intermediate algebra problems you can use for practice ... · intermediate algebra problems you can...
TRANSCRIPT
Intermediate Algebra problems you can use for practice. Remember, you may not use a calculatorwhen you take the assessment test. Use these problems to help you get up to speed._________________________________________________________________________________________Solve the equation.
1) x + 44
-3x - 12
10= 1
A) 24 B) 6
C) - 24 D) -48
Solve the problem.
2) The difference of a number and 8 is the sameas 34 less the number. Find the number.
A) 21 B) -13
C) -21 D) 13
3) The population of a town is currently 22,000.This represents an increase of 80% from thepopulation 5 years ago. Find the population ofthe town 5 years ago. Round to the nearestwhole number if necessary.
A) 12,222 B) 4400
C) 17,600 D) 27,500
4) P = 2L + 2W for L
A) L =P - 2W
2 B) L = P - 2W
C) L =P - W
2 D) L = P - W
5) I =nE
nr + R for n
A) n = IR(Ir - E) B) n =-IR
Ir - E
C) n =IR
Ir + E D) n =-R
Ir - E
Solve.
6) The average price (in dollars) to rent a studioin a certain city can be approximated by theequation p = 34.0t + 646 where t is the numberof years since 1990. Solve this equation for tand use the new equation to determineapproximately what year it will be when theaverage price of a studio in this city reaches$1326.00.
A) 2012 B) 2013
C) 2010 D) 2011
Solve the linear inequality. Express the solution usingset-builder notation and interval notation. Graph thesolution set. NOTE: A square bracket, i.e. [, is the same asa filled in circle. A round bracket, i.e. (, is the same as anopen circle.
7) 3x - 9 < 4(x - 3)
A) {x|x < -3}; (- , -3)
B) {x|x > -21}; (-21, )
C) {x|x > 3}; (3, )
D) {x|x < 21}; (- , 21)
Solve the inequality. Graph the solution set, and state thesolution set in interval notation.
8) |x - 4| + 2 9
A) [-3, 9]
B) [-3, 11]
C) (-3, 11)
D)
List the intercepts of the graph.
9)
A) (0, -2), (0, 8), (4, 0)
B) (0, -2), (8, 0), (0, 4)
C) (-2, 0), (0, 8), (4, 0)
D) (-2, 0), (0, 8), (0, 4)
Find the domain of the function.
10) f(x) =2x - 3x + 6
A) {x|x 6} B) {x|x 32
}
C) {x|x -6} D) {x|x -6, 32
}
11) f(x) = x2 + 3
A) {x|x > -3} B) {x|- < x < }
C) {x|x -3} D) {x|x -3}
Find the slope of the line that goes through the givenpoints.
12) (-2, -1), (9, -1)
A) -211 B) -
27
C) 0 D) Undefined
Find an equation of the line with the given slope andcontaining the given point. Express your answer inslope-intercept form.
13) m = -3, (-6, 5)
A) y = -3x + 13 B) y = -3x - 13
C) y - 5 = x + 6 D) y - 5 = mx + 6
14) m = -23
, (5, 5)
A) y = -32
x -252 B) y =
23
x -253
C) y = -23
x +253 D) y = -
23
x -253
15) m is undefined, (5, -1)
A) y = 5 B) x = 5
C) x = -1 D) y = -1
Use the given conditions to write an equation for the linein slope-intercept form.
16) Passing through the point (2, 1) andperpendicular to y = 3x - 3
A) y = 3x +53 B) y = -3x +
53
C) y =13
x +53 D) y = -
13
x +53
Determine whether the ordered pair is a solution of thesystem of linear equations.
17) 4x = 18 - y3x = 7 - 4y
; (5, -2)
A) Yes B) No
Solve the system of equations using elimination.
18) 3x - 6y = -78x - 5y = -5
A) 4133
, 533 B) 5
33, -
4133
C) 533
, 4133 D) -
4133
, -533
Simplify the expression. All exponents should be positiveintegers.
