mathacle pset ---- algebra, mixed...

Mathacle

PSet ---- Algebra, Mixed Topics Level ---- 1 Number ----- 1 Name: ___________________ Date: _____________ Midterm Exam – Each question is worth one point. 1. ( ( | 2.6 |))− − − = (A) |-2.6| (B) -|2.6| (C) 2.6 (D) –(-|-2.6|)

2. | 4 | | 4 |

31

− −− + =−

(A) -3 (B) -11 (C) 5 (D) 3 3. ( 3 )( 12)y− − = (A) 15y− (B) 3 12y− − (C) 36y (D) 15− 4. 2( )( )( )x x x− − − = (A) 43x− (B) 3x− (C) 3x (D) 4x−

Mathacle

PSet ---- Algebra, Mixed Topics Level ---- 1 Number ----- 1 Name: ___________________ Date: _____________ 5. ( 3)( 4)( 2)t− − − = (A) 6 24t − (B) 9t − (C) 3 10t− + (D) 3 6t− − 6. Solve 3 6x y− + = for y (A) 3 6y x= − + (B) 3 6y x= − − (C) 3 6y x= + (D) 3 6y x= −

7. Solve 1

2 52

x y− = for y

(A) 2 5y x= + (B) 4 5y x= − (C) 4 10y x= + (D) 4 10y x= − 8. Solve 3 2 1a b a b+ = + + for a (A) 1a = − (B) 1a = (C) 1a b= − + (D) 1a b= −

Mathacle

PSet ---- Algebra, Mixed Topics Level ---- 1 Number ----- 1 Name: ___________________ Date: _____________

9. Solve 5

, ______4 2

xx= =

(A) 10

(B) 8

5

(C) 1

10

(D) 5

2

10. 4 8

2 , ______3

yy

− +− = =

(A) 1

4−

(B) 5

4

(C) 5

4

−

(D) 4

5

−

11. Simplify 2 22(3 3 )x x x+ − = (A) 22 6x x− + (B) 25 6x− + (C) 25 6x x− + (D) 2 32x x−

Mathacle

PSet ---- Algebra, Mixed Topics Level ---- 1 Number ----- 1 Name: ___________________ Date: _____________ 12. Simplify 2 3 2 3 2(3 ) (2 )x y y = (A) 4 1236x y

(B) 4 106x y

(C) 4 126x y

(D) 4 1036x y 13. Simplify 2( 5)( 1) __________x x− + + = (A) 3 24 5x x+ − (B) 3 25 5x x x− + − + (C) 3 24 5x x+ + (D) 3 26 5x x− + 14. Simplify 2 2 3 3(1 )(2 )(3 )xy x y x y = (A) 6 65x y

(B) 5 55x y

(C) 6 66x y

(D) 5 56x y 15. Factor 2 17 30x x+ + (A) ( 2)( 15)x x− + (B) Prime (C) ( 2)( 15)x x+ + (D) ( 15)( 2)x x− +

Mathacle

PSet ---- Algebra, Mixed Topics Level ---- 1 Number ----- 1 Name: ___________________ Date: _____________ 16. Factor 2 25 6x xy y− − (A) ( 5 )( )x y x y− + (B) Prime (C) ( 6 )( )x y x y− − (D) ( 6 )( )x y x y− + 17. Factor ( 1) ( 1)x x x+ − + = (A) 2( 1)x + (B) Prime (C) ( 1)( 1)x x− +

(D) 2( 1)x − 18. Factor 2 2 4x x− − (A) ( 2)( 2)x x+ + (B) Prime (C) ( 2)( 2)x x+ − (D) ( 4)( 1)x x− + 19. Factor 23 10 3x x+ + (A) (3 1)( 3)x x− + (B) Prime (C) (3 1)( 3)x x+ + (D) ( 3)( 3)x x+ +

