Download Honors Segment Two Exam Review You are near the end! Make

Honors Segment Two Exam Review
You are near the end! Make sure prior to taking this honors segment exam that you have studied the
following concepts. Practice each problem by yourself, like you would a test. Check your answers after
you have completed all problems. If you have any questions, make sure to contact your teacher.
-----------------------------------------------------------------------------------------------------------------------------------------Match each conic section on the right with one equation from the left.
7) Find the center of the circle x 2  6 x  y 2  2 y  26  0
8) Find the vertex of y  3x 2  5
9) Find the directrix and axis of symmetry to the equation y 
1 2
x
28
10) Match each graph on the left with an equation on the right.
11) Find the length of the major and minor axis in the ellipse
x2 y 2

1
16 4
12) Find the intercepts of the hyperbola
x2 y 2

1
9
1
13) Write an equation to a circle with radius of 4 and center of (4,-3).
14) The equation 2 x3  3x 2  4 x  15  0 has how many solutions?
15) List all the possible solutions to 2 x3  3x 2  4 x  15  0
16) Simplify
x2  2x  3
x2 1
17) Solve for x in 4 x  4  16
18) Find the Least Common Denominator of
x 1 x 1
x
,
, 2
2
x  4 x  3 x  1x  6
19) Solve x 3  4 x 2  1x  6  0 and list all solutions.
20) Find the remainder when dividing 2 x 3  3 x  7 by (x+2).
21) Multiply
22) Divide
2 y  6 6 y  12

3 y  6 2 y  10
9 y 2 3 y3

2x 6x
23) (4+3i) is a solution to a polynomial equation. Name another solution to the same equation.
24) Find the vertical asymptote f ( x) 
5
x7
25) Match each equation with the value for x.
26) Exponential equations must have a(n) __________ in the exponent position.
27) The Domain is all the real numbers for g ( x)  3x , what is the Range?
28) The Domain is all the real numbers for f ( x)  x3 , what is the Range?
 x2  3 , x  0

29) What is the range value when x=3? f ( x)   4
,x 0

 x 1
30) Solve x3  7 x 2  10 x  0
31) Find the radius of a circle with an area of 24. Round your answer to the nearest hundredth.
32) Find the third term in the expansion (2 x  1)4
20
33) Find
 2i  5
i 1

34) Find
 3(2 / 3)
i
i 0
35) The FBI witness protection program has 8 choices for first names, choices for last names, and 10 US
cities to pick from. How many hidden identities can they create?
36) Find the sum of the first 10 terms in the following geometric sequence: 5, 10, 20, 40, …
37) Find the 15th term in the arithmetic sequence: 2, 7, 12, 17, …
38) Match the central tendency with the value using the set of data: 7, 8, 9, 10, 7, 9, 8, 6, 7
39) Match the central tendency with the value using the set of data: 1, 2, 3, 4, 4, 6
40) Simplify
3
5 2
41) If h( x)  x 2  2 and g ( x )  5 x find g (h( x)) .
42) If h( x)  x 2  2 and g ( x )  5 x find h( g ( x)) .
43) Simplify
3
64a5b7
44) Solve for x in
3x
2

2x  5 x  3
45) Solve for x in
8
6
4
 
x  2x x x  2
2
Answer to be looked at after you have complete each question (place in sealed envelope) 
Matching: 1) Ellipse 2)Circle radius six 3) Parabola up 4) Parabola down 5)hyperbola 6) circle radius seven
 6 
 =9 and
 2 
2
7) Center is (3,-1) First complete the square by adding 
 2 
  =1:
 2 
2
x 2  6 x  (9)  y 2  2 y  (1)  26  (9  1) then rewrite as ( x  3)2  ( y  1)2  36
8) (0,5) Use
b
2
to find the x value of zero, then use x=0 in the original equation y  3x  5 to find y=5.
2a
9) directrix y=-7 axis of symmetry=0
10) ellipse B, Parabola A, Circle D, Hyperbola C
11) Major axis is twice the square root of the larger denominator.
2  16  8
Minor axis is twice the square root of the smaller denominator.
12) The x intercepts are found by placing 0 in for y:
2 4  4
x 2 02
  1 so x  3 , intercepts are (3,0) and (-3,0)
9 1
02 y 2
Sketch the graph to see them, or know that solving

 1 will lead to y 2  1 which doesn’t exist.
9 1
13) Use
( x  h)2  ( y  k )2  r 2 sub in ( x  (4))2  ( y  (3))2  (4)2 to get ( x  4)2  ( y  3)2  16
14) The leading coefficient tells us there are three solutions to the equation.
15) 
15 15 5 5 3 3 1 1
, , , , , , ,
1
2 1 2 1 2 1 2
16) Factor
( x  1)( x  3)
( x  3)
, Cancel to get the final answer of
( x  1)( x  1)
( x  1)
17) Add four:
4 x  20 Then divide by four:
x  5 Then square both sides: x  25
18) (x+3)(x-2)(x+2) OR x  3x  4 x  12
3
2
19) Solutions are 1, -2, and -3
20) Sub in -2 for x:
2(2)3  3(2)  7 continue to solve: 2(-8)+-6-7 Finish with -16-6-7 = -29
Answer to be looked at after you have complete each question (place in sealed envelope) 
21) Factor
2( y  3) 6( y  2)
( y  3)
2
2y  6
, Now cancel items
simplify to get


3( y  2) 2( y  5)
1
( y  5)
y5
22) Multiply by the second reciprocal:
9
9 y2 6x
 3 Reduce or cancel items to get:
y
2x 3 y
23) The conjugate is always a solution (the come in pairs) (4-3i)
24) vertical asymptote is x=-7
25) 1D 2C 3F 4A 5G 6B 7E
26) Exponential equations must have a variable in the exponent position.
27) The range is the set of all positive numbers.
28) The range is the set of all real numbers.
29) Sub 3 in for x in the bottom piece since 3 is greater than or equal to zero,
4
Answer range=1
3 1
30) {x| 0 < x < 2 or x > 5}
31) Solve for r in 24   r getting r=2.76
2
32) Expanded looks like this: 16 x  32 x  24 x  8 x  1 The third term is 24x cubed.
4
33) Solved by
2
20
  3  35  = 320
2

34) Find
3
a1
3
 3(2 / 3) Solved by 1  r = 1  .6667  9.00000009
i
i 0
35)
8  7 10  560
36) 5,115
37) 72
38) mean=7.88 median=8 mode=7 fake=7.66
39) mean=3.33 median=3.5 mode=4 fake=3
Answer to be looked at after you have complete each question (place in sealed envelope) 
40) Solve
3
5 2
by multiplying by
5 3 6
5 2
5 3 6
getting
reduced to
23
5 2
25  4
41) g (h( x)) = g ( x 2  2)  5( x 2  2)  5x 2  10
42) h( g ( x)) = h(5 x)  (5 x)2  2  5 x 2  2
43)
4ab2  3 a2b1
44) Cross multiply to get 3x  9 x  4 x  10 left side 3 x  13 x  10  0 factor (3x+2)(x-5)=0 Ans: -2/3, +5
2
45) Common Denominators:
2
8
6( x  2)
4( x)
leads to 8+6(x-2)=4x or 8+6x-12=4x and x=2


x( x  2) x( x  2) ( x)( x  2)