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DSPM 0800 COMPREHENSIVE REVIEW
- Identify the terms in the expression
a x . Sec. 7-1. a. 15, x , 3, a , 7 b. 15 x , 3 7 a c. 15 x , 3 a , 7 d. 15 x , 3 7 ,^ a
- Identify the terms in the expression
x x
(^). Sec. 7-1. a.
x x
b. 2 x , x 1, 3 c. x^2 , x , 1, 3 d. x^2^ , x , 3
- Identify the variable terms in the expression (^) x^2 x 4. Sec. 7-1. a. (^) x^2 b. x c. (^) x^2 and x d. 4
- Identify the constant terms in the expression 3 x^2 6 x 4. Sec. 7-1. a. 3 b. 6 c. 13 d. 4
- Identify the numerical coefficient in the term 3 x . Sec. 7-1. a. 1 (^3) b. 1 3 c. -3^ d. -
- State the expression 6 x^ ^9 in words. Sec. 7-1. a. 6 times the difference of a number and 9 b. 9 less than 6 times a number c. 6 x ’s minus 9 d. 6 times a number times -
- State the equation 6(^ x^ ^ 9)^ ^27 in words. Sec. 7-1. a. The product of 6 and the difference of a number and 9 equals 27. b. The product of 6 and the difference of 9 and a number equals 27. c. Six times a number, decreased by 9, is 27. d. Six times the product of -9 and a number equals 27.
- Write the following statement in symbols: Twice the sum of a number and 8 is 40. Sec. 7-1. a. 2 x^ ^8 ^40 b. 2 ( x 8) 40 c. x^2 8 40 d. 2(^ x^ ^ 8)^ ^40
- Write the following statement in symbols: 8 divided into a number is 3. Sec. 7-1. a. 38 ^ x b. (^8) x^ ^3 c. 8^ x^ d. 8 x^ ^3
- Simplify: 3(2^ y^ ^ 4)^ y Sec. 7-1. a. 6 y^ ^12 ^ y b. 7 y^ ^12 c. 5 y^ ^12 d. 7 y^ ^12
- Simplify: ^ 3(^ a ^ 2)^ ^5 Sec. 7-1. a. 3 a 11 b. 3 a 1 c. 3 a 10 d. 3 a 3
- Simplify: ^ 8(5^ x^ ^3 y ^ 15) Sec. 7-1. a. 40 x^ ^24 y ^120 b. ^40 x^ ^24 y ^120 c. ^40 x^ ^11 y ^120 d. ^40 x^ ^24 y ^120
- Simplify: ^ (^ x^ ^ 2)^ ^ 3(3^ x ^ 9) Sec. 7-1. a. 8 x 25 b. 8 x 29 c. 10 x 25 d. 10 x 29
- Solve: y^ ^7 ^3 Sec. 7-2. a. y = 10 b. y = 4 c. y = -10 d. y = -
- Solve: x 9 2 x Sec. 7-2. a. x = 9 b. x = -1 c. x = -9 d. x = 2
- Solve: 1 3 5 x Sec. 7-2. a. 3 x (^5) b. 5 x (^3) c. x = 15 d. 2 x (^25)
- Solve: x 20 Sec. 7-2.
a. 11 b. 6 c. 3.5 d. 12
- A table top is four times as long as it is wide. The distance around the sides is 140 inches. Find the length and width. Use the formula P^ ^2 l^ ^2 w. Sec. 7-3. a. Length 56 inches, width 14 inches b. Length 14 inches, width 56 inches c. Length 132 inches, width 33 inches d. Length 37 inches, width 33 inches
- Solve:
x x (^) Sec. 7-4. a. x = 2 b. x = 14 c. x^ 14 1 d. x = 16
- Solve:
S (^) Sec. 7-4. a. S = 34 b. 1 S (^34) c. 5 S (^8) d. 8 S 5
- Solve:
x 5 (^) Sec. 7-4. a. x^ 18 5 b. x^ ^185 c. x^ ^701 d. x^ ^1514
- A mechanic can install an engine in 5 hours. How many engines can be installed in 30 hours? Sec. 7-4. a. 150 b. 6 c. 5 d. 35
- One optical scanner reads a stack of sheets in 20 min. A second scanner reads the same stack in 12 min. How long does it take for both scanners together to process one stack of sheets? Sec. 7-4. a. 6 min. b. 10 min. c. 30 min. d. 7.5 min.
- Solve: 2.3 x – 4.1 = 0.5 Sec. 7-4. a. x = 0.02 b. x = 0.2 c. x = 2 d. x = -1.
- Solve: 0.22 + 1.6 x = -0.9 Sec. 7-4.
a. x = -0.314 b. x = -0.425 c. x = -7 d. x = -0.
