Download Math 2 Test 2

October 4th and 5th , 2011
Math 2 Test 2
GO Gold and Green!!
MM2N1. Students will represent and operate with complex numbers.
a. Write square roots of negative numbers in imaginary form.
b. Write complex numbers in the form a + bi.
c. Add, subtract, multiply, and divide complex numbers.
d. Simplify expressions involving complex numbers.
2
2
MM2A3. Students will analyze quadratic functions in the forms f(x) = ax + bx + c and f(x) = a(x – h) + k.
c. Investigate and explain characteristics of quadratic functions, including domain, range, vertex, axis of symmetry, zeros, intercepts, extrema, intervals
of increase and decrease, and rates of change.
d. Explore arithmetic series and various ways of computing their sums.
MM2A4. Students will solve quadratic equations and inequalities in one variable.
b. Find real and complex solutions of equations by factoring, taking square roots, and applying the quadratic formula.
c. Analyze the nature of roots using technology and using the discriminant.
d. Solve quadratic inequalities both graphically.
Section I. Multiple Choice
1.
a.
Choose the best answer.
What is the solution to the equation 3x 2  x  1  0 ?
x
1
13

6
6
b.
1
11
x   i
6
6
(MM2N1 a, b, d MM2A4 b)
c.
1
13
x   i
6
6
c.
3  4i
d.
2. What is the conjugate of 3  4i ? (MM2N1 c)
a.
3.
 3  4i
b.
7i
How many real roots does the quadratic function shown in the graph have?
a.
b.
c.
d.
4.
Simplify. (2  4i )  (7  11i ) .
a.  5  15i
9 15i
 3  4i
( MM2A4 c)
0
1
2
3
(MM2N1 c)
b.  5  7i
5. What is the sum of 2  4i and 7  11i ?
a.
d.
b.
c. 9  15i
d. 9  7i
( MM2N1 c)
9 15i
c.
24
d.
24i
x
1
11

6
6
6.
What is the solution to the inequality x 2  6 x  40 ?
 10  x  4
a.
b.
c. x  10 or x  4
( MM2A4 d)
 4  x  10
d. x  4 or x  10
7. Solve the equation  3x 2  4 x  6  0 .
(MM2N1 a, b, d and MM2A4 b)
(Make sure the answer is in simplest form.)
a.
8.
x
4  56i
3
b. x 
4  64i
3
c.
x
 4  14i
3
What is the solution to the inequality 2 x 2  11x  21  0 ?
x  7 or x  1.5
 1.5  x  7
a.
c.
9. Find the quotient
b.
d.
d.
x
 2  14i
3
(MM2A4 d)
x  1.5 or x  7
 7  x  1.5
3  2i
. (MM2N1 c)
1 i
a. 2  i
b.
5i
2
c.
10. How many different real zeros does the function
1 i
d.
1 i
2
f ( x)  49 x 2  84 x  36 have?
(MM2A4 c)
Hint: use the discriminant.
a.
0
b.
1
c.
2
d.
3
11. The first term of a sequence is 12 and the common difference is - 7. What is the 25th term?
a.
-281
b.
180
c.
281
d.
-156
12. What is the explicit formula that represents the nth term of the following sequence?
6, 4, 2, 0, -2, -4,….
a.
an  2n  8
b.
an  6n  8
c.
an  2n  8
d.
a n  6n  8
(MM2A3 d)
(MM2A3 d)
13. Given the following sequence find:
S5
(MM2A3 d)
76, 95, 114, 133, 152, 171, 190, 209, 228, ..
a.
570
b.
741
c.
931
d.
14. Which equation could you use to solve 0  4 x 2  3x  2 ?
1140
(MM2A4 b)
a.
x
 3  32  4(4)( 2)
2(4)
b.
x
 3  (3) 2  4(4)(2)
2(4)
c.
x
3  (3) 2  4(4)( 2)
2(4)
d.
x
3  (3) 2  4(4)(2)
2(4)
15. What is the square of
a.
33 56i
4  7i ?
b.
Section II. Free Response
(MM2N1 c)
 33 56i
c.
 33 56i
d.
33  56i
Make sure all answers are in simplest form.
16. Find the nature of the roots using the discriminant.
x 2  16 x  61  0
(MM2A4 c)
17. Find the nature of the roots using the discriminant.
x 2  3 x  4
(MM2A4 c)
18. Simply each of the following:
a) i15
b) i30
(MM2N1 d)
c) i77
d) i48
19. Simplify.
  80
(MM2N1 a)
20. Simplify.
5  27
(MM2N1 a)
21. Simplify.
8 
22.

 25 2   121

(3  4i) 3
23. Given the following sequence find S 35 .
-8, -4, 0, 4, 8, …..
(MM2N1 c)
(MM2N1 c)
(MM2A3 d)
Sn 
n(a1  an )
2