# Question
 
1
Simplify the expression.

( x + 5 ) + ( 6x - 7 )

  5x - 6
  7x - 2
  10x - 4
  6x + 2
  7x + 12
 
2
Simplify the expression.

( 6x 2 - 2x + 2 ) + ( 7x 2 - 7x - 5 )

  4x 2 - 1x + 1
  13x 2 - 9x - 3
  3x 2 - 4x - 5
  5x 2 - 3x - 9
3
Simplify the expression.

4( x + 6 ) - 5( x 2 - 7x + 3 ) + 3( x - 5 )

  - 2x 2 + 12x - 29
  - 5x 2 + 42x - 6
  - 3x 2 + 26x + 9
  - 4x 2 + 24x - 10
4
Multiply mentally.

( x + 3 )( x + 2 )

  x 2 + 6x + 18
  x 2 + 8x + 6
  x 2 + 5x + 6
  x 2 + 7x + 6
 
5
Multiply mentally.

( 5a + 7 )( 4a + 7 )

  18a 2 + 12a + 7
  20a 2 + 63a + 49
  23a 2 + 22a + 26
  19a 2 + 19a + 8
6
Multiply mentally.

( x + 6 ) 2

  x 2 + 9x + 15
  x 2 + 14x + 26
  x 2 + 13x + 8
  x 2 + 12x + 36
7
Simplify the expression.

( 5x + 2 ) ( 6x 2 + 3x + 3 )

  7x 3 + 25x 2 + 19x + 15
  30x 3 + 27x 2 + 21x + 6
  8x 3 + 11x 2 + 12x + 9
  3x 3 + 10x 2 + 21x + 16
8
Simplify the expression.

( x - 3 )( 5x - 5 ) - ( x + 2 )( x - 5 )

  7x 2 - 11x + 27
  3x 2 - 6x + 7
  2x 2 - 27x + 19
  4x 2 - 17x + 25
9
Use the binomial theorem to expand the binomial

( x + 3 ) 3

  x 3 + 6x + 9
  x 3 + 3x 2 + 9x + 27
  x 3 + 9x 2 + 27x + 27
  x 3 + 27
10
The number of desks in one row is 8d + 2. How many desks are there in a room of 5d - 3 rows if they are arranged in a rectangular arrangement?
  37d 2 - 8d - 5
  40d 2 - 14d - 6
  42d 2 - 13d - 12
  41d 2 - 13d - 11

 
       
 
11
Factor the expression completely.

45xy - 15x

  5x ( 3 - 9y )
  5y ( 9x - 3 )
  5y ( 3 - 9x )
  5x ( 9y - 3 )
 
 
12
Factor the expression completely.

x 2 - 5x - 50

  (x - 10) ( x - 5)
  (x - 10) ( x + 5)
  (x + 10) ( x + 5)
  (x - 5) ( x + 10)
 
 
13
Factor the expression completely.

3x 2 - 5x - 28

  ( 3x - 7 ) ( x + 4 )
  ( 3x + 7 ) ( x - 4 )
  ( x + 7 ) ( 3x - 4 )
  ( x - 7 ) ( 3x + 4 )
 
       
14
Factor the expression completely.

4x 2 + 29x + 30

  ( x - 5 ) ( 4x - 6 )
  ( 4x - 5 ) ( x - 6 )
  ( x + 5 ) ( 4x + 6 )
  ( 4x + 5 ) ( x + 6 )
 
       
15
Factor the expression completely.

5x 3 - 10x 2 - 40x

  x ( 5x - 10 ) ( x + 4 )
  x ( 5x + 10 ) ( x - 4 )
  x ( x + 10 ) ( 5x - 4 )
  x ( x - 10 ) ( 5x + 4 )
 
       
16
If possible, completely factor the expression.

18x 2 + 126

  not factorable
  18 ( x + 7 ) ( x + 7 )
  ( 18x + 7 ) ( x + 7 )
  18 ( x 2 + 7 )
 
 
17
If possible, completely factor the expression.

x 4 - 256

  not factorable
  ( x - 16 ) ( x + 16 ) ( x 2 + 4 )
  ( x - 4 ) ( x + 4 ) ( x 2 + 16 )
  ( x - 4 ) 2 ( x + 4 ) 2
  ( x - 4 ) 2 ( x 2 + 16 )
 
