Download Elementary Algebra Sample Review Questions 1) Simplify: (x8) 7 2

Elementary Algebra
Sample Review Questions
7
8
1) Simplify: (x )
1)
2) Multiply and simplify any radicals in your answer. Assume that all variables
2)
represent positive real numbers.
3) Evaluate: -
( 11 + 5)( 17 - 5)
5
x - 8 for x = 11
9
3)
24x9 + 32x4 - 36x2
4) Divide.
4x2
4)
5)
Solve for the variable.
5)
6)
Solve: 11x - 7 > 10x - 4
6)
7)
Solve by using the square root property. x2 = 144
7)
8)
Solve: 3z(8z - 5) = 0
8)
q+3=7
9) Multiply and simplify any radicals in your answer. Assume that all variables
represent positive real numbers.
9)
(6 11 + 7)(2 11 + 9)
10) Find the slope of a straight line that passes through the given pair of points.
10)
(-9, -6) and (-3, 8)
11) Find the missing coordinate to complete the ordered pair.
y = -x + 8
12) Factor:
13) Simplify:
11)
(4, )
35x5y + 45xy3
12)
13)
4(-2)(4)(2)
14) Solve by using the square root property.
15) Solve for the indicated variable:
F=
3x2 - 15 = 0
9
5
C + 32 for C
1
14)
15)
16) Scores in golf can be positive or negative integers. For example, a score of 8 over
16)
par can be represented by +8 and a score of 1 under par can be represented by -1.
If Donna had scores of 5 over par, 7 under par, and 8 under par for three games of
golf, what was her total score?
17) Solve
for the indicated variable:
18) Solve
for y:
21) Solve
A=
1
bh for b
2
s8t9
s2t
for x:
17)
18)
4(y + 3) = 5(y - 5)
19) Solve for the indicated variable:
20) Divide:
P = 2L + 2W for L
19)
20)
6x + x = 21
21)
1
Bh
3
22)
22) Solve for h. V =
23) Write an algebraic expression for the quantity. Let y represent the unknown
23)
value.
Four less than three-fourths of a number.
24) Factor: 40x
24)
+ 20
25) A local animal shelter accepts abandoned cats and dogs. They usually receive
25)
three times as many cats as dogs. They estimate that 80% of the cats and 90% of
the dogs that come in need some kind of medical treatment. If they treated 297
animals last year, how many cats and dogs did they take in?
26) Double the sum of a number and 6 is the same as 15 more than triple the same
26)
number. Find the number.
27) Find
the area of a triangle whose altitude is 5 inches and whose base is 17 inches.
28) Solve:
27)
28)
-8x + 9 + 6x = -3x + 14
29) Solve: 6x + 4 = -2 + 2x
29)
2
30) 30 marbles are to be divided into three bags so that the second bag has three
30)
times as many marbles as the first bag and the third bag has twice as many as the
first bag. If x is the number of marbles in the first bag, find the number of
marbles in each bag.
31) For three days in a row, volunteers picked up trash on a particular beach. They
31)
picked up a total of 615 pounds. On the second day they collected 21 pounds
more than on the first day. On the third day, they picked up 42 pounds less than
on the first day. How many pounds of trash did they pick up on the first day?
32) Larry makes $18 per hour for a 40-hour week and time an a half for every hour
32)
over 40 hours. If Larry made $1098 last week, how many overtime hours did he
work?
33) A triangular region has a perimeter of 101 meters. The first side is two-thirds of
33)
the second side. The third side is 11 meters shorter than the second side. What are
the lengths of the three sides of the triangular region?
34) Divide. Leave your answer in exponent form. Assume that all variables in any
denominator are nonzero.
66x2y7
35) Divide. Leave your answer in exponent form. Assume that all variables in any
denominator are nonzero.
34)
11x9y2
35)
x14
x13
36) Kevin invested part of his $10,000 bonus in a certificate of deposit that paid 6%
36)
annual simple interest, and the remainder in a mutual fund that paid 11% annual
simple interest. If his total interest for that year was $700, how much did Kevin
invest in the mutual fund?
37) Write an algebraic expression for the quantity. Let x represent the unknown
37)
value.
Five fewer than a number.
38) Simplify:
-15x8y3
25x5y11
38)
39) Factor:
9x - 108 + xy - 12y
39)
3
x7 - 10x6 + 9x5
40) Factor:
40)
41) The sum of two numbers is 10, and the sum of their squares is 52. Find the
41)
numbers.
