e) 17
d) C  1.8( F  32)
e) none of these
Solve 1  3n  7 .
 8

a)   n  2 
 3

8
8
b) {n<-2 or n>  } c) {-2<n<  }
3
3
17) Solve 6h  4  2h 17.
a) {h < 3.25}
b) {h > 3.25}
d) {n< 
c) {h < -3.25}
8
or n>2}
3
8
e) {n<-2 or n> }
3
d) {h > -3.25}