       
18
If possible, completely factor the expression.

x 2 + 2x + 12

  ( x + 1 ) ( x + 6 )
  ( x - 1 ) ( x - 6 )
  ( x + 2 ) ( x + 12 )
  not factorable
  ( x - 2 ) ( x - 12 )
 
       
19
What are the dimensions of a rectangle whose area is x 2 - 6x - 55 square feet?
  ( x + 11 ) ft by ( x - 5 ) ft
  11 ft by 5 ft
  ( x - 11 ) ft by ( x + 5 ) ft
  6 ft by 55 ft
 
 
20
Factor the expression.

6x2y2 + 11x2yz - 10x2z2

  x 2 ( 5y + 2z ) ( 3y - 2z )
  x 2 ( 2y + 5z ) ( 2y - 3z )
  x 2 ( 2y + 5z ) ( 3y - 2z )
  x 2 ( 5y + 2z ) ( 2y - 3z )

 
 
21
Solve the equation

x - 5 = 14

  19
  16
  23
  9
 
 
22
Solve the equation

5(W + 6) - 6(W + 12) = 0

  24
  -42
  -24
  42
 
       
23
Solve the equation

x 3 = 9x

  3
  3, -3, 1
  0
  3, -3, 0
 
 
24
Solve the equation

x 2 - 6x + 5 = 0

  2, 1
  no solutions
  1, 5
  1
 
 
 
       
26
Solve the equation

9x 2 = 2x

 
 
 
 
 
       
27
Use a calculator to obtain solutions correct to the nearest hundredth.

  7.60 , -0.53
  6.45 , 0.62
  12.90 , 1.24
  3.23 , 0.31
 
 
28
Use a calculator to obtain solutions correct to the nearest hundredth.

68.38 x 2 - 4.12 x - 185.21 = 0

  1.68 , -1.62
  1.42 , -1.90
  1.86 , -1.45
  1.34 , -1.29
 
       
29
Young's Rule for calculating a child's dosage for medication is

If a 12-year-old child's dose of a particular medication is 20 mg, what is the adult's dose?

  40 mg.
  30 mg.
  35 mg.
  48 mg.
 
       
30
Al-Khw�rizm� solved the equation x 2 + 10x = 39.
Here is a translation of his solution:

. . . a square and 10 roots are equal to 39 units. The question therefore in this type of equation is about as follows: What is the square which combined with ten of its roots will give a sum total of 39? The manner of solving this type of equation is to take one-half of the roots just mentioned. Now the roots in the problem before us are 10. Therefore take 5, which multiplied by itself gives 25, an amount which you add to 39 giving 64. Having taken then the square root of this which is 8, subtract from it half the roots, 5, leaving 3. The number three therefore represents one root of this square, which itself, of course is 9. Nine therefore gives the square.

Follow these directions to solve the equation

x 2 + 12x = 85

  5
  7
  4
  9
 
       
31
Graph the solution set of the inequality.

 
 
 

 
 
32
Graph the solution set of the inequality.

 
 
 
 
       
33
Solve the inequality.

 
 
 
 

 
       
34
Solve the inequality.

 
 
 
 
 
       
35
Solve the inequality.

 
 
 
 
 
 
36
Solve the inequality.

 
 
 
 
 
 
37
Solve the inequality.

 
 
 
 
 
 
 
 
 
 
38
Suppose that eight times a number is added to 24 and the result is positive. What are the possible numbers?
  Any number less than - 2.
  Any number greater than - 3.
  Any number greater than 7.
 
 
39
If a number is nine less than twice its opposite, what are the possible numbers?
  The number is 2.
  The number is - 7.
  The number is - 3.
 
       
40
Current postal regulations state that no package may be sent if its combined length, width, and height exceed 72 in. What are the possible dimensions of a box to be mailed with equal height and width if the length is two times the height?
  The height and width must each be 21 in. or less and the length 36 in. or less.
  The height and width must each be 18 in. or less and the length 36 in. or less.
  The height and width must each be 18 in. or less and the length 18 in. or less.
 
41
The first step in the problem-solving procedure is not choosing a variable, but rather translating the main idea into symbols. Carry out the first step for the following problem.

If you subtract sixteen from twice a number, the result is eight. What is the number?