19) -6a13b-3
3a7b-9
A) -2b6
a6 B) -2a6
b6
C) -2a6b6 D) -2a6b6
Simplify the expression.
20) (-5)2 · 100
A) -25 B) 125
C) -125 D) 25
Perform the indicated operation. Express the solution inscientific notation.
21) (8 × 10-5) · (6.1 × 10-3)
A) 4.88 × 10-7 B) 4.88 × 1015
C) 488 × 10-8 D) 48.8 × 10-7
22) 12.74 × 107
4.9 × 108
A) 2.6 × 10-1 B) 2.6 × 1015
C) 5.2 × 1015 D) 5.2 × 10-1
Factor the difference of two squares completely.
23) 25 - 16x2
A) (5 + 4x)(5 - 4x) B) (5 + 4x)2
C) (5 - 4x)2 D) Prime
24) ab4 - 121a3b2
A) a(b2 + 11ab)(b2 - 11ab)
B) ab2(b + 11a)(b - 11a)
C) ab2(b - 11a)2
D) Prime
Find the product.
25) -5x6(11x7 + 6x4 + 12)
A) -55x7 - 30x4 - 60
B) -55x13 - 30x10
C) -55x13 + 6x4 + 12
D) -55x13 - 30x10 - 60x6
Solve the system of equations using substitution.
26) x - 6y = -42-5x - 5y = -35
A) (0, 7) B) (-7, 0)
C) (1, 6) D) no solution
Factor the sum or difference of two cubes completely.
27) x3 + 27
A) (x + 3)(x2 + 9)
B) (x - 3)(x2 + 3x + 9)
C) (x - 27)(x + 1)(x - 1)
D) (x + 3)(x2 - 3x + 9)
28) 64y3 - 1
A) (64y - 1)(y2 + 4y + 1)
B) (4y - 1)(16y2 + 1)
C) (4y - 1)(16y2 + 4y + 1)
D) (4y + 1)(16y2 - 4y + 1)
Factor completely, or state that the polynomial is prime.
29) 40x2 + 2x - 24
A) (5x + 4)(8x - 6)
B) 2(5x + 4)(4x - 3)
C) (2x + 8)(4x - 3)
D) 2(5x - 4)(4x + 3)
30) 2x3 + 2000
A) 2(x + 10)3
B) 2(x3 + 1000)
C) 2(x + 10)(x2 - 10x + 100)
D) Prime
Find the special product.
31) (7x + 12)2
A) 7x2 + 168x + 144
B) 49x2 + 144
C) 49x2 + 168x + 144
D) 7x2 + 144
32) (6x - y)2
A) 36x2 - 12xy - 2y2
B) 36x2 + y2
C) 36x2 - 12xy + y2
D) 36x2 - 6xy + y2
Factor the polynomial completely. If the polynomialcannot be factored, say it is prime.
33) x2 - 5xy - 24y2
A) (x - 3y)(x + y) B) (x + 3y)(x - 8y)
C) (x - 3y)(x + 8y) D) Prime
34) 10x2 + 7x - 12
A) (2x - 3)(5x + 4) B) (10x + 3)(x - 4)
C) (2x + 3)(5x - 4) D) Prime
Factor completely, or state that the polynomial is prime.
35) x3 - 4x2 - 36x + 144
A) (x + 4)(x + 6)(x - 6)
B) (x - 4)(x + 6)(x - 6)
C) (x - 4)(x - 6)2
D) Prime
Find the intercepts of the graph of the function.
36) g(t) = t2 + 6t - 16
A) (8, 0), (2, 0), (0, - 16)
B) (-8, 0), (2, 0), (0, - 16)
C) (-8, 0), (1, 0), (0, - 16)
D) (8, 0), (-2, 0)
Factor the polynomial completely.
37) x4 - 8x2 + 7
A) (x2 - 1)(x2 - 7) B) (x2 + 1)(x2 + 1)
C) (x2 + 1)(x2 - 7) D) Prime
Find the values of x such that the given function has thestated value.