Mathacle

PSet ---- Algebra, Mixed Topics Level ---- 1 Number ----- 1 Name: ___________________ Date: _____________ 20. Find the GCF of 24 and 36 (A) 12 (B) 2 (C) 4 (D) 6 21. Shelley made six less sales calls than Clark. Shelley and Clark made a total of 30 sales calls. How many sales calls did each make? (A) Shelley made 10 and Clark made 20 (B) Shelley made 18 and Clark made 12 (C) Shelley made 16 and Clark made 14 (D) Shelley made 12 and Clark made 18 22. Factor 3 2 2 3c d c d− = (A) 2 2( 1)c d d −

(B) 2 2( 1)c d c −

(C) 2 2( )c d c d−

(D) 3 3c d 23. Express (3 1)(2 3)x x− − as a polynomial (A) 26 11 3x x− + (B) 26 11 3x x+ + (C) 26 3 11x x− + (D) 26 11 3x x− −

Mathacle

PSet ---- Algebra, Mixed Topics Level ---- 1 Number ----- 1 Name: ___________________ Date: _____________ 24. Express (4 1)(2 3)x x− + as a polynomial (A) 28 10 3x x+ − (B) 28 2 3x x+ + (C) 26 2 3x x+ − (D) 26 10 3x x+ − 25. Express (2 3)(2 3)x x+ − as a polynomial (A) 24 6 9x x− − (B) 24 6 9x x+ − (C) 24 9x − (D) 24 5x x+ 26. A wooden rod 47 in long is sawed into two pieces. One piece is 4 in. shorter than 2 times of the length of the other. What is the length of the longer piece? (A) 29 (B) 30 (C) 31 (D) 32 27. Lee bicycled 4 km less than Wing. The sum of the distances they bicycled was 24 km longer than what Lee traveled. How far did Lee go? (A) 18 (B) 19 (C) 20 (D) 21

Mathacle

PSet ---- Algebra, Mixed Topics Level ---- 1 Number ----- 1 Name: ___________________ Date: _____________ 28. If the slope is -2 and y-intercept is -10, then the linear equation is: ________ (A) 2 10y x= + (B) 2 10y x= − − (C) 10 2y x= − − (D) 10 2y x= − + 29. Four less than n less two: ___________. (A) 4 2n− − (B) 4 2n< − (C) 4 2n− + (D) 2 4n − − 30. Four less than a half of three more than a number

(A) 1

4 22

x< −

(B) 1

4 ( 3)2

x− +

(C) 1

(3 ) 42

x+ −

(D) 1

4 ( 3)2

x< +

Mathacle

PSet ---- Algebra, Mixed Topics Level ---- 1 Number ----- 1 Name: ___________________ Date: _____________ 31. Solve 2 13 31x + = (A) 8 (B) 9 (C) 10 (D) 11

32. Solve 4 85

x− =

(A) 4 (B) 60 (C) 20 (D) 20− 33. Solve 10 2(3 4) 0x x− + = . (A) 2 (B) 1

(C) 1

2

(D) 2−

34. If 3( 1) 0x + = , what does 5

5

x

x

−+

equal? _________.

(A) 1

4

(B) 4

(C) 3

2

(D) 2

3

Mathacle

PSet ---- Algebra, Mixed Topics Level ---- 1 Number ----- 1 Name: ___________________ Date: _____________ 35. Find the slope of the line that passes through (1,1) and (-1,0).

(A) 1

2

−

(B) 1

2

(C) 0 (D) No Slope 36. Find the slope of the line that passes through (-1,0) and (1,6). (A) 3−

(B) 1

3

−

(C) 1

3

(D) 3

37. Find the slope and y-intercept of the line that whose equation is 1

32

y x= − .

(A) 1

, 32

−

(B) 1

3,2

−

(C) 2, 3 (D) 3, 2− 38. Find the slope and y-intercept of the line that whose equation is y x= − . (A) 1, 0 (B) 1, 0− (C) No Slope and y-intercept is one (D) No Slope, and no y-intercept

