Download March Regional Precalculus Test

March Regional Precalculus Test
1. Solve for x for the following equation: sin x  sin 2x  0 given the restriction
0  x  2 .
a)

2
,
3
b) 0,
2
2
, 2  c) 0,
,
3
3
d) 0, 2
e) NOTA
2. A marketing firm advertises only in magazines. An analysis shows that of all
potential customers 20% buy their products. Of the customers that buy, 35% have seen
 the ads. Of the customers that don’t buy, 40% have seen the ads. Find the percent of
those who have seen the ads that will buy the products, to the nearest percent.
a) 17%
b) 18%
c) 19%
d) 20%
e) NOTA
3. Solve for x:
3
1 2x  4 x 2  8x 3  .... Assume that the pattern continues to infinity.
4
1
1
1
a)
b)
c)
d) 2
e) NOTA
6
2
2
the distance between the polar coordinates (8, 30 0 ) and (10,  210 0 ) .
4. Find
b) 4 21
c) 9 3
d) 2 61
e) NOTA
 a) 2 21
5. Change the polar equation r 2  sec 2 
to rectangularform.
2
2
a) x  y  1
b) x  y  1
c) x 2  y 2  1
d) x 2  y 2  1

e) NOTA
  7 
12 
tan  Arc sin  
6. Evaluate. cosArc
24 
13 


a)

36
325
b)
204
325
c)
36
325
d)
204
325
e) NOTA
7. A card is drawn from a standard deck (no jokers). Find the probability that the card is
red or an ace.

6
1
7
15
a)
b)
c)
d)
e) NOTA
13
2
13
26

8. Which of the following vectors is perpendicular to the vectors (-2, 3, 1) and (4, 1, -3)?
a) (5,1, 7)
b) (5, 2, 4)
c) (10, 2, 14)
d) (9, 10,12)
e) NOTA

9. In triangle ABC, AB = 12, BC =15, and Angle B = 60 degrees. Find the length of AC.
a) 3 61
b) 179
c) 199
d) 3 21
e) NOTA

March Regional Precalculus Test
10. Simplify:
sec 2 x  sin 2 x  cos2 x 
sin 2 x
tan x
 tan x 
cot x
sec 2 x
2
tan x
sec x  1
a)
b)
c) tan x
2
2tan x

11. Solve for x:

x sin 60   x cos60
0 2
a) 1,
1
3
1 1
b) ,
2 3
d) 1 cot x
e) NOTA
1
 sin1500
2
1
1
c) 1,
d) 1,
e) NOTA
2
3
0
 many points of intersection do r  4 and r  6cos have?
12. How
a) one
b) two
c) three
d) four
e) NOTA

13. Two cards are drawn from a standard deck (no jokers) without replacement. Find the

card are chosen.
probability that one red card and one black
1
25
13
26
a)
b)
c)
d)
e) NOTA
2
51
51
51
14. Find the equation of a plane normal to v = 6i – 3j + k and containing the
point (3, 2, -5).
a) 3x + 2y – 
5z = 7 b) 6x – 3y – z = 0 c) 6x – 3y + z = 7 d) 3x – 2y – 5z = 0 e) NOTA
15. Find the equations of all the asymptotes of :
7
1
, x  1, y 
2
2
7
8
d) x  , x  1, y 
2
7
a) x 
b) x  2, x  4, y 
e) NOTA
8
7
y
x 2  2x  8
2x 2  5x  7
c) x  2, x  4, y 
1
2

16. Find the cross product u  v  given the vectors u  4i  5 j  3k and v  7i  j  4k

a) 19
b) 5 51
c) 17i  5 j  31k
d) 17i  5 j  31k
e)NOTA
3 4
5 7

17. Given the following
matrices, A     B  
find the value of 2AB2 .
, 
2
6
2
1





14 34
138 132
118 286
472 1168
a) 
d) 
 b) 
 c) 

 e) NOTA
40 
208 
44
300 348 
148
592  796 



March Regional Precalculus Test
18. If the eccentricity of a conic is 2, then the conic is a
a) circle
b) ellipse c) hyperbola d) parabola
e) NOTA
19. There are 10 juniors and 6 seniors in Mu Alpha Theta chapter at Smith High. A
committee of 3 juniors and 3 seniors is being formed to organize the end of the year
party. How many committees can be formed?
a) 604800
b) 2400
c) 1560
d) 140
e) NOTA
20. Find the fourth term of 2x  6 .
a) 8640x 4
b)  8640x 4
c) 34560x 3
6

d)  34560x 3
e) NOTA
2
2
21. The area enclosed
 by the ellipse 16(x  3)  25(y  7)  400 is
a) 20
b) 21
c) 400
d) 1680
e) NOTA
22. Find the cube root of 64cis30 0 which lies in the third quadrant when it is graphed.

a) 4cis200 0
b) 4cis210 0
c) 4cis230 0
d) 4cis250 0
e) NOTA

23. What is the 
equation of the tangent to y  x 2  2x  1 at the point (2,1) in slope
intercept form?

a) y = 2x – 3
b) y = 2x
c) y = 0
d) y = x + 1
e) NOTA
24. What is

x 2  2x  3
6x 2 13x  7 ?
lim
x 
a)  3
b)
7
6
c)
1
6
d)
3
7
e) NOTA

25. Find the number of distinct permutations that can be made by the letters in the word
SEMINOLE.
 a) 40320
b) 20160
c) 5040
d) 2520
e) NOTA
x 6
2
26. Solve for x: 3 1 4  0

0 5 1
4
4
a)
b)
7
7


c)
48
19
d)
48
19
e) NOTA
March Regional Precalculus Test
27. A jar contains 5 black marbles and 7 white marbles. 4 marbles are drawn, one at a
time and without replacement. What is the probability that there will be exactly 2 of each
color?
7
14
14
7
a)
b)
c)
d)
e) NOTA
99
99
33
33
28. There are 33 students in Mr. Smith’s class. 25 students take Math, 21 take Science
and 18 take History. 8 students take all 3 classes, 4 take only Math, 5 take only Science
 History. Every student takes at least one of the three classes. How
and 1 takes only
many students take Math and Science only?
a) 2
b) 4
c) 6
d) 7
e) NOTA
29. In triangle XYZ, YZ = 18, X  120 0 , Y  45 0. Find the length of XZ.
a) 36 6
b) 18 2
c) 6 2
d) 6 6
e) NOTA
30. Find the number 
of positive integral divisors of 6732.
a) 72 b) 36 c) 18 d) 9 e) NOTA