  16 - 2( number ) = 8
  2( number ) - 8 = 16
  2( number ) - 16 = 8
  2( number ) + 16 = - 8
 
 
42
The first step in the problem-solving procedure is not choosing a variable, but rather translating the main idea into symbols. Carry out the first step for the following problem.

A diagonal brace is to be placed in the wall of a room. The height of the wall is 9 ft, and the wall is 14 ft long. What is the exact length of the brace, and what is the length of the brace to the nearest foot?

  9 + 14 = LENGTH OF BRACE
  14 - 9 = LENGTH OF BRACE
  14 2 - 9 2 = ( LENGTH OF BRACE ) 2
  9 2 + 14 2 = ( LENGTH OF BRACE ) 2
 
       
43
If you add seven to twice a number, the result is seventeen. What is the number?
  13
  8
  5
  2
 
       
44
The sum of three consecutive integers is 117. What are the integers?
  38, 39, 40
  114, 115, 116
  117, 0, 0
  39, 40, 41
 
 
45
A house and a lot are appraised at $246,600. If the value of the house is five times the value of the lot, how much is the house worth?
  $205,500
  $49,320
  $197,280
  $41,100
 
 
46
A professional gambler reported that at the end of the first race at the track he had doubled his money. He bet $27 on the second race and tripled the money he came with. He bet $54 on the third race and quadrupled his original bankroll. He bet $72 on the fourth race and lost it, but still had $36 left. With how much money did he start?
  $108
  $81
  $27
  $54
 
 
47
Two persons are to run a race, but one can run 11 meters per second, whereas the other can run 5 meters per second. If the slower runner has a 60-meter head start, how long will it be before the faster runner catches the slower runner, if they begin at the same time?
  11 sec
  8.5 sec
  10 sec
  9.5 sec
 
       
48
Two joggers set out at the same time from their homes 21 miles apart. They agree to meet at a point somewhere in between in an hour and a half. If the rate of one is 6 mph faster than the rate of other, find the rate of each.
  10 mph and 1 mph
  4 mph and 1 mph
  4 mph and 10 mph
  3 mph and 1 mph
 
       
49
The hypotenuse of a right triangle is 15.0, and one leg is 6.0 units shorter than the other. Find the dimensions of the figure (rounded to the nearest tenth).
  13.7, 12.0, 15.0
  13.7, 7.7, 15.0
  9.0, 12.0, 15.0
  9.0, 7.7, 15.0
 
       
50
The annual rate, r, compounded annually, it takes for 1 dollar to grow to D dollars in 2 years is given by the formula D = ( 1 + r ) 2 . Find the rate necessary for a dollar to double in 2 years.
  41.4%
  73.2%
  141.4%
  38.7%
 
 
51
A cement mixture calls for 36 pounds of cement for 3 gallons of water. What is the ratio of cement to water?
  13 to 1
  1 to 14
  1 to 13
  1 to 12
  12 to 1
 
52
A cement mixture calls for 78 pounds of cement for 3 gallons of water. What is the ratio of water to cement?
  1 to 26
  1 to 28
  27 to 1
  1 to 27
  26 to 1
 
53
Tell whether the pair of ratios forms a proportion.

  yes
  no
 
54
Insert >, < , or = as appropriate in the expression.

  =
  >
  <
 
55
Solve the proportion for the item represented by a letter.

  S = 395
  S = 392
  S = 394
  S = 390
 
56
A moderately active 140-pound person will use 2,100 calories per day to maintain that body weight. How many calories per day are necessary to maintain a moderately active 155-pound person?
  2,330 calories
  2,325 calories
  2,320 calories
  2,315 calories
 
 
57
Find V', when V = 12, P = 2, T = 200, P' = 8, and T' = 400.

  6
  7
  4
  1
 
58
The pitch of a roof is the ratio of the rise to the half-span. If a roof has a rise of 8 feet and a span of 56 feet, what is the pitch?

 
 
 
  7
 
59
If the property tax on a $300,000 home is $2,760, what is the tax on a $100,000 home?
  $912
  $930
  $920
  $928
 
60
To dilute a medication you can use the following formula. How many units of a 10% solution are needed to prepare 600 units of a 6% solution?

  360 units
  370 units
  390 units
  380 units
  600 units
 
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