38) f(x) = x2 + 8x; f(x) = 48
A) x = 12 or x = 4 B) x = -12 or x = 4
C) x = 12 or x = -4 D) x = -12 or x = 1
Multiply the rational expression. Express the product as arational expression in lowest terms.
39) 80xx2 - 25
·10x - 50
8x2
A) 100xx + 5 B) 10
x(x + 5)
C) 100x(x + 5) D) 64
x(x + 5)
40) 6w - 36w2 + 1w
·w2 + 8w + 7
w2 - 13w + 42
A) 6(w - 7)w(w + 7) B) 6(w + 7)
w - 7
C) 6(w + 7)w(w - 7) D) 6
w
Determine the domain of the rational function.
41) R(x) =2
x - 7
A) {x|x 7} B) {x|x -7}
C) {x|x 0} D) {x|x 0, x 7}
Perform the indicated operation and simplify the result.
42) 4x2 - 17x + 5x2 - 15x + 54
-3x2 - 9x - 7x2 - 15x + 54
A) x - 2x + 9 B) x2 - 8x + 12
x2 - 15x + 54
C) x - 2x - 9 D) x + 2
x - 9
43) 2xx - 5
+7
5 - x
A) 2x + 7x - 5 B) -5x
x - 5
C) 2x - 75 - x D) 2x - 7
x - 5
Add or subtract, as indicated, and simplify the result.
44) 910a3b
-8
15ab2
A) 27b - 16a2
30a3b2 B) 27b - 8a2
30a3b2
C) 27b - 16a2
30a2b3 D) 27b + 16a2
30a3b2
45) y + 9y + 2
-y + 9y - 9
A) 11(y + 9)(y + 2)(y - 9) B) -11(y + 9)
(y + 2)(y - 9)
C) -7(y + 9)(y + 2)(y - 9) D) 0
Multiply, and then simplify if possible. Assume allvariables represent positive real numbers.
46) 2( 50 + 10)
A) 10 + 2 5 B) 20
C) 100 + 2 5 D) 10 + 4 5
Use the product rule to simplify the expression. Assumethat the variables can be any real number.
47) 405k7q8
A) 9q4 5k7 B) 9k3q4 5k
C) 9k3q4 5 D) 9k7q8 5k
Divide and simplify.
48) 3 250x132x
A) 5x4 x B) x4 35
C) x4 32 D) 5x4
Simplify the radical expression. Assume that all variablesrepresent positive real numbers.
49) 75k7q8
A) 5q4 3k7 B) 5k3q4 3
C) 5k3q4 3k D) 5k7q8 3k
Simplify the radical.
50)3
(-6)3
A) -18 B) -6
C) 18 D) 6
51)5
(x - 1)5
A) -x + 1 B) |x - 1|
C) -|x - 1| D) x - 1
Evaluate the expression, if possible.
52) 64-4/3
A) 256
B) 1256
C) -1
256
D) not a real number
Multiply, and then simplify if possible. Assume allvariables represent positive real numbers.
53) ( 2 + 5)2
A) 10 + 2 10 B) -3 + 2 10
C) 7 + 2 10 D) 7 - 2 10
Add or subtract. Assume all variables represent positivereal numbers.
54) 2 125 - 3 20 - 4 45
A) -8 5 B) 7 5
C) -7 5 D) 2 5
Rationalize the denominator and simplify. Assume that allvariables represent positive real numbers.
55) 57 - 9
A) 5 7 - 4574
B) -5 7 + 45
74
C) -5 7 - 45
74D) 5 7 + 45
74
Simplify the complex rational expression.
56)
4a
+ 1
4a
- 1
A) 4 - a2 B) a2
4 - a2
C) 4 D) 4 + a4 - a
Solve for x.
57) 11x = 1
A) x = 1 B) x =111
C) x = 0 D)
Solve the equation by completing the square.
58) x2 + 10x + 15 = 0
A) {5 - 15, 5 + 15}
B) {5 + 10}
C) {-5 - 10, -5 + 10}
D) {-10 + 15}
Solve the rational inequality.
