1. ( ) ÷ 1 = (A) 1818 (B) 1414 (C) 4 15 (D) 1212 (E) ( ) ÷ 1 = ÷ 1 = = ( ) ÷ 1 = ÷ 1 = = SAT

2.x 2 – 2 x when x = – 2 ? (A)– 8 (B)– 4 (C) 0 (D) 4 (E) 8 x 2 – 2 x when x = – 2 ? (– 2 ) 2 – 2 (– 2 ) = = 8 x 2 – 2 x when x = – 2 ? (– 2 ) 2 – 2 (– 2 ) = = 8SAT

3. Kate read 96 pages in 2 hours and 40 minutes. What was Kate’s average rate of pages per hour? (A)24 (B)30 (C)36 (D)42 (E)48 x = x = x = x = 6 6 = 36 x = x = x = x = 6 6 = 36SAT

4.For how many integer values of x will 7/8 be greater than ¼ and less than 1/3 ? (A)6 (B)7 (C)12 (D)28 (E)Infinite many 1 > 7 > 1 3 x 4 ( 1 > 7 > 1 ) 12 x 3 x 4 4 x > 84 > 3 x _______________________________________________________________________________________ 4 (22) > 84 > 3 (22) > 84 > 66 4 (23) > 84 > 3 (23) > 84 > 69 4 (24) > 84 > 3 (24) > 84 > 72 4 (25) > 84 > 3 (25) > 84 > 75 4 (26) > 84 > 3 (26) > 84 > 78 4 (27) > 84 > 3 (27) > 84 > 81 1 > 7 > 1 3 x 4 ( 1 > 7 > 1 ) 12 x 3 x 4 4 x > 84 > 3 x _______________________________________________________________________________________ 4 (22) > 84 > 3 (22) > 84 > 66 4 (23) > 84 > 3 (23) > 84 > 69 4 (24) > 84 > 3 (24) > 84 > 72 4 (25) > 84 > 3 (25) > 84 > 75 4 (26) > 84 > 3 (26) > 84 > 78 4 (27) > 84 > 3 (27) > 84 > 81SAT

5.What is the average (arithmetic mean) of 2 x + 5, 5 x – 6, – 4 x + 2 ? (A) x (B)x + 1 (C) 3 x (D)3 x + 3 (E) 3 x x x – 6 – 4 x x x + 1 = x x x – 6 – 4 x x x + 1 = x SAT

7.In this triangle, what is the degree measure of angle B ? (A)45 (B)60 (C)65 (D)75 (E)80 < B + < C + < A = 180⁰ < B + 45⁰ + 70⁰ = 180⁰ < B + 115⁰ = 180⁰ < B = 180⁰ – 115⁰ = 65⁰ < B + < C + < A = 180⁰ < B + 45⁰ + 70⁰ = 180⁰ < B + 115⁰ = 180⁰ < B = 180⁰ – 115⁰ = 65⁰SAT 45⁰ B C A 70⁰

8. For all x ≠ 0, x 2 + x 2 + x 2 = x 2 (A)3 (B)3 x (C) x2x2 (D) x3x3 (E) x4x4 x 2 + x 2 + x 2 = x 2 3 x 2 = 3 x 2 x 2 + x 2 + x 2 = x 2 3 x 2 = 3 x 2SAT

8. For all x ≠ 0, x 2 + x 2 + x 2 = x 2 (A)3 (B)3 x (C) x2x2 (D) x3x3 (E) x4x4 x 2 + x 2 + x 2 = x 2 3 x 2 = 3 x 2 x 2 + x 2 + x 2 = x 2 3 x 2 = 3 x 2SAT

9.The equation x 2 = 5x – 4 has how many distinct real solutions ? (A)0 (B)1 (C)2 (D)3 (E)Infinitely many x 2 = 5 x – 4 x 2 – 5 x + 4 = 0 ( x – 4 ) ( x – 1 ) = 0 x = 4 or 1 x 2 = 5 x – 4 x 2 – 5 x + 4 = 0 ( x – 4 ) ( x – 1 ) = 0 x = 4 or 1SAT

10. Which of the following sets of numbers has the property that the sum of any two numbers in the set is also a number in the set ? I.The set of even integers II.The set of odd integers III.The set of prime numbers (A)I only (B)III only (C)I and II only (D)I and III only (E)I, II, and III = 4 Ex where odd integers doesn’t work = 8 Ex where prime doesn’t work = 6 Even Integers does work = 4 Ex where odd integers doesn’t work = 8 Ex where prime doesn’t work = 6 Even Integers does workSAT