Mathacle

PSet ---- Algebra, Mixed Topics Level ---- 1 Number ----- 1 Name: ___________________ Date: _____________ 39. Find the equation of a line with slope 1− that passes through (2,3). (A) 3y x= + (B) 2y x= − (C) 5y x= − + (D) 2y x= − + 40. In which quadrant is the graph of (3,-5)? (A) I (B) II (C) III (D) IV 41. In which quadrant is the graph of (-4,-10)? (A) I (B) II (C) III (D) IV 42. Where is the graph of (0,3) in the coordinate plane? (A) in Quadrant II (B) in Quadrant III (C) on the x-axis (D) on the y-axis 43. Find the slope of the line whose equation is y-1=0? (A) 1 (B) 0 (C) Undefined (D) -1

Mathacle

PSet ---- Algebra, Mixed Topics Level ---- 1 Number ----- 1 Name: ___________________ Date: _____________ 44. Solve for c in the equationc by a+ = . (A) c a by= − (B) 2c a b= + (C) c by a= −

(D) y a

cb

−=

45. Solve for y in the equation 143 =+ yx . (A) 4 1 3y x= −

(B) 4 1

3 4y x= − +

(C) 3 1

4 4y x= − +

(D) 4 1 3y y= +

46. Solve 1

3 4

x x +=

(A) 1 (B) 3 (C) no solution (D) 0

47. Solve 3 3 5

5 3

x x− +=

(A) 4−

(B) 6

17

(C) 17

6

−

(D) 4

Mathacle

PSet ---- Algebra, Mixed Topics Level ---- 1 Number ----- 1 Name: ___________________ Date: _____________ 48. The tuition rates for in-state residents to attend a state college are shown in the graph below

In which year, the tuition is $6,000? (A) 1 (B) 2 (C) 3 (D) 4

49. If 12x is 10 less than 2x, what is the value of 2x? (A) 1 (B) 0 (C) -1 (D) -2

Mathacle

PSet ---- Algebra, Mixed Topics Level ---- 1 Number ----- 1 Name: ___________________ Date: _____________ 50. Which equation represents the graph below?

(A) 1

14

y x= +

(B) 1

14

y x−= −

(C) 3

12

y x−= −

(D) 2

13

y x= −

51. The line that represents the equation 3 2y x= − contains the point ( , )k k . Find k.

(A) 4 (B) 3 (C) 2 (D) 1 52. 16 _____________= (A) 1 (B) 2 (C) 4± (D) 4

Mathacle


53. Find the slope from the graph:

(A) 4

5−

(B) 3

2

(C) 5

3

(D) 4

5

54. 5300 _____________x =

(A) 2100 3x x

(B) 210 3x x

(C) 10 3x x

(D) 310 3x

Mathacle


55. The graph below represents Karen’s Marathon Time vs. Distance chart.

During which time period do you think Karen run slower: in interval A or B? (A) A (B) B (C) Can’t decide. (D) Same.

56.

Which of the following are the coordinates of a point on the line l in the xy-plane above? (A) ( 3, 1)− − (B) (5, 5)− (C) (0,0) (D) (3, 3)− 57.

Mathacle


In the figure above, the slope of line segment AB is 1

3

−. What is the value of k ?

(A) 20 (B) 19 (C) 18 (D) 17

58. Which line(s) above has or have the negative slope. (A) a, c only (B) b, c only (C) c, d only (D) a, d only

Mathacle

PSet ---- Algebra, Mixed Topics Level ---- 1 Number ----- 1 Name: ___________________ Date: _____________ 59.

In the figure above, what is the slope of line l ?

(A) r

s

−

(B) s

r

(C) s− (D) r− 60.

Which is the y-intercept of line above?

(A) (0,3) (B) (3,0) (C) 0 (D) 2

Mathacle


61. 3 8 _____________= (A) 3

(B) 2 2 (C) 2

(D) 32 2 62. Which is an equation of the line that passes through the points (2,3) and (4,5)?