42) Factor:
43) Solve:
44) Solve:
45) A
49x2 - 9
42)
3x
6
3x2 + 12
=
x+2 x-2
x2 - 4
6
x2 + 3x
+
43)
3
2
+
x x+3
44)
line has a slope of -5. What is the slope of a line parallel to it?
45)
2
and y-intercept (0, -5).
7
46)
46) Find an equation of the line with slope
47) Find
47)
the slope and y- intercept: y = -4x + 6
48) Solve the system by graphing.
48)
3x + y = -1
2x + y = -2
49) Dmitri needs 7 liters of a 43% solution of sulfuric acid for a research project in
molecular biology. He has two supplies of sulfuric acid solution: one is an
unlimited supply of the 49% solution and the other an unlimited supply of the
35% solution. How many liters of each solution should Dmitri use?
4
49)
50) Solve:
50)
x - 6y = -2
-7x - 7y = -35
51) A sphere has an area A and a radius r. The radius of the sphere is r =
A
.
4
51)
Rewrite this expression by rationalizing the denominator and simplifying.
52) Multiply and simplify any radicals in your answer. Assume that all variables
52)
represent positive real numbers.
( 11 + 5)( 17 - 5)
53) Solve: (2 - 19x)2 = 86
53)
54) Solve:
49x2 - 5 = 28x
54)
55) Solve:
x2 = 3 - 8x
55)
56) Translate the English statement into an inequality.
56)
The number of people the school can hold is at most 120. (Use the variable p for
number of people.)
57) Solve for x:
x-
1
5
=
6 12
57)
58) The rectangular part of the field shown below is 169 yd long and the diameter of
58)
each semicircle is 16 yd. Find the cost of fertilizing the field at $0.35 per square
yard.
59) A
number divided by eight is 168. What is the number?
59)
60) Factor: 9x2 + 18x + 8
60)
61) Multiply:
61)
(-4x - 1)(-2x - 7)
5
62) A window washer accidentally drops a bucket from the top of a 64-foot building.
62)
The height h of the bucket after t seconds is given by h = -16t2 + 64. When will
the bucket hit the ground?
63) Multiply.
(4x + 12)(x + 11)
63)
2 11x
=
7
3
64)
64) Solve for x:
65) Holly bought a sweater on sale for 40% off the original price. If she saved $36,
65)
what was the original price?
66) Find
the slope and the y-intercept.
66)
y = -4x + 6
67) Graph the region described by the inequality.
4x + y
67)
-2
68) Simplify:
68)
16y2 - 49x2
xy
4 7
y x
69) Write
in scientific notation.
69)
57,000,000
70) Solve by the quadratic formula. If there are no real roots, say so.
+5=0
6
2m2 + 8m
70)
71) Simplify. Be sure to rationalize all denominators. Assume that all variables
represent positive real numbers.
71)
5
2
72) Complete the ordered pairs so that each is a solution of the linear equation. Then
72)
plot each solution and graph the equation by connecting the points by a straight
line.
y = 2x + 6
(0, )
(1, )
(-1, )
73) Use the Pythagorean theorem to find the length of the third side of the right
73)
triangle. Leave any irrational answers in radical form.
6
10
b
74) Write
in scientific notation.
75) Multiply.
74)
0.000152
75)
(x - 8y)(x + 2y)
76) Translate the graph to an inequality using the variable x.
76)
77) Find the solution to the system of equations by the substitution method.
x + 4y = 27
-7x + 3y = -3
77)
7
78) Graph the equation by plotting the intercepts. y =
1
x+3
2
78)
79) Write an algebraic expression for the quantity. Let x represent the unknown value. 79)
Eight greater than a number.
80) Solve
the inequality.
80)
15x - 15 > 5(2x + 2)
81) Sue took her collection of nickels and dimes to deposit in the bank. She has five
81)
fewer nickels than dimes. Her total deposit was $29.45. How many dimes did she
deposit?
82) Perform the indicated operations.
82)
(6x2 - 18x + 12) - (3x2 + 3x - 10)
83) Factor. x2 - 17x + 72
83)
84) Factor
84)
by grouping. 9x - 108 + xy - 12y
85) Factor.
2x2 - 20x + 50
85)
86) On a buying trip in Los Angeles, Rosaria Perez ordered 120 pieces of jewelry: a
86)
number of bracelets at $5 each and a number of necklaces at $7 each. She wrote a
check for $780 to pay for the order. How many bracelets and how many
necklaces did Rosaria purchase?