11. Bob’s average (arithmetic mean) score after 4 tests is 89. What score on the 5 th test would bring Bob’s average up to exactly 90? (A)90 (B)91 (C)92 (D)93 (E)94 89 x 4 = x 5 = 450 So, the difference between the 2 gives us the total needed to average – 356 = x 4 = x 5 = 450 So, the difference between the 2 gives us the total needed to average – 356 = 94SAT

12. The price s of a sweater is reduced by 25% for a sale. After the sale, the reduced price is increased by 20%. Which of the following represents the final priceo f the sweater ? (A)1.05 s (B).95 s (C).90 s (D).85 s (E).80 s Sale price is 25 % off or.75 s Post sale price is increased by 20 % The increase =.75 s x.2 =.15 s Then we add.75 s +.15 s = 90 s Sale price is 25 % off or.75 s Post sale price is increased by 20 % The increase =.75 s x.2 =.15 s Then we add.75 s +.15 s = 90 sSAT

13. How many distinct prime factors does the number 36 have ? (A)2 (B)3 (C)4 (D)5 (E) x 18 2 x 3 x 6 2 x 3 x 2 x x 18 2 x 3 x 6 2 x 3 x 2 x 3SAT

15. If the area of a triangle is 36 and its base is 9, what is the length of the altitude to that base? (A)2 (B)4 (C)6 (D)8 (E)12 A T = 1 hb = h (9) = 36 2 h (9) = 36 2 h = h = 8 A T = 1 hb = h (9) = 36 2 h (9) = 36 2 h = h = 8SAT

15. Let a  be defined for all positive integers a by the equation a  = a – a If x  = 3, what is the value of x ? 4 6 (A)18 (B)28 (C)36 (D)40 (E)54 If a  = a – a 4 6  x  = x – x 4 6 If x  = 3  3 = x – x (3 = x – x ) = 3 x – 2 x 36 = x If a  = a – a 4 6  x  = x – x 4 6 If x  = 3  3 = x – x (3 = x – x ) = 3 x – 2 x 36 = xSAT

16. Betty has q quarters, d dimes, n nickels and no other coins in her pocket. Which of the following represents the total number of coins in Joan’s pocket ? (A)q + d + n (B)5q + 2d + n (C).25q +.10d +.05n (D)( ) (q + d + n ) (E)25q + 10d + 5n This is a “TRAP” question: The problem only asks for the total # of coins, NOT the total value of coins, which is what you are lead to think. This is a “TRAP” question: The problem only asks for the total # of coins, NOT the total value of coins, which is what you are lead to think.SAT

17.Which of the following is an equation for the graph above ? (A)y = –2 x + 1 (B)y = x + 1 (C)y = x + 2 (D)y = 2 x + 1 (E)y = 2 x + 2 The slope is 2 and the y-intercept is 2, so the answer is y = 2 x + 2 SAT

18. If an integer is divisible by 6 and 9, then the integer must be divisible by which of the following ? I.12 II.18 III.36 (A)I only (B)II only (C)I and II only (D)II and III only (E)I, II, and III Prime factors of 6 are 2 x 3, so any # divisible should have at least one 2 and one 3 as factors Prime factors of 9 are 3 x 3, so any # divisible should have at least two 3’s as factors  Any # divisible by both should have at least one 2 and two 3’s and the first possibility is 2 x 3 2 or and 36 require two 2’s in its prime factorization  12 doesn’t have a 2 nd prime factor of 3 36 does work in some cases by NOT all, such as the most obvious one, 6 x 9 or 54. Prime factors of 6 are 2 x 3, so any # divisible should have at least one 2 and one 3 as factors Prime factors of 9 are 3 x 3, so any # divisible should have at least two 3’s as factors  Any # divisible by both should have at least one 2 and two 3’s and the first possibility is 2 x 3 2 or and 36 require two 2’s in its prime factorization  12 doesn’t have a 2 nd prime factor of 3 36 does work in some cases by NOT all, such as the most obvious one, 6 x 9 or 54.SAT

19. In this figure, O is the center of the circle and P, O, and Q are collinear. If < ROQ measures 50⁰, what is the degree measure of <RPQ ? (A)20 (B)25 (C)30 (D)35 (E)40 < POR =180⁰ – 50 ⁰ = 130 ⁰ PO = OR (all radii are =) < RPQ = <PRO (base <‘s of Isosceles are =) and < QPR + <PRO = 50 ⁰  < RPQ =25 < POR =180⁰ – 50 ⁰ = 130 ⁰ PO = OR (all radii are =) < RPQ = <PRO (base <‘s of Isosceles are =) and < QPR + <PRO = 50 ⁰  < RPQ =25SATQ O P R 50⁰ ?

