MATH HONORS 2: Final Exam Review Answers
1 3 3 2
x  x  3x  4
2
2
3
2
2. (k  2k  22k  40)  (k  4)  k 2  2k  14   16(k  4)
1.
f  x 
Quotient:
k
2
 2k  14 
Remainder: -16
1 1 2 35 78
1 3 33
3. (a)
(b) P(6)  0
(c) x  6, 4  3, 4  3
1 3 33 111
4.
5.
k2
x  3, x  1, y  2
6.
x  10 , Note: x  
7. b  4 , Note: b  2, 4
8. C.V. z  2, 1,3,9
Set Notation: z 
5
2
2  z  1  3  z  9 Interval Notation:  2, 1   3,9 
x3  10 x 2  20 x
3x 2  11x  10
2c 3  3c 2  39c  12
10.
 c  3 c  1 c  5 
9.
11. A = 1, B = 7, C = 3
12. Horizontal Translation of 5 units and a Vertical Translation of –3 units.
(Note: if you include direction then all values should be positive)


1
5
x–Intercept:  4, 0 
13. (a) Asymptotes: x  5, x  4, y  0 Hole:  0, 
9
y
8
7
6
5
4
3
2
1
-9
-8
-7
-6
-5
-4
-3
-2
-1
x
1
-1
-2
-3
-4
-5
-6
-7
-8
-9
2
3
4
5
6
7
8
9
(b) Domain: x 

(c) Range: y 
x  4,0,5
y  0,
1
5

Interval Notation:
 , 4    4, 0    0,5  5,  
Interval Notation:
1
1
 , 0    0,    ,  

5
5
(d) See previous page.
14. Calculator Question
y
6
5
4
3
2
1
(-1.21,0)
x
(1.17,0)
-1.8 -1.6 -1.4 -1.2 -1 -0.8 -0.6 -0.4 -0.2
-1
0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3
-2
-3
-4
-5
-6
-7
-8
-9
(-0.0218,-9.32)
15. 2 Real Solutions (2 Real Unequal Roots) because discriminant is greater than zero.
16. (a) x = –1 (b) (–1, –32)
(c) f  x   2  x  1  32
2
17. (a) or x  1
(b) x  9 or x  1
18. f  x   2  x  3 x  5

(d) f  x   2  x  3 x  5

19. 8  6a 2  12ai  a 3i or in complex form 8  6a 2  a 3  12a i
2  39i
61
1 2
1 2
21. x   i 5 or x   i 5
3 3
3 3
1
22. Domain: x  x 
Range:
3
23. y  9 x 2  6 x  4
2
24. C.V. x   , 4
3
2


Set Notation: x    x  4 
3


20.


y 
y  3
 2

Interval Notation:   , 4 
 3 
25. f 1  x   1  x  1 or f 1  x   1  x  1
26. (a) ( g
27. x  4
f )(4)  9
(b) ( f
g )( x 2  3)  2 x 2  1
1
(c) f (2) 
1
2

28. (a) Function with an inverse that is also a function.
(b) Function with an inverse that is not a function.
2
3x  2
30. y  3  x  4 x  1
29. f 1 ( x) 
31. a = 1, b = –5, c = 3
32.
y
4
3
2
1
x
-4
-3
-2
-1
1
2
3
4
-1
-2
-3
-4
33. Many Possible solutions. Below is one example.
f ( x)  x 2  16 and g ( x)  2 x
1
4 x  2


34. f ( x)  1

1
 2 x 1

10
35. (a) a
7a 4 c c
(b)
b2
(c) x  y 3
if, x  0
if, x  0
if, x  0
(d) x9a (or x 4 x a )
(e) 3a
36. A shift to the right by 5 units and a shift downwards by 3 units
37. Approximately 7163 (or 7160 ) people would be expected to visit the island in the year 201
38. x  1.7
39. $2818.40 (or $2818 , or $2820 )
40. 1.96 weeks (or 2 weeks)
2 1  1
A CB
3
 5 10
42. 

 8 10
1 3
43. B  

 2 3
41. X 
44. (a) A  11
 4 1
 11 11 
1  4 1
(b) A1  
(or

)
11  3 2 
 3 2 
 11 11 
(c) A singular matrix means that it has no inverse, occurring when the matrix’s determinant is equal to zero.
Since the determinant of matrix A is 11 which is not equal to zero, matrix A is non-singular.
45. m  p , n  q
 3 2 2 
4
x
 4 






46. Use the matrices A  1
2 3 , B   1  ,and X   y  . Then AX=B and X   29

 21
 1 1 1 
12 
 z 
1
47. (a) x 
36
3
(b) x 
2
(c) x  10
(d) x  44
48. 43.2 mg
49. x 
ln 18  5
3
 7
5

51. x 
4
50.
5 7
,
8 8
 2  3
, ,
(b) x   , 
4
3 3 4
52. (a) x 
53.
54.
55.
56.
57.
58.
Use calculator to check your graph.
Proof – answer is given
Proof – answer is given
A = –2, C = 1
A = 0.8, B = 0.5, D = –1.2
3 32
2 3 3
[Hint: use sum identity with
60. 5.16 degrees
61. 52.6 yards
62. (a) about 90.0 degrees
(b) 51.7 square kilometers
63. 67 ways [ 7  5  4  8 ]
1
2
4
64. 37.5%
[ 6  ]
65. 51.3%
[(.75)(.60) + (.25)(.25)]
cos(  30)
]
sin(  30)