59) x +60x
< 16
A) (0, 6) (10, ) B) (- , 0) (6, 10)
C) (- , 0) (10, ) D) (0, 6) (6, 10)
Solve for x.
60) 4-x =164
A) x =116 B) x = 3
C) x = -3 D) x =13
Simplify the radical expression. Assume that all variablesrepresent positive real numbers.
61)3
6 ·3
-36
A) -6 B) -216
C) 6 D) 6 6
Complete the square for the binomial. Then factor theresulting perfect square trinomial.
62) x2 - 14x
A) x2 - 14x - 49 = (x - 7)2
B) x2 - 14x + 196 = (x - 14)2
C) x2 - 14x - 196 = (x - 14)2
D) x2 - 14x + 49 = (x - 7)2
Add or subtract, as indicated, and simplify the result.
63) 3y2 - 3y + 2
+5
y2 - 1
A) 8y - 7(y - 1)(y + 1)(y - 2)
B) 30y - 7(y - 1)(y + 1)(y - 2)
C) 8y - 7(y - 1)(y - 2)
D) 7y - 8(y - 1)(y + 1)(y - 2)
Solve the equation.
64) log3 (2x + 2) = log3 (30)
A) x = 56 B) x = 14
C) x = 16 D) x = 64
65) log2 (x + 4) - log2 (x + 3) = 1
A) x = 2 B) x = - 2
C) x = 1 D) no solution
66) log2 (x + 1) + log2 (x - 5) = 4
A) x = 8 B) x = 7
C) x = -3 D) x = 7, x = -3
Solve the equation. Give an exact solution.
67) e4x = 6
A) 4 ln 6 B) 32
e
C) ln 46 D) ln 6
4
68) 2x + 7 = 3
A) log 3log 2
- 7
B) log 3 - log 2 - log 7
C) log 2log 3
+ log 7
D) log 2log 3
+ 7
Rationalize the denominator. Assume that all variablesrepresent positive real numbers.
69) 47
A) 4 77
B) 53
C) 16 7 7
D) 4 7
Solve the equation.
70) x4 - 20x2 + 64 = 0
A) {2, 4} B) {4, 16}
C) {-2i, 2i, -4i, 4i} D) {-2, 2, -4, 4}
Simplify the complex rational expression.
71)x9
-1x
1 +3x
A) 9x + 3 B) x - 3
9
C) 9x - 3 D) x + 3
9
Evaluate the expression, if possible.
72) 278
-1/3
A) -23 B) -
32
C) 32 D) 2
3
Solve the equation.
73) 2x + 1 = x - 3
A) {2, 8} B) {8}
C) {-4, 43
} D) {-4}
74) 10x - 9 - 9 = 0
A) {81} B) {9}
C) {365
} D) no real solution
Solve the rational inequality.
75) x - 1x + 3
> 0
A) (-3, 1) B) (- , -3) (1, )
C) (1, ) D) (- , -3)
Solve the equation.
76) 1 +1y
=42y2
A) y = -7 or y = 6
B) y = 7 or y = -6
C) y = 7 or y = 6
D) y = -17
or y =16
77) m -3m
= 2
A) m = -3 or m = 1
B) m = -13
or m = 1
C) m = -1 or m =13
D) m = -1 or m = 3
78) 6x + 4
-9
x - 4=
3x2 - 16
A) x = 67 B) x = 63
C) x = -21 D) x = 21
Solve.
79) A ladder that is 26 feet long is 10 feet from thebase of a wall. How far up the wall does theladder reach?
A) 24 ft B) 4 ft
C) 576 ft D) 2 194 ft
Use the quadratic formula to solve the equation.
80) 8x2 + 24x = - 17
A) -6 - 704
, -6 + 704
B) -24 - 24
, -24 + 24
C) -6 - 216
, -6 + 216
D) -6 - 24
, -6 + 24
81) 8x2 + 1 = 3x
A) -3 - i 2316
, 3 + i 2316
B) 3 - i 2316
, -3 + i 2316
C) 3 - i 2316
, 3 + i 2316
D) -3 - i 2316
, -3 + i 2316