Download INTERMEDIATE ALGEBRA REVIEW FOR TEST 1

INTERMEDIATE ALGEBRA
REVIEW FOR TEST 1
Write the set using the roster method.
1) a) {x ∣ x is a counting number less than 7}
b) {x|x is a whole number between 4 and 8}
Let A = {0, 2, 4, 6, 8, 10}, B = {0, 3, 6, 9}, C = {0, 1, 2, 3, 4, 5, 6,
7, 8, 9, 10}, and D = {0, 4, 8}. Answer True or False to the
statement.
2) a) A ⊆ C
b) ∅ ⊆ A
c) C ⊆ B
d) D ⊂ D
12) z 2 - 3z + 3 for z = 4
13) -2x2 + 3x + 7 for x = -3
14)
x2 - 10x + 5
for x = -5
x2 + 2x - 1
15) 7 + 9y for y = Fill in the blank with the appropriate symbol, ∈ or ∉ .
3) a) -9 ________ {x|x is an integer}
b) 0 ________ {2, 4, 6, ...}
List all the elements of B that belong to the given set.
2
4) B = {17, 8, -10, 0, , 4, 0.62, -8π, 0.444......}
3
a) Whole numbers
b) Integers
c) Rational numbers
d) Irrational numbers
e) Real numbers
16) If a rock falls from a height of 30 meters above
the ground, the height H (in meters) after x
seconds is approximately H = 30 - 4.9x2.
Evaluate the expression for x = 2 seconds.
(Round your answer to the nearest tenth.)
Simplify the algebraic expression by combining like
terms.
17) a) 9x + 3 - 4x + 5
2
1
1
b) x - x +
x
3
4
12
c) 10(y + 8) - 3
d) -7(10r + 10) + 6(2r + 7)
Evaluate the expression.
|5(-4)| - |1 - 11|
5)
-96
6) 24 - [7 - (4 - 10)] + (4 - 6)3
7)
Determine which of the given numbers are in the domain
of the variable.
13
18)
; x = -3, x = 0, x = 3, x = 13
x-3
6 + (-3)2 + 7 · 4
7 · (5 - 3)
19)
8)
2 - 43 - 5
1+2
20)
Express the English phrase using an algebraic expression.
9) a) The sum of a number y and 97
b) The product of 8 and a number x
c) 4 less than 7 times a number z
d) The product of -36 and the sum of a
number and 11
e) The quotient of 21 times a number x and -8
Evaluate the expression for the given value of the variable.
10) 4x + 2 for x = -5
x
; x = -6, x = 0, x = 1, x = 6
2
x - 6x
x+5
x2 + 14x + 45
; x = -9, x = -5, x = 0, x = 9
Determine if the number is a solution to the equation.
21) 4m - 2 = -3m - 39, m = -5
Solve the equation.
22) 3x - 6 = 12
23) x - 9.9 = -10.4
24) 8x + 12 = 2x + 48
11) 5(x + 6) + 6 for x = -10
8
3
Page 2
25) 5(y - 6) = 7y - 30
37) A = P + Prt for P
26) -2(k - 4) - (-3k + 7) = 2
38) aw = b2w - cx for w
27)
x x
- =9
6 8
28)
x + 4 3x - 12
=1
4
10
Identify each equation as being an identity, contradiction,
or conditional equation.
29) a) -5(x + 3) - 8 = 2x - 7(x + 5)
b) -3x + 7(3x - 5) = -13 - 4x
c) 24x + 13(x + 1) = 37(x + 1) - 24
Solve the problem.
30) Inclusive of a 6.9% sales tax, a diamond ring
sold for $2458.70. Find the price of the ring
before the tax was added. (Round to the
nearest cent, if necessary.)
31) After a 17% price reduction, a boat sold for $
23,240. What was the boat's price before the
reduction? (Round to the nearest cent, if
necessary.)
32) Nancy invested $600 at a simple interest rate of
9% for 4 years. How much interest did she
earn?
Write an algebraic equation and use it to solve the
problem.
33) A freight train leaves a station traveling at 32
km/h. Two hours later, a passenger train leaves
the same station traveling in the same direction
at 52 km/h. How long does it takes the
passenger train to catch up to the freight train?
34) A canoe and a motorboat travel toward each
other from a distance of 70 miles. The
motorboat travels 12 miles per hour faster than
the canoe. The two boats pass each other after
2.5 hours. How fast does each boat move?
Solve for y.
35) 2x - 5y = 7
36) A =
1
bh for b
2
Solve.
39) The formula for the perimeter of a rectangle is
P = 2L + 2W. Solve the formula for L. Use this
formula to find the length of the rectangle if
the perimeter, P, is 34 feet and the width, W, is
9 feet.
40) The surface area S of a right circular cylinder is
given by the formula S = 2πrh + 2πr2 , where r
is the radius and h is the height.
a) Solve the formula for h.
b) Determine the height of a cylinder whose
surface are is 72π square centimeters and
whose radius is 4 centimeters.
Write the interval as an inequality involving x. Graph the
inequality.
41) a) x > -2
b) x ≤ 4
c) -4 ≤ x ≤ 0
d) 3 ≤ x < 7
Solve the linear inequality. Express the solution using
interval notation. Graph the solution set.
