Summer Form A1. ,andreduce completely. Whatis. x + y 12 ) e) 1 2

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1 Texas A&M University Summer 2006 Mathematics Placement Exam Form A1 1. Consider the line passing through the points (5, 10) and (8, 19). Which of the following points also lies on the line? a) (4, 9) b) ( 1, 1) c) (10, 25) d) (25, 10) e) (5, 11) 2. Soap powder is packed in cube-shaped cartons. One such carton measures 8 cm on each side. The company manufacturing these cartons decides to increase the length of each edge of the carton by 15 percent. How much does the volume increase? a) (9.2) b) (8.15) c) 3(9.2) 2 3(8) 2 d) 3(8.15) 2 3(8) 2 3. Perform the indicated operation: the numerator of the result? a) x + yz b) 11yz +48x c) 59xyz d) Given log b 5= 1,thenlog 4 b 25 = a) 2 4 b) log 5 25 c) 2 d) 5 e) Find all solutions to the equation x 2 e x 2xe x 3e x =0. a) x =0,x =3,x = 1 b) x =3,x = 1 c) x = 3, x =1 d) x =0,x = 3, x =1 e) x = 3 ( 11 4 x + y 12 ),andreduce completely. Whatis z

2 6. The number of bacteria in a colony is growing exponentially. At 1:00 pm, the number of bacteria was 1800 and at 5:00 pm the number of bacteria was Which of the following expressions gives the number of bacteria at time t, wheret is measured in hours after 1:00 pm? a) N(t) = 36000(20) t 4 b) N(t) = 36000(2) t 4 c) N(t) = 1800(20) t 4 d) N(t) = 1800(2) t 2 e) N(t) = 1800(20) t 2 7. If f(x) =5x 2 + 7, find and simplify a) 5a +10h b) 5h +20a c) 15h +10a d) 10a +5h e) 5h +5a f(a + h) f(a),whereh 0. h 8. Find all x - intercepts of the polynomial p(x) = 8x 4 x 3 +9x 2. a) x =0,x = 9 8, x =1 b) x =0,x = 9 8, x = 1 c) x = 1 8, x =9 d) x =0,x = 1 8, x =9 e) x = 1 8, x = 9 9. Factor the following expression completely: 3x 3 (3x 7) 2 + x 4 (8)(3x 7)(3). a) 24x 3 (3x 7)(11x 15) b) 3x 3 (3x 7)( 5x 15) c) x 3 (3x 7)(11x 7) d) 8x 3 (3x 7)(6x 15) e) 3x 3 (3x 7)(11x 7) 10. Which of the following is equal to a) e 6 b) e 5 e +1 e 6 c) e +1 e 3 d) e +1 e) e e 3 e 1 + e 2?

3 11. Find the domain of f(x) = a) (3, 5) b) (3, 5] c) [3, 5] d) (, 5] e) (3, ) 12. Simplify a 3 5 a 1 5. a) a 6 5 b) a 1 25 c) a 2 d) a e) a 2 5 a Simplify (4 x)(8 3 x). a) 32 3 x b) 32 6 x 5 c) 32 6 x d) 32 5 x 6 e) 32 x 5 log(x 3) 10 2x. 14. Find the domain of the function f(x) = x 2 x. a) x>0 b) x<0orx>1 c) x 1 d) x 0orx 1 e) 0 x If f(x) =4 5x 3 + x, which of the following is true about the end behavior of f(x)? a) As x, f(x) and as x, f(x). b) As x, f(x) and as x, f(x). c) As x, f(x) and as x, f(x). d) As x, f(x) and as x, f(x).

4 16. The graph of f(x) = 5(x 2) is a stretch and/or translation of the graph of g(x) =x 2 as: a) Stretch vertically by a factor of 5, then shift left 2 and up 3. b) Stretch vertically by a factor of 5, then shift right 2 and up 3. c) Stretch vertically by a factor of 2, then shift right 3 and down 5. d) Stretch vertically by a factor of 5, then shift left 3 and down Which number is larger, 1 x or 1,giventhatx and y are positive integers and x>y? y a) 1 y b) 1 x c) More information is needed to determine which is larger. d) They are the same. 18. Solve the following logarithmic equation: ln(x + 15) ln(3 2x) = 4ln2. a) x =0.25 b) x =2 c) x =1 d) x =0.5 x 19. Perform the indicated operation x 2 x 2 x x 2 +7x 18 2 x 2 +10x +9 completely. In reduced form, the numerator is: a) 9x +2 b) 5x 1 c) 6x 4 d) 9x 2 e) 6x Simplify the following complex fraction: x x. x x and reduce a) x +14 b) 7x +8 c) x +14 x x d) 8+6x

5 21. Find the zero(s) of the rational expression below: 6x 2 +25x +21 5x 2 +19x +12 a) x = 6 7 b) x = 3 c) x = 4 5 d) x = The angle of elevation to the top of a building is found to be 70 o from the ground at a distance of 450 feet from the base of the building. Using this information, which expression below could be used to calculate the height of the building? a) height = 450 cot 70 o b) height = 450 tan 70 o c) height = 450 sin 70 o d) height = 450 cos 70 o ( ) 4x Simplify the following expression: a) 20y12 x 7 b) 20y35 x 10 c) 1024y35 x 10 y 35 d) 1024x Multiply and express your answer in exponential form: xy 2 z 2 4 x 2 y 3 z a) x 5 6 y z b) x 1 6 y 1 2 z 1 6 c) x 5 6 y z d) x 1 6 y 1 2 z 1 5 y 7

6 25. The figure below consists of 4 squares of equal size. The area of the whole figure is 36 sq. in. Find the length of the diagonal from A to C. a) 3 5in. b) 9 3in. c) 3 D C. 17 in. d) 3 51 in. A B 26. If xy =1andx is greater than 0, which of the following statements are true? i) Asx increases, y decreases. ii) Asx increases, y increases. iii) Whenx