- The distance formula is d rt (distance equals rate times time). If a given trip took 350.8 miles at 50 miles per hour, how long did the trip take to the nearest hour? Sec. 7-4. a. 5 hours b. 6 hours c. 7 hours d. 8 hours
- The simple interest formula is I^ ^ prt (interest equals principal times rate times time). Find the rate if the amount of interest is $2,484, the principal is $4,600, and the time is 3 years. Sec. 7-4. a. 0.18% b. 1.8% c. 18% d. 180%
- Find the simple interest on an investment of $800 at 8 12 %^ for 2 years. Sec. 7-4. a. $128 b. $136 c. $68 d. $13,
- Find the area of a square whose side is 3.25 km if the formula for the area is (^) A s 2. Sec. 7-5. a. 10.5625 km 2 b. 6.25 km^2 c. 1.803 km 2 d. 111.5664 km^2
- Using the total resistance formula 1 2 1 2 t
R R
R
R R
, find the total resistance of two resistances of 10 ^ (ohms) and 9 ^. Round to tenths. Sec. 7-5. a. 4.7^ ^ b. 0.2^ ^ c. 5.6^ ^ d. 4.5^
- Solve for d : s r d Sec. 7-5. a. d s r b. d r s c. d r s d. d rs
- Solve for t : v^ v^0^ ^32 t Sec. 7-5. a. t^ v^^ ^ v 0 ^32 b. 0 32 v v t
c. 0 32 v v t
d. t^ v^^ ^32 v 0
For problems 51-54, use the following rectangular coordinate system: -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10
- 1 2 3 4 5 6 7 8 9 x y A B C D E F G
- What are the coordinates of point G? Sec. 9-1. a. (0, 7) b. (7, 0) c. (0, -7) d. (-7, 0)
- What are the coordinates of point E? Sec. 9-1. a. (-3, -7) b. (-7, -3) c. (3, 7) d. (-3, 7)
- Which point is the origin? Sec. 9-1. a. A b. F c. G d. C
- Which point has coordinates (8, -2)? Sec. 9-1. a. B b. A c. F d. D
- Represent the equation 3 x^ ^ y ^9 as a function. Sec. 9-1. a. f^ ( ) x^^ ^3 x ^9 b. f^ ( ) x^^ ^3 x ^9 c. f^ ( ) x^^ ^3 x ^9 d. f^ ( ) x^^ ^3 x ^9
- Which of these tables is a table of solutions for the equation y^ ^5 x ^1? Sec. 9-1. a. b. c. d. x y -5 1 0 1 2 1 x y -1 - 0 1 1 6 x y -1 6 0 1 1 - x y -1 5 0 0 1 -
- Graph the equation y^ ^5 x ^1. Sec. 9-1. a. -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10 - - - - - - - - - - 1 2 3 4 5 6 7 8 9 x y b. -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10
1 2 3 4 5 6 7 8 9 x y c. -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10 - - - - - - - - - - 1 2 3 4 5 6 7 8 9 x y d. -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10
1 2 3 4 5 6 7 8 9 x y
- Which of the coordinate pairs is a solution for the equation x^ ^2 y ^4? Sec. 9-1. a. (6, 1) b. (6, -1) c. (0, 4) d. (-8, 6)
- Find the specific solution for y^ ^3 x ^1 when x = -2. Sec. 9-1.
a. (-2, 7) b. (-2, 1) c. (-2. -7) d. ^ 2,^13
- Find the specific solution for 2 x^ ^ y ^8 when y = 10. Sec. 9-1. a. (8, 10) b. (-1, 10) c. (1, 10) d. (-5, 10)
- Determine the slope of a line through (3, 3) and (3, 0) Sec. 9-3. a. 1 b. -1 c. 0 d. Undefined Use the following table for problems 70-71. Use the initial year of the academic year as the reference (e.g., for 1997-1998, use 1997). Academic Year Public Four-Year Public Two-Year 1992-1993 $3,102 $1, 1993-1994 3,285 1, 1994-1995 3,407 1, 1995-1996 3,447 1, 1996-1997 5,547 1, 1997-1998 3,644 1, 1998-1999 3,742 1, 1999-2000 3,766 1, 2000-2001 3,796 1, 2001-2002 4,004 1, 2002-2003 4,263 1, 2003-2004 4,729 1, 2004-2005 5,132 2,
