SAT II Math Episode 1 Part 7 pot

Math Practice Exercises and Solutions by Topic 115
ARCO ■ SAT II Math www.petersons.com/arco
2. The correct answer is (A).
log
b
x = 1+c
b
1+c
= x
3. The correct answer is (D). log 2xy = log 2 + log x + log y
4. The correct answer is (C). From the graph, 2
0
= 1, 2
1
= 2, 2
2
= 4 and 2
3
= 8 where y is the
exponent and x is the power of 2.
Thus, 2
y
= x or y = log
2
x
5. The correct answer is (4 and 5). Let log
3
92

= x, then 3
x

= 92.
Since 3
4
= 81 and 3
5
= 243, x is between 4 and 5
6. The correct answer is (D). P = K10
-xt
7. The correct answer is (B). If log
r
6 = S, log
r
3 = T, then
7. EQUATIONSQUADRATIC AND RADICAL
1. The correct answer is (9). x
2
+ 6x + c = 0
2. The correct answer is (3).
Part IV116
www.petersons.com/arco ARCO ■ SAT II Math
3. The correct answer is .
4. The correct answer is (4).
5. The correct answer is (3).
Check both values in original equation.
x = 3 is the only root
Math Practice Exercises and Solutions by Topic 117
ARCO ■ SAT II Math www.petersons.com/arco
6. The correct answer is (0). x
2
+ y

2
= 4 graphs as a circle of radius 2 with center at the origin.
y = 4 graphs as a horizontal line 4 units above the x-axis.
There are no intersections.
7. The correct answer is
.
6r – s = 10 or s = 6r –10
Substitute this value of s in original equation.
8. The correct answer is .
Part IV118
www.petersons.com/arco ARCO ■ SAT II Math
9. The correct answer is ( ).
Substitute a = 1, b = –6, c = 7.
10. The correct answer is (8,4). x + y = 12 or y = 12 – x
x
2
+ y
2
= 80
Substitute y = 12 – x.
8. INEQUALITIES
1. The correct answer is (x > 3).
Math Practice Exercises and Solutions by Topic 119
ARCO ■ SAT II Math www.petersons.com/arco
2. The correct answer is .
3. The correct answer is .
When q = 90°,
When q = 180°, x =10
When 90° <q<180° ,
< x<10

4. The correct answer is (D).
5. The correct answer is (p < –3).
6. The correct answer is (D).
If x > y, in (A), (B), and (C), we are adding, dividing, and subtracting z from both sides of the
inequality; none of these operations affects the inequality when z is a positive number. In (E),
since x > y and they are both positive numbers,
must be greater than 1. In (D), we wrote the
reciprocal of the two fractions in (B), and this changes the inequality.
Part IV120
www.petersons.com/arco ARCO ■ SAT II Math
7. The correct answer is (B).
Since t > 0, y > x
8. The correct answer is (A).
(B), (C), (D), and (E) all show increases as t increases when t > 1. In (A), t is in the denomina-
tor, and
decreases as t increases beyond 1.
9. VERBAL PROBLEMS
1. The correct answer is (20). Let x = no. of liters of water to be evaporated.
2. The correct answer is (24). Let x = no. of hours to fill the tank.
3. The correct answer is .
r mph (r + 155)mph
5r mi 0 5(r + 15)mi
Math Practice Exercises and Solutions by Topic 121
ARCO ■ SAT II Math www.petersons.com/arco
4The correct answer is (46). Let t = ten’s digit of original number
u = unit’s digit of original number
10t + u = original number
10u + t = number with reversed digits
t + u = 10
(from the given information)

The original number is 46.
5. The correct answer is (53,55).

6. The correct answer is ($4000 at 5%, $8000 at 7%).
Let x = amount invested at 5%
y = 2x = amount invested at 7%
Part IV122
www.petersons.com/arco ARCO ■ SAT II Math
10. GEOMETRY
1. The correct answer is (35º).
Let PT be a diameter of Circle O.
2. The correct answer is (36º). Let 2x = smallest angle in degrees, 3x and 5x = other two angles
in degrees.
3. The correct answer is (120º).
m (alernate interior angles), and m
Angle x is an exterior angle of ∆DEF and is
equal to the sum of the measures of the two remote interior angles.
x= 50º + 70º = 120º
Math Practice Exercises and Solutions by Topic 123
ARCO ■ SAT II Math www.petersons.com/arco
4. The correct answer is (240).
5. The correct answer is (150).
Part IV124
www.petersons.com/arco ARCO ■ SAT II Math
6. The correct answer is (24).
The tangent is perpendicular to the radius
at the point of tangency.
In right triangle OTP
7. The correct answer is (96 - 16π).
Math Practice Exercises and Solutions by Topic 125