20. A wooden cube with volume 64 is sliced in half horizontally,. The two halves are then glued together to form a rectangle solid which is not a cube. What is the surface area of this new solid? (A)128 (B)112 (C)96 (D)56 (E)48 E 3 = 4 x 4 x 4 = 64 Two rectangle solids 4 x 4 x 2, when glued 2 x 4 x 8 Then Top and Bottom = 8 x 4 = 32 or 64 total Then Front and Back = 8 x 2 = 16 or 32 total Then two sides = 4 x 2 = 8 or 16 total E 3 = 4 x 4 x 4 = 64 Two rectangle solids 4 x 4 x 2, when glued 2 x 4 x 8 Then Top and Bottom = 8 x 4 = 32 or 64 total Then Front and Back = 8 x 2 = 16 or 32 total Then two sides = 4 x 2 = 8 or 16 totalSAT 64 E 3 = 4 x 4 x 4 = Grand total of 6 sides = = 112

21. A drawer contains 6 blue socks, 12 black socks and 15 white socks. If one sock is chosen at random, what is the probability that it will be black? (A) 1414 (B) 1313 (C) 3838 (D) 1212 (E) blue 12 black 15 white 32 Total Black 12 = 3 Total blue 12 black 15 white 32 Total Black 12 = 3 Total 32 8SAT

22. Danielle drives from here home to the store at an average speed of 40 miles per hour. She returns home along the same route at an average speed of 60 miles per hour. What is her average speed, in miles per hour, for her entire trip ? (A)45 (B)48 (C)50 (D)52 (E)55 This is a TRAP question ! We are NOT given enough information to use a distance formula. So we need to improvise by selecting a distance that is easy to work with. Since we have speeds of 40 and 60 mph, why not use a multiple of both, such as, 120 Distance = rate x time (going trip) 120 = 40 t where t = 3 hours (return trip) 120 = 60 t where t = 2 hours Now 240 = 5 r, where r = 48 miles per hour This is a TRAP question ! We are NOT given enough information to use a distance formula. So we need to improvise by selecting a distance that is easy to work with. Since we have speeds of 40 and 60 mph, why not use a multiple of both, such as, 120 Distance = rate x time (going trip) 120 = 40 t where t = 3 hours (return trip) 120 = 60 t where t = 2 hours Now 240 = 5 r, where r = 48 miles per hourSAT

23. What is the area of a right triangle if the length of one leg is a and the length of the hypotenuse is c ? (A) ac 2 (B) ac – a 2 2 (C) a 3 + c 3 2 (D)a c 2 – a 2 2 (E) a 2 + c 2 c 2 = a 2 + b 2 c 2 – a 2 = b 2 √ c 2 – a 2 = b A T = ½ h b A = 1 a ( √ c 2 – a 2 ) 2 c 2 = a 2 + b 2 c 2 – a 2 = b 2 √ c 2 – a 2 = b A T = ½ h b A = 1 a ( √ c 2 – a 2 ) 2SAT c2c2c2c2 b2b2b2b2 a2a2a2a2

24. In ∆ PRS, RT is the altitude to side PS and QS is the altitude to side PR. If RT = 7, PR – 8 and QS = 9, what is the length of PS ? (A) (B) (C) 7 8 (D) (E) A T = ½ h b Using altitude QS and side PR = ½ 9 8 = 36 Using altitude RT with side PS = ½ 7 PS = 36 7 PS = 36 then, PS = 36 2 = A T = ½ h b Using altitude QS and side PR = ½ 9 8 = 36 Using altitude RT with side PS = ½ 7 PS = 36 7 PS = 36 then, PS = 36 2 = SATP Q R ST

25. There are 3 routes from River City to Bayville. There are 4 routes from Bayville to Eagles Mere. There are 3 routes from Eagles Mere to Twin Peaks. If a driver must pass through Bayville, and Eagles Mere exactly once, how many possible ways are there to go from River City to Twin Peaks. (A)6 (B)10 (C)12 (D)24 (E)36 River City [ 3 ] x Bayville [ 4 ] x Eagles Mere [ 3 ] = Twin Peaks [ 36 ] River City [ 3 ] x Bayville [ 4 ] x Eagles Mere [ 3 ] = Twin Peaks [ 36 ]SAT