Download Algebra II/Trig Keeping in Shape

Algebra II/Trig
Keeping in Shape- Quarter 3
If you are finished early with the class work at any point during the quarter, you may work on any of the following
questions in this packet. These questions are from the SAT exam and the SAT II exams. Some questions are
review from previous courses and some are from our current material. You may not know how to answer every
question because this covers all content from the first 3 quarters and what we may not have learned it yet. At the
end of the marking period you have the option of handing this packet in as an extra assignment to improve your
average.
SAT Questions:
1) If a and b are positive integers and 9(3a )  3b , what is a in terms of b?
A. b – 2
B. b – 1
C. b
D. b + 1
E. b + 2
2) If the function f is defined by f ( x) 
x6
, for what values of x does f(x) = 20 ?
3
3) If a-2 = 4, which of the following could be the value of a?
A. – 2
B. – ¼
C. 0
D. ¼
E. ½
4) Since the beginning of 1990, the number of squirrels in a certain wooded area has tripled during
every 3-year period of time. If there were 5,400 squirrels in the wooded area at the beginning of
1999, how many squirrels were in the wooded area at the beginning of 1990?
5) If the function f is defined by f(x) = 3x + 4, then 2f(x) + 4 =
A. 5x + 4
B. 5x + 8
C. 6x + 4
D. 6x + 8
E. 6x + 12
6) The price of a certain item was $10 in 1990 and it has gone up by $2 per year since 1990. If this
trend continues, in what year will the price by $100?
7) Let the function f be defined by f(x) = 5x – 2a, then a is a constant. If f(10) + f(5) = 55, what is
the value of a?
A. – 5
B. 0
C. 5
D. 10
E. 20
8) The first of three numbers is 3 times the second number. The third number is 30 more than the
second number. If the third number is represented by t and the sum of the first and second
numbers is 180, which of the following equations could be used to find the value of t?
A. 3t + t = 180
B. 3t + (t – 30) = 180
C. 3(t – 30) + t = 180
D. 3(t – 30) + (t – 30) = 180
E. 3(t – 30) + (t – 30) + t = 180
2
9) If x 3  y , what does x4 equal in terms of y?
A. y2
B.
C.
D.
E.
y
8
3
y3
y5
y6
10) If 5k-2 + 52 = 50, what is the value of k?
A. 2
B. 4
C. 5
D. 10
E. 2
11) For all m and n, (3m + n)(m2 – n) = ?
A. 3m3 + 2m2 – 2n
B. m3 – 2n2
C. 2m2 – n – n2
D. 3m2 + 3mn – 2n2
E. 3m3 – 3mn + m2n – n2
12) A proofreader can read 40 pages in one hour. How many pages can this proofreader in 90
minutes?
A. 45
B. 60
C. 150
D. 360
E. 940
13) If 3 < 3t – 6 < 18, which of the following must be true?
1)
2)
3)
4)
5)
Y=5
5<t<6
4<t+1<9
12 < 3t < 24
t < 3 of t > 8
14) If x and y are real numbers and the square of y is equal to the square root of x, which of the
following must be true?
I.
x = y4
x0
II.
III.
y0
A.
B.
C.
D.
E.
I only
I and II only
I and III only
II and III only
I, II, and III
15)
(A)
(B)
(C)
(D)
(E)
16) In a + bi form, the multiplicative inverse of 2 + 6i is
(A)
(B)
(C)
(D)
(E)
17) If 5 and – 1 are both zeros of the polynomial P(x), then a factor of P(x) is
(A)
(B)
(C)
(D)
(E)
18) A positive rational root of the equation
is
(A)
(B)
(C)
(D)
(E)
19) The sum of the roots of
(A)
(B)
(C)
(D)
(E)
is
20) If the two solutions of
possible values of c?
are imaginary, which of the following describes all
(A)
(B)
(C)
(D)
(E)
SAT MATH SUBJECT TEST - LEVEL 1 QUESTIONS:
21) If b2x+1 = b3x-1 for all values of b, what is the value of x?
A. 2
B. 3/2
C. 2/3
D. – 2
E. – 3
22) If y = x3 – 1.5, for what value of x is y = 2 ?
A. 0.79
B. 1.14
C. 1.52
D. 1.87
E. 6.50
23) In triangle PQR, <Q is a right angle. Which of the following is equal to cos P ?
A.
PQ
PR
B.
PR
PQ
C.
PR
QR
D.
QR
PQ
E.
QR
PR
24) If angle A is an acute angle and
A.
B.
C.
D.
E.
sin 2 A
 2.468 , what is the value of tan A?
cos 2 A
1.234
1.571
2.468
4.936
6.091
25) If the cube root of the square root of a number is 2, what is the number?
A. 16
B. 32
C. 36
D. 64
E. 256
26) (sin 2   cos 2   3) 4 
A. 256
B. 81
C. 64
D. 32
E. 16
27) At the end of 1990, the population of a certain town was 6,250. If the population increases at the
rate of 3.5 percent each year, what will the population of the town be at the end of 2005?
A. 9,530
B. 9.740
C. 9,950
D. 10,260
E. 10,470
28) If logax2 = 5, what is the value of logax?
A. 5/2
B. 7
C. 10
D. 25
E. 32
SAT MATH SUBJECT TEST - LEVEL 2 QUESTIONS:
29) If A is the degree measure of an acute angle and sin A = 0.8, then cos (90 – A) =
A. 0.2
B. 0.4
C. 0.5
D. 0.6
E. 0.8
30) The relationship between a reading C on the Celsius temperature scale and a reading F on the
5
Fahrenheit temperature scale is C  ( F  32) and the relationship between a reading on the
9
Celsius temperature scale a reading K on the Kelvin temperature scale is K  C  273 . Which of
the following expresses the relationship between readings on the Kelvin and Fahrenheit
temperature scales?
5
A. K  ( F  24)
9
5
B. K  ( F  305)
9
5
C. K  ( F  32)  273
9
5
D. K  ( F  32)  273
9
5
E. K  ( F  32)  273
9
31) The graph of the rational function f, where f ( x) 
A.
B.
C.
D.
E.
0 only
4 only
5 only
0 and 4 only
0, 4, and 5
32) If cos x = 0.4697, then sec x =
A. 2.1290
B. 2.0452
C. 1.0818
D. 0.9243
E. 0.4890
5
, has a vertical asymptote at x =
x  8 x  16
2
33) To the nearest degree, what is the measure of the smallest angle in a right triangle with sides of
lengths 3, 4, and 5?
A. 27o
B. 30o
C. 37o
D. 45o
E. 53o
34) The formula A = Pe0.08t gives the amount A that a savings account will be worth after an initial
investment P is compounded continuously at an annual rate of 8 percent for t years. Under these
conditions, how many years will it take an initial investment of $1,000 to be worth approximately
$5,000?
A. 4.1
B. 5.0
C. 8.7
D. 20.1
E. 23.0
35) If sin θ > 0 and sin θcos θ < 0, then θ must be in which quadrant?
A. I
B. II
C. III
D. IV
E. There is no quadrant in which both conditions are true.
36) If 0  x 
A.
B.
C.
D.
E.