ARCO ■ SAT II Math www.petersons.com/arco
8. The correct answer is .
Let radius of circle be 1.
Side of square is 1 + 1 =2.
9. The correct answer is (130º).
From noon to 4:00
PM., the hour hand has moved from 12 to 4: of 360º = 120º. In the next 20
minutes it moves
of the distance from 4:00 to 5:00: of 30º = 10º.
120º + 10º = 130º
10. The correct answer is (125).
Part IV126
www.petersons.com/arco ARCO ■ SAT II Math
11. The correct answer is (6).
12. The correct answer is (56).
13. The correct answer is (3).
14. The correct answer is .
Cross-multiply.
Math Practice Exercises and Solutions by Topic 127
ARCO ■ SAT II Math www.petersons.com/arco
15. The correct answer is (108°).
16. The correct answer is (2).
The locus of points 10 ft. from T is a
circle of radius 10. The locus of points
12 ft from F consists of two parallel
lines 12 ft from F on each side. The
circle and one parallel line intersect in
two points.
17. The correct answer is (C). The only statement that has the same truth value as the given statement is
the contrapositive of the original statement. This is the converse of the inverse of the original statement.

18. The correct answer is (4).
The locus of points 4 units from P is a circle
of radius 4 with center at P. The locus
of points 3 units from the given line consists
of two parallel lines 3 units from the
line. The two parallel lines intersect the
circle in 4 points.
Part IV128
www.petersons.com/arco ARCO ■ SAT II Math
19. The correct answer is (1).
The locus of points 8 cm from P consists
of two planes parallel to P and 8 cm from
it. The locus of points 12 cm from Q is a
sphere of radius 12 and center at Q. The
sphere intersects one of the parallel planes
in one point (point of tangency).
20. The correct answer is (1080°). The sum of the interior angles of an n-sided polygon is (n – 2) 180°
= 720°. Divide by 180.
The second polygon has 6 + 2 = 8 sides.
Sum of the measures of its interior angles = 180(8 – 2)
= 180(6) = 1080°
11. TRIGONOMETRY
1. The correct answer is (C).
Math Practice Exercises and Solutions by Topic 129
ARCO ■ SAT II Math www.petersons.com/arco
2. The correct answer is (2). cos x(cos x – 2) = 0
3. The correct answer is (I and III). Curves intersect in Quadrants I and III.
4. The correct answer is . Let x = arc tan .

tan

sin
x
x
=
=⋅=
2
2
2
3
3
6
3
5. The correct answer is .
Part IV130
www.petersons.com/arco ARCO ■ SAT II Math
6. The correct answer is .
7. The correct answer is (90°, 210°, 330°).
8. The correct answer is (1). Let x = arc sin 1, y = arc cos 1.
sin x = 1, x = 90°
cos y = 1, y = 0°
Math Practice Exercises and Solutions by Topic 131
ARCO ■ SAT II Math www.petersons.com/arco
9. The correct answer is (B).
cos A
10. The correct answer is (A). Use the law of sines to find angle B.
Thus B may be acute or obtuse.
11. The correct answer is (cot
θθ
θθ
θ

).
Part IV132
www.petersons.com/arco ARCO ■ SAT II Math
12. The correct answer is .
13. The correct answer is .
14. The correct answer is .
Square both sides.
Math Practice Exercises and Solutions by Topic 133
ARCO ■ SAT II Math www.petersons.com/arco
15. The correct answer is (15).
16. The correct answer is (cot 28°). cot x is positive in Quadrant III, so that cot 208° is positive.
cot 208° = cot (208° - 180°) = cot 28°
17. The correct answer is (2).
Graph y = 2 sin x and y = cos 2x on same set of axes in interval -π ≤ x ≤π. Graph shows 2 values.
18. The correct answer is
.
Part IV134
www.petersons.com/arco ARCO ■ SAT II Math
19. The correct answer is (B). Use law of sines.
B may have two values, one acute or one obtuse. Also, since a < b, two triangles may be constructed.
20. The correct answer is
12. GRAPHS AND COORDINATE GEOMETRY
1. The correct answer is (20).
In
∆∆
∆∆
∆PQR, use QR = 8 as base and PH = 5 as altitude.