Algebra 2 Exam
Briarwood Math Tournament 2016
1) What is the sum of the terms in the infinite geometric sequence with first term 24
and common ratio 1/4?
a) 30
32
c) 36
d) 48
e) NOTA
2) Solve for x: log1248 - log12x = 2
a) ln(3)
b) 3
c) 1
d) 1/3
e) NOTA
3) If it takes three hours for Bill to paint a room, and 100 minutes for Brian to do the
same room, how many minutes will it take them to paint five rooms, working together?
a) 360 min.
a)350 min.
c)
2250
min.
7
d) 340 min.
e) NOTA
⎡ 3 0 ⎤
⎡ 1 0 ⎤
4) If A = ⎢
⎥ and ⎢
⎥ = AB, which of the following is a possible value of B?
⎣ 5 −2 ⎦
⎣ 0 1 ⎦
⎡
⎢
I. ⎢
⎢
⎢
⎣
⎤
1
0 ⎥
3
⎥
5
1 ⎥
− ⎥
6
2 ⎦
a) I only
⎡ −2 0 ⎤
II. ⎢
⎥
⎣ −5 3 ⎦
b) II only
⎡ −2 −5 ⎤
III. ⎢
⎥
3 ⎦
⎣ 0
c) III only
d) I and II only
e) NOTA
Algebra 2 Exam
Briarwood Math Tournament 2016
5) What is the fifth term of the arithmetic sequence whose first three terms are x - 3,
2x + 1, and x + 18?
a) x + 6.5
35
2
c)
91
2
d) 45
e) NOTA
10
6) Evaluate
∑ (−2i)
n
n=1
a) 246 - 182i
b) -820 - 410i
c) -1023 + 511i d) -1024 + 512i e) NOTA
7) Find the equation of a parabola with a focus at (-2,3) and directrix at y = -1.
a)
y = x 2 + 4x + 5
b)
c)
d)
1
y = (x + 2)2 + 1
8
1
y = (x + 2)2 + 1
2
1
y = (x − 2)2 − 1
2
e) NOTA
8) Two of the roots of the cubic equation with integer coefficients and leading
coefficient of 1 are 1 +3i and 4. What is the coefficient of the linear term of the
equation?
a) 40
b) 18
c) 2
d) -2
e) NOTA
9) Find the area of the region that satisfies the following inequalities:
(x + 3)2 + (y + 4)2 ≤ 36
x<0
a) 12p − 9 3
b) 6π
c) 4p + 3 2
d) 8p − 3 2
e) NOTA
Algebra 2 Exam
Briarwood Math Tournament 2016
10) When a complex number, z, is multiplied by the complex number on less than
itself, the result is equal to the cube of z subtracted by 3. What is the sum of all
possible values of z?
a) -6
11) If sin A =
a) −
b) -2
c) 0
e) NOTA
7
p
3p
, where < A <
, what is tan A?
25
2
2
7
24
b) −
24
7
12) Evaluate:
3 −1 2
−2 0 4
5 −3 −4
a) 25
b) 27
13.) Evaluate:
p
p
csc
3 +
2
2p
3p
cos
sin
3
2
tan
d) 1
c) −
24
25
c) 32
a) 1
b) 2 3 − 1
c) 2 3
d) 2 3 + 1
e) NOTA
24
25
e) NOTA
d) 36
e) NOTA
d)
Algebra 2 Exam
Briarwood Math Tournament 2016
14.) If event A occurs, the probability that event B also occurs is ⅖. If event A does
not occur, the probability that event B also does not occur is ⅓. If the probability that
either A or B (or both) occurs is ¾, what is the probability that both A and B occur?
a) 1/10
b) 3/40
c) 1/15
d) 1/20
e) NOTA
d) 16
e) NOTA
d) y = 0
e) NOTA
15.) Evaluate: log 8 81⋅ log 9 125 ⋅ log 25 16
a) 90
b) log16
c) 4
16.) Find the asymptotes for the following function.
f (x) =
a) y=0
x= 1, -1
x 2 + 5x + 6
(x + 3)(x 2 − 1)
b) x = -3, -2
c) y = 0
x = -3, 1, -1
17.) A group of friends splits the cost of a cabin at a ski resort evenly. If one fewer
person had come, the cost per person would have gone up by five dollars. If two
more people had come, the cost would have gone down four dollars. What was the
cost of the cabin, in dollars?
a) $10
b) $300
c) $2
d) $30
e) NOTA
Algebra 2 Exam
Briarwood Math Tournament 2016
18.) For what values of x, 0 deg rees ≤ x < 360 deg rees , does cot x = 1?
a) 450, 2250
b) 900, 2700
19.) Given that f (x) =
a)
8 − 3x
5x
b)
c) 1350, 3150
d) 00, 1800
e) NOTA
8
, what is f −1 (x)?
3 + 5x
3 + 5x
8
c)
8 − 3x
5x
d)
8x
3x + 5
e) NOTA
20.) For what values of x does x2 - 7x + 17 > 5 ?
a) x > - 4
b) x < -3 or x > 4
c) x < 3
d) x > 4 or x < 3
e) NOTA
21.) Solve for f: 2 f −416 f +4 = 8 3 f −3
a) −
3
2
b)
3
2
c)
21
4
7
3
e) NOTA
22.) If r = 4 is a solution to 6r − 7qr 3 + 11 = 5 , what is the value of q?
a) −
15
224
b)
15
224
c) −
5
16
d)
5
16
e) NOTA
Algebra 2 Exam
Briarwood Math Tournament 2016
23.) What is the minimum set of quadrants which contains the set of points satisfying
−3y − x < 5 and −3x < −4?
a) I
b) I, IV
c) I, II, IV
d) I, III, IV
e) NOTA
24.) Determine the absolute value of (4 − 3i)(5 + 2i).
a) 26 + 7i
b) 14 + 23i
c) 5 29
d)
33
d)
2
e) NOTA
25.) Solve for x: 4 3x+2 = 128
a) 0.5
b) - 1
c) 1
e) NOTA
TB1) Solve for x: log 3 (log 8 (log 6 x)) = −1
TB2) Determine the center of the conic section with equation
4x 2 + y 2 − 24x + 6y + 9 = 0 .
TB3) Two dice are rolled behind a screen. A friend of yours looks at the dice and tells
you (honestly) that there are no sixes. What is the probability there is at least one
five?
Algebra 2 Exam
Briarwood Math Tournament 2016
ANSWER SHEET:
QUESTION
ANSWER
QUESTION
ANSWER
1
B
21
C
2
D
22
B
3
C
23
B
4
A
24
C
5
C
25
A
6
B
TB1
36
7
B
TB2
( 3, -3 )
8
B
TB3
9
25
9
E
24p + 9 3
10
D
11
A
12
D
13
E
−2 3 − 1
14
A
15
C
16
A
17
D
18
A
19
A
20
D
Algebra 2 Exam
Briarwood Math Tournament 2016