42) a) x + 5 < 4
b) 5x - 2 > 4x + 4
6x + 6
c)
< -27
2
d)
3
1
x > (2x - 3)
4
5
Write the interval as an inequality involving x. Graph the
inequality.
43) a) (1, ∞)
b) [-5, -1]
c) (-∞, -7]
d) (-3, 1)
Graph the equation by plotting points.
44) y = x2 + 4
45) y = |x| - 3
Page 3
Graph the equation.
46) x + y = -1
Find the slope of the line, or state that the slope is
undefined if appropriate.
56) a)
y
47) y = 2x - 4
5
48) y =
1
x
5
49) y = 4x - 5
-5
5
x
5
x
50) 2x - y = 6
-5
Graph the line.
51) y + 3 = 2(x + 4)
b)
y
52) y - 3 = -
5
1
(x - 2)
3
Find the coordinates of the y-intercept and the coordinates
of all x-intercepts.
53)
-5
y
10
-5
5
-10
-5
5
10
-5
x
Find the slope of the line containing the given pair of
points. If the slope is undefined, state so.
57) a) (1, 2) and (9, 12)
b) (-4, -8) and (-2, 1)
-10
Graph the specified line.
58) The line with slope
Find the following for the given equation.
54) -2x + 5y = 10
a) the x-intercept
b) the y-intercept
c) the slope
d) Graph the equation.
Graph the equation.
55) a) x = -4
b) y = 3
1
that passes through the
4
point (0, 2)
Find an equation of the line containing the given pair of
points. Write your final answer in slope-intercept form.
59) (-3, -1) and (-1, -9)
60) (5, -4) and (10, -7)
Answer Key
Testname: IAREVIEW1SP11
1) a) {1, 2, 3, 4, 5, 6}
b) {5, 6, 7}
2) a) True b) True
c) False d) False
3) a) ∈ b) ∉
4) a) 17, 0, 4
b) 17, -10, 0, 4
2
c) 17, -10, 0, , 4, 0.62, 0.444...
3
d) -8π
e) {17,
5) -
8, -10, 0,
2
,
3
5
48
6) 3
43
7)
14
8) 19
9) a) 97 + y or y + 97
b) 8x
c) 7z - 4
d) -36(x + 11)
21x
e)
-8
10) -18
11) -14
12) 7
13) -20
40
14)
7
15) 17
16) 10.4 meters
17) a) 5x + 8
1
b) x
2
c) 10y + 77
d) -58r - 28
18) x = -3, x = 0, x = 13
19) x = -6, x = 1
20) x = 0, x = 9
21) No
22) 6
23) -0.5
24) 6
25) 0
26) 1
27) 216
28) 24
4, 0.62, -8π, 0.444......}
29) a) Contradiction
b) Conditional equation
c) Identity
30) $2300
31) $28,000
32) $216
33) 3.2 hours
34) canoe: 8 mph
motorboat: 20 mph
2x - 7
35) y =
5
36) b =
2A
h
37) P =
A
1 + rt
38) w =
-cx
a - b2
39) L = 8 feet
40) a) h =
S - 2πr2
2πr
b) 5 centimeters
41) a) (-2, ∞)
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
-4
-3
-2
-1
0
1
2
3
4
5
6
7
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
b) (-∞, 4]
-7
-6
-5
c) [-4, 0]
-7
-6
d) [3, 7)
-7
-6
Answer Key
Testname: IAREVIEW1SP11
42) a) (-∞, -1)
45)
y
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
10
6
b) (6, ∞)
5
-1
0
1
2
3
4
5
6
7
8
9
10 11 12 13
c) (-∞, -10)
-14
d)
-
-13
-10
-12
-11
-10
-9
-8
-7
-5
5
10
x
5
10
x
5
10
x
-5
-6
12
,∞
7
-10
46)
-6
-5
-4
-3
-2
-1
0
1
2
3
y
43) a) x > 1
-7
-6
10
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
-3
-2
-1
0
1
2
3
4
5
6
7
5
b) -5 ≤ x ≤ -1
-10
-7
-6
-5
-4
-5
-5
c) x ≤ -7
-10
-12 -11 -10 -9
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
d) -3 < x < 1
47)
y
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
10
7
44)
5
y
10
-10
-5
5
-5
-10
-5
5
-5
-10
10
x
-10
Answer Key
Testname: IAREVIEW1SP11
48)
51)
y
-10
y
10
10
5
5
-5
5
10
x
-10
-5
-5
-5
-10
-10
49)
5
10
x
5
10
x
52)
y
-10
y
10
10
5
5
-5
5
10
x
-10
-5
-5
-5
-10
-10
53) (0, -3), (-4, 0)
54) a) x-intercept: (-5, 0)
b) y-intercept: (0, 2)
2
c) slope:
5
50)
y
10
5
y
10
-10
-5
5
10
x
5
-5
-10
-10
-5
5
-5
-10
d)
10
x
Answer Key
Testname: IAREVIEW1SP11
55) a)
y
10
5
-10
-5
5
10
x
5
10
x
5
10
x
-5
-10
b)
y
10
5
-10
-5
-5
-10
56) a) -
3
2
b) 0
5
57) a)
4
b)
9
2
58)
y
10
5
-10
-5
-5
-10
59) y = -4x - 13
3
60) y = - x - 1
5