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). [...]... acute or obtuse 11 The correct answer is (cot θ) ARCO ■ SAT II Math www.petersons.com/arco 13 2 Part IV 12 The correct answer is 13 The correct answer is 14 The correct answer is Square both sides www.petersons.com/arco ARCO ■ SAT II Math Math Practice Exercises and Solutions by Topic 13 3 15 The correct answer is (15 ) 16 The correct answer is (cot 28°) cot x is positive in Quadrant III, so that cot... The correct answer is ARCO ■ SAT II Math 6 3 www.petersons.com/arco 13 0 Part IV 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° www.petersons.com/arco ARCO ■ SAT II Math Math Practice Exercises and Solutions by Topic 13 1 9 The correct answer is (B) cos A 10 The correct answer is (A)... www.petersons.com/arco 12 6 Part IV 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 www.petersons.com/arco ARCO ■ SAT II Math Math Practice Exercises and Solutions by Topic 12 7 15 The correct answer is (10 8°) 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... 2) 18 0° = 72 0° Divide by 18 0 The second polygon has 6 + 2 = 8 sides Sum of the measures of its interior angles = 18 0(8 – 2) = 18 0(6) = 10 80° 11 TRIGONOMETRY 1 The correct answer is (C) www.petersons.com/arco ARCO ■ SAT II Math Math Practice Exercises and Solutions by Topic 12 9 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.. .Math Practice Exercises and Solutions by Topic 8 The correct answer is 12 5 Let radius of circle be 1 Side of square is 1 + 1 =2 9 The correct answer is (13 0º) From noon to 4:00 PM., the hour hand has moved from 12 to 4: minutes it moves of the distance from 4:00 to 5:00: of 360º = 12 0º In the next 20 of 30º = 10 º 12 0º + 10 º = 13 0º 10 The correct answer is (12 5) ARCO ■ SAT II Math www.petersons.com/arco... (208° - 18 0°) = 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 ARCO ■ SAT II Math www.petersons.com/arco 13 4 Part IV 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... the circle in 4 points ARCO ■ SAT II Math www.petersons.com/arco 12 8 Part IV 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 (10 80°) The sum of the interior... 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... 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 www.petersons.com/arco ARCO ■ SAT II Math . of 30º = 10 º. 12 0º + 10 º = 13 0º 10 . The correct answer is (12 5). 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. Solutions by Topic 12 3 ARCO ■ SAT II Math www.petersons.com/arco 4. The correct answer is (240). 5. The correct answer is (15 0). Part IV124 www.petersons.com/arco ARCO ■ SAT II Math 6. The correct. answer is (3). 14 . The correct answer is . Cross-multiply. Math Practice Exercises and Solutions by Topic 12 7 ARCO ■ SAT II Math www.petersons.com/arco 15 . The correct answer is (10 8°). 16 . The correct