(A) 2 1y x= + (B) 2 3y x= − (C) 2y x= − (D) 1y x= +

63. 3 22 12 _____________p q =

(A) 2 12pq q

(B) 4 3pq p

(C) qpq2

(D) 4pq p

64. Find the complete solutions of 2 121, _____________x x= = (A) 11 (B) 11− (C) 11, 11− (D) 121±

Mathacle

PSet ---- Algebra, Mixed Topics Level ---- 1 Number ----- 1 Name: ___________________ Date: _____________ 65. What is the value of the expression3(2 1)x y− − , if 3x = and 5y = − ? (A) 10 (B) 20 (C) 26− (D) 26 66. Which expression is equivalent to 2 23 ( 4 1)x x x+ − ? (A) 4 3 23 12 3x x x+ − (B) 4 2 23 12 3x x x+ + (C) 4 2 23 12 3x x x+ − (D) 4 3 23 12 3x x x− +

67. Which of the following is equivalent to 3 4

4 3

x y

x y?

(A) y

x

(B) x

y

(C) xy

(D) 77 yx

68. Which of the following is equivalent to ( )223x y− ?

(A) 4 29x y−

(B) 4 26x y−

(C) 4 29x y

(D) 4 26x y

Mathacle

PSet ---- Algebra, Mixed Topics Level ---- 1 Number ----- 1 Name: ___________________ Date: _____________ 69. Which of the following is equivalent to 4 4 23 x y− ?

(A) ( )229x y−

(B) ( )22 23 x y

(C) ( )22 23 x y−

(D) ( )229x y−

70. 2 40 4, _____________x x− + = =

(A) 2 11±

(B) 2 11 (C) 6±

(D) 2 11− 71. The relationship shown in the table is a direct variation: x Y 2 10 3 15 4 20 5 25 Which equation best represents this relationship? (A) 10 10y x= − (B) 10+= xy (C) 5y x=

(D) 1

5y x=

Mathacle

PSet ---- Algebra, Mixed Topics Level ---- 1 Number ----- 1 Name: ___________________ Date: _____________ 72. Solve ( 5)( 2) 0, _________y y y− + = = ? (A) 2, 5− (B) 2, 5− (C) 5− (D) 2 73. Solve (3 4)(4 2) 0, ________x x x− + = = ?

(A) 4 1

,3 2

−

(B) 3

, 24

−

(C) 4 1

,3 2

−

(D) 4

3−

74. Solve 23 22 7 0, _________x x x+ + = = ?

(A) 1

, 73

− −

(B) 7 1

,3 3

− −

(C) 1

, 73

(D) 3

, 17

−

Mathacle


75. Solve 15

2 3 32

x y

x y

+ = + =

(A) 2, 13x y= = (B) 8, 8x y= = (C) 7, 8x y= = (D) 2,13 == yx 76. If 2( ) 2f x x x= − , then ( 3) ________f − = (A) 15 (B) 14 (C) 13 (D) 12 77. If ( ) 3f x x= − , then (2 1) ________f k − = (A) 2 2k− (B) 6 3k− − (C) 4 2k− (D) 3 2k−

78. If 3 4

( )2

xh x

− += , find ( ) (2 ) 1 __________g x h x= − =

(A) 6 5

2

x− +

(B) 3 1x− +

(C) 3 4

2

x− +

(D) 3 1x +

Mathacle

PSet ---- Algebra, Mixed Topics Level ---- 1 Number ----- 1 Name: ___________________ Date: _____________ 79. x ( )f x ( )g x

-1 5 -2

0 3 3

1 -3 5

2 2 0

3 0 3

Several values of the functions ( )f x and ( )g x are shown in the above table. For what x is ( ) (1)f x g= ? (A) 1− (B) 1 (C) 0 (D) 2

80.

The figure above shows the graph of ( )y g x= . If the function h is defined by

( ) 2 ( ) 1h x g x= − , what is the value of (2)h ? (A) 3 (B) 2 (C) 1 (D) 0

Mathacle

PSet ---- Algebra, Mixed Topics Level ---- 1 Number ----- 1 Name: ___________________ Date: _____________ 81. The ratio of the number of boys to the number of girls is 5:4 in a class. There are 32 girls. How many boys are there in the class? (A) 43 (B) 42 (C) 41 (D) 40 82.