2
and sin x = 3 cos x, what is the value of x?
0.322
0.333
0.340
1.231
1.249
37) If loga3 = x and loga5 = y, then loga 45 =
A. 2x + y
B. x2 + y
C. x2y
D. x + y
E. 9x + y
38) Where defined, csc(2θ)sin(2θ) =
A. 1
B. 0
C. – 1
D. 2 csc(4θ)
E. 2 sec(4θ)
39) If (6.31)m = (3.02)n , what is the value of
A.
B.
C.
D.
E.
m
?
n
-0.32
0.32
0.48
0.60
1.67
40) If ln(x) = 1.25, then ln(3x) =
A. 1.10
B. 1.37
C. 1.73
D. 2.35
E. 3.75
41) During a thunderstorm, the distance between a person and the storm varies directly as the time
interval between the person seeing the flash of lighting and hearing the sound of thunder. When a
storm is 4,000 feet away, the time interval between the person seeing the lightning flash and
hearing the thunder is 3.7 seconds. How far away from the person is the storm when this time
interval is 5 seconds?
A. 2,960 feet
B. 4,650 feet
C. 5,405 feet
D. 6,284 feet
E. 7,304 feet
42) If x = 3/2 is a solution to the equation 5(4x – k)(x – 1) = 0, what is the value of k?
A. 2/3
B. 1
C. 4
D. 5
E. 6
43) A sum of $10,000 is invested at a rate of 10 percent, with interest compounded semiannually. The
value, in dollars, of this investment after t years is given by V(t) = 10,000(1.05)2t . Approximately
how much greater is the value of this investment at the end of 2 years than the same amount
nt
r

invested at the rate of 10 percent compounded annually? [Hint: Use the formula A  P1   ]
 n
A. $55
B. $200
C. $500
D. $1,075
E. $1,155
x

44) If cos   , where 0    and 0 < x < 3, then sin θ =
3
2
A.
9  x2
3
B.
x2  9
x
C.
9  x2
x
D.
3  x2
3
E.
3  x2
x
45) If ( )
( )
(A)
(B)
(C)
(D)
(E)
46) When a certain radioactive element decays, the amount of any time t can be calculated using the
function ( )
, where a is the original amount and t is the elapsed time in years. How
many years would it take for an initial amount of 250 milligrams of this element to decay to 100
milligrams?
(A)
(B)
(C)
(D)
(E)