87) Find the area of a circular flower bed whose diameter is 3056 feet. (Use
as an approximate value.)
8
= 3.14
87)
88) ABC phone company charges $20 per month plus 3¢ per minute for phone calls.
88)
XYZ phone company charges $16 per month plus 5¢ per minute for phone calls.
How many minutes of phone calls should be made each month to make XYZ
phone company a better deal?
89) Write an equation of the line.
89)
90) Write an algebraic expression for the quantity. Let x represent the unknown
90)
value.
A value decreased by five.
91) The distance that an object falls when it is dropped varies directly as the square of
91)
the amount of time since it was dropped. An object falls 128 feet in 2 seconds.
Find the distance the object falls in 4 seconds.
92) Translate to an inequality.
92)
The distance is less than 459 inches.
93) Factor: 15x2
93)
+ 26x + 8
94) A random check of air flights last month showed that 109 of the 160 flights
94)
checked arrived on time. If the inspectors check 250 flights next month, how
many can be expected to arrive on time? (Round to the nearest whole number.)
95) Simplify. Be sure to rationalize the denominator. Assume that all variables
95)
represent positive real numbers.
22 - 3
22 + 3
96) Combine like terms: 4a + 8b - 4 + 3b + 7a + 6
9
96)
Answer Key
Testname: SHORT REVIEW- ELEMENTARY ALGEBRA
1) x56
2) 187 +
127
3) 9
85 -
55 - 5
6x7 + 8x2 - 9
q = 46
x>3
x = ±12
5
8) z = , z = 0
8
4)
5)
6)
7)
9) 195 + 68 11
7
10)
3
11) (4, 4)
12) 5xy(7x4 + 9y2 )
13) -64
14) x = ± 5
5
15) C = (F - 32)
9
16) -10 or 10 under par
P - 2W
17) L =
2
18) y = 37
2A
19) b =
h
20) s6 t8
21) x = 3
3V
22) h =
B
23)
3x
-4
4
24) 20(2x + 1)
25) 90 dogs, 270 cats
26) -3
27) 42.5 in.2
28) x = 5
29) x = -
3
2
30) 1st bag = 5 marbles; 2nd bag = 15 marbles; 3rd bag = 10 marbles
31) 212 pounds
32) 14 hours
33) first side = 28 m;
second side = 42 m;
third side = 31 m
10
Answer Key
Testname: SHORT REVIEW- ELEMENTARY ALGEBRA
34)
x7
6y5
35) x
36) $2000
37) x - 5
3x3
38) 5y8
39) (x - 12)(9 + y)
40) x5 (x - 9)(x - 1)
41) 4 and 6
42) (7x + 3)(7x - 3)
43) No solution
5
44)
x
45) -5
46) y =
2
x-5
7
47) m = -4; (0, 6)
48) (1, -4)
49) 49% solution: 4 liters; 35% solution: 3 liters
50) (4, 1)
A
51) r =
2
187 + 85 2 ± 86
53) x =
19
52)
54) x =
55 - 5
5
1
,x=7
7
55) x = -4 ±
56) p 120
7
57) x =
12
19
58) $1016.74
59) 1344
60) (3x + 4)(3x + 2)
61) 8x2 + 30x + 7
62) 2 sec
63) 4x2 + 56x + 132
64) x =
6
77
65) $90.00
66) m = -4; (0, 6)
11
Answer Key
Testname: SHORT REVIEW- ELEMENTARY ALGEBRA
67)
68) 4x + 7y
69) 5.7 × 107
-4 ± 6
70) m =
2
71)
10
2
72) (0, 6)
(1, 8)
(-1, 4)
73) 8
74) 1.52 × 10-4
75) x2 - 6xy - 16y2
76) x -2
77) (3, 6)
12
Answer Key
Testname: SHORT REVIEW- ELEMENTARY ALGEBRA
78)
79) x + 8
80) x > 5
81) 198 dimes
82) 3x2 - 21x + 22
83) (x - 8)(x - 9)
84) (x - 12)(9 + y)
85) 2(x - 5)(x - 5)
86) 30 bracelets and 90 necklaces
87) 7,331,221.76 ft2
88) Less than 200 minutes
89) y = 2x - 6
90) x - 5
91) 512 feet
92) x < 459
93) (3x + 4)(5x + 2)
94) 170 flights
25 - 2 66
95)
19
96) 11a + 11b + 2
13