The figure above shows the graph of the function h. Which of the following is closes to

(6)h ? (A) 1 (B) 2 (C) 3 (D) 4 83. Let the function f be defined by ( ) 2 1f x x= − . If 3 ( ) 27f p = , what is the value of

(2 )f p ? (A) 20 (B) 19 (C) 18 (D) 17

Mathacle


84. Simplify

222

2

−

(A) 5

1

2

(B) 1

32

(C) 1

64

(D) 8

1

2

85. Simplify

20

2

4 3

3

−

−

⋅

(A) 63

(B) 6

1

3

(C) 5

1

3

(D) 53

86. Simplify

3 3 23

2

h j k

jk

− −

(A) 3 3

3

3

2

j k

h

(B) 3 3

4

2

3

j k

h

(C) 3 3

2

2

3

h k

j

(D) 2

3 3

3

2

j

h k

Mathacle

PSet ---- Algebra, Mixed Topics Level ---- 1 Number ----- 1 Name: ___________________ Date: _____________ Questions #87 - #90 refer to the table below: Item initial

Price New Price

Price Increase

% of increase

Jeans $25 $30 X W School Lunch

$1.60 $2.00 Y K

Haircut $10.00 $14.00 Z Z 87. What is Y, the price increase of School Lunch? (A) $5 (B) $0.40− (C) $0.40 (D) $4 88. What is K, the percent of price increase of School Lunch? (A) 40% (B) 25% (C) 25%− (D) 0.40% 89. What is total price increase of Jeans and School Lunch combined? (A) $6.40 (B) $5.40 (C) 40.4$ (D) $3.40 90. What is percent of price increase of Jeans and School Lunch combined? (A) %68.25 (B) 25.65% (C) 20.30% (D) 15.30%

Mathacle

PSet ---- Algebra, Mixed Topics Level ---- 1 Number ----- 1 Name: ___________________ Date: _____________ Answer Key: 1. B 2. A 3. C 4. D 5. A 6. C 7. D 8. B 9. A 10. A 11. C 12. A 13. B 14. C 15. C 16. D 17. C 18 B 19. C 20. A 21. D 22. C 23. A 24. A 25. C 26. B 27. C 28. B 29. D 30. C

31. B 32. D 33. A 34. C 35. B 36. D 37. A 38. B 39. C 40. D 41. C 42. D 43. B 44. A 45. C 46. B 47. C 48. A 49. D 50. B 51. D 52. D 53. A 54. B 55. B 56. C 57. B 58. C 59. A 60. A

61. C 62. D 63. B 64. C 65. B 66. A 67. B 68. C 69. D 70. C 71. C 72. B 73. C 74. A 75. D 76. A 77. C 78. B 79. A 80. C 81. D 82. D 83. B 84. C 85. C 86. D 87. C 88. B 89. B 90. C

Mathacle

PSet ---- Algebra, Mixed Topics Level ---- 1 Number ----- 1 Name: ___________________ Date: _____________ Answer Sheet: 01. _______ 02. _______ 03. _______ 04. _______ 05. _______ 06. _______ 07. _______ 08. _______ 09. _______ 10. _______ 11. _______ 12. _______ 13. _______ 14. _______ 15. _______ 16. _______ 17. _______ 18 _______ 19. _______ 20. _______ 21. _______ 22. _______ 23. _______ 24. _______ 25. _______ 26. _______ 27. _______ 28. _______ 29. _______ 30. _______

31. _______ 32. _______ 33. _______ 34. _______ 35. _______ 36. _______ 37. _______ 38. _______ 39. _______ 40. _______ 41. _______ 42. _______ 43. _______ 44. _______ 45. _______ 46. _______ 47. _______ 48. _______ 49. _______ 50. _______ 51. _______ 52. _______ 53. _______ 54. _______ 55. _______ 56. _______ 57. _______ 58. _______ 59. _______ 60. _______

61. _______ 62. _______ 63. _______ 64. _______ 65. _______ 66. _______ 67. _______ 68. _______ 69. _______ 70. _______ 71. _______ 72. _______ 73. _______ 74. _______ 75. _______ 76. _______ 77. _______ 78. _______ 79. _______ 80. _______ 81. _______ 82. _______ 83. _______ 84. _______ 85. _______ 86. _______ 87. _______ 88. _______ 89. _______ 90. _______

mathacle pset ---- algebra, mixed...

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