- What is the rate of change in tuition for public two-year colleges from 1996 to 1998? Sec. 9-3. a. $22 b. $88 c. -$44 d. -$
- What is the rate of change in tuition for public four-year colleges over the entire period? Sec. 9-3. a. $0.006 b. $169.17 c. $116.10 d. $2,
- Determine the nature of the line passing through (4, 5) and (-4, -1). Sec. 9-3. a. Positive slope b. Negative slope c. Zero slope d. Undefined slope
- Determine the nature of the line passing through (0, 0) and (5, 0). Sec. 9-3. a. Positive slope b. Negative slope c. Zero slope d. Undefined slope
- Find the equation of the line with slope ^52 passing through (3, 2). Sec. 9-4. a. y^ ^25 x ^165 b. y^ ^25 x ^165 c. y^ ^25 x ^195 d. y^ ^25 x ^195
- Find the equation of the line with slope 4 passing through (2, 3). Sec. 9-4. a. y^ ^4 x ^11 b. y^ ^4 x ^5 c. y^ ^4 x ^5 d. y^ ^4 x ^9
- Find the equation of the line passing through (-2, -3) and (3, 6). Sec. 9-4. a. y^ ^95 x ^575 b. y^ ^95 x ^35 c. y^ ^59 x ^35 d. y^ ^95 x ^35
- Find the equation of the line passing through (-1, -3) and (3, 4). Sec. 9-4. a. 7 37 y 4 x (^4) b. 7 37 y 4 x 4 c. 7 5 y 4 x (^4) d. 7 5 y 4 x 4
- Which equation matches the line through (3, 9) and (-3, 9)? Sec. 9-4. a. x = 3 b. x = -3 c. y = 9 d. y = -
- A salesperson sells 100 items and earns $4,500 in one month, and in another month 300 items were sold resulting in $7,000 earnings. Write the equation that relates the earnings to the amount of sales. Sec. 9-4. a. y^ 0.08^ x ^3250 b. y^ 12.5^ x 56, 050 c. y^ 12.5^ x ^4500 d. y^ 12.5^ x ^3250
- Find the equation of the line with slope -5 and y -intercept (0, -7). Sec. 9-4. a. y^ ^5 x ^7 b. y^ ^5 x ^7 c. y^ ^5 x ^7 d. y^ ^5 x ^7
- Solve the system of equations:
a b a b
Sec. 10-2. a. (9, 1) b. (5, 3) c. No solution d. Infinite number of solutions
- Solve the system of equations:
x y x y
Sec. 10-2. a. (1, -1) b. (3, -1) c. No solution d. Infinite number of solutions
- In 1 year, Sholanda Brown earned $280 on two investments totaling $5,000. If she received 5% and 6% rates of return, how much did she invest at each rate? Sec. 10-4. a. $3,000 at 5%, $2,000 at 6% b. $2,000 at 5%, $3,000 at 6% c. $2,500 at 5%, $2,500 at 6% d. $1,000 at 5%, $4,000 at 6%
- A painter paid $22.50 for 2 quarts of white shellac and 5 quarts of thinner. If 3 quarts of shellac and 2 quarts of thinner cost the painter’s helper $14.50, what is the cost of each quart of shellac and thinner? Sec. 10-4. a. Shellac $3.00, thinner $4. b. Shellac $3.50, thinner $2. c. Shellac $2.00, thinner $3. d. Shellac $2.50, thinner $3.
- Simplify and write with positive exponents: x^2 x 4 Sec. 11-1. a. x^16 b. x^8 c. x^6 d. 1 x^2
- Simplify and write with positive exponents: (^) x^5 x ^2 x^2 Sec. 11-1. a. (^20)
x b. (^) x^5 c. (^) x^20 d. (^) x^9
- Simplify and write with positive exponents: 8 5 x x Sec. 11-1. a. x^3 b. (^3)
x c. x^13 d. (^13)
x
- Simplify and write with positive exponents: 8 8 x x Sec. 11-1. a. (^) x^16 b. 1 c. (^) x^8 d. x
- Simplify and write with positive exponents: 3 5 x x Sec. 11-1. a. (^) x^2 b. (^) x^8 c. (^2)
x d. (^8)
x
95. Simplify and write with positive exponents:
3 4 x (^) Sec. 11-1. a. (^) x^7 b. (^) x^12 c. (^) x^81 d. (^) x^34
96. Simplify and write with positive exponents:
2 5 2 x y Sec. 11-1. a. 2 5 x y b. 4 10 x y c. 4 25 x y d. 2 10 x y
- Simplify and write with positive exponents: 2 8 a b
Sec. 11-1. a. (^16) a b b. 2 8 a b c. 2 64 a b d. 2 16 a b
- The expression (^3) x^2 2 x 8 is a: Sec. 11-2. a. monomial b. binomial c. trinomial d. not a polynomial
- The expression 3 x^ is a: Sec. 11-2. a. monomial b. binomial c. trinomial d. not a polynomial
- The expression
x is a: Sec. 11-2. a. monomial b. binomial c. trinomial d. not a polynomial
- The degree of the term 6 x^5 is Sec. 11-2. a. 6 b. 5 c. 1 d. 11
- Subtract: (5 x^2^ 3 x 2) (4 x^2 8 x 4) Sec. 11-3. a. (^) x^2 5 x 6 b. (^) x^2^ 11 x 2 c. (^) x^2 11 x 6 d. (^) x^2^ 5 x 4
- Multiply: 3 4 4 x ( 3 x ) Sec. 11-3. a. x^7 b. 7 x^7 c. 12 x^12 d. 12 x^7
- Multiply: 2 ( x x^3 7 x^2 15) Sec. 11-3. a. (^) 2 x^4^ 14 x^3 30 x b. (^) 2 x^4^ 14 x^3^ 30 x^2 c. (^) 2 x^4^ 14 x^3 30 x d. (^) 2 x^4^ 14 x^3 30
- Multiply: (^ y^ ^ 7)(^ y ^ 5) Sec. 11-3. a. 2 y 12 y 35 b. 2 y 12 y 35 c. 2 y 12 y 35 d. 2 y 12 y 35
- Multiply: (^ x^ ^ 3)(2^ x ^ 5) Sec. 11-3. a. 2 x^2 11 x 15 b. 2 x^2 11 x 15 c. 2 x^2 x 15 d. 2 x^2 x 15
- Multiply: (6^ y^ ^ 5)(6^ y ^ 5) Sec. 11-3. a. 36 y^2 60 y 25 b. 36 y^2 60 y 25 c. 36 y^2 25 d. 12 y^2 10
- Multiply: 2 (5 3 m ) Sec. 11-3. a. 25 30 m 9 m^2 b. 25 30 m 9 m^2 c. 225 m^2 d. 25 9 m^2
- Divide and express the answer with positive exponents: 9 4
x x Sec. 11-3. a. (^5) x^5 b. (^5) x^13 c. (^45) x^13 d. (^) x^5
- Divide and express the answer with positive exponents: (^3)
x x Sec. 11-3. a.
x b. (^2)
3 x c.
x d. (^3)
3 x
- Divide:
x x x x
Sec. 11-3. a. 3 x^2 9 x 18 b. 2 x^2 4 x 7 x c. 2 x^3 4 x^2 7 x d. 2 x^2 4 x 7
- Divide: 5 x 2 15 x^2 4 x 4 Sec. 11-3. a.
x x
b.
x x
c. 3 x 2 d. 3 x 2
- Graph the inequality on the number line and write in interval notation: x 3 Sec. 17-1. a. 0 1 2 3 4 5 6 7 8 9 1011121314
b. 0 1 2 3 4 5 6 7 8 9 1011121314
]
( , 3]
c. 0 1 2 3 4 5 6 7 8 9 1011121314
d. 0 1 2 3 4 5 6 7 8 9 1011121314
[
[3, )
- Graph the inequality on the number line and write in interval notation: x 9 Sec. 17-1. a. 0 1 2 3 4 5 6 7 8 9 1011121314
b. 0 1 2 3 4 5 6 7 8 9 1011121314
]
( , 9]
c. 0 1 2 3 4 5 6 7 8 9 1011121314
d. 0 1 2 3 4 5 6 7 8 9 1011121314
[
[9, )
- Solve and graph the inequality: 10 x 18 8 x Sec. 17-2. a.
-14 -12 -10-9-8 -7 -6-5 -4 -3-2-1 0 x^ ^9 b.
-14 -12 -10-9-8 -7 -6-5 -4 -3-2-1 0 x^ ^9 c. 0 1 2 3 4 5 6 7 8 9 1011121314
x 9 d. 0 1 2 3 4 5 6 7 8 9 1011121314
x 9
- Solve and graph the inequality: 12 ^5 x^ ^6 ^ x Sec. 17-2. a.
[
-7-6 -5-4 -3-2 -1 0 1 2 3 4 5 6 7 x^ ^1 b.
]
-7-6 -5-4 -3-2 -1 0 1 2 3 4 5 6 7 x^ ^1 c.
[
-7-6 -5-4 -3-2 -1 0 1 2 3 4 5 6 7 x^ ^1 d.
]
-7-6 -5-4 -3-2 -1 0 1 2 3 4 5 6 7 x^ ^1
- Solve and graph the inequality: 8 x^ ^ (3^ x ^ 2)^ ^12 Sec. 17-2. a.
]
-7-6 -5-4 -3-2 -1 0 1 2 3 4 5 6 7 x^ ^2 b.
[
-7-6 -5-4 -3-2 -1 0 1 2 3 4 5 6 7 x^ ^2 c.
]
14 x 5 d.
[
14 x 5
- Solve and graph the inequality: x^ ^ y ^6 Sec. 17-2. a. -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10 - - - - - - - - - - 1 2 3 4 5 6 7 8 9 x y b. -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10
1 2 3 4 5 6 7 8 9 x y c. -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10 - - - - - - - - - - 1 2 3 4 5 6 7 8 9 x y d. -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10
1 2 3 4 5 6 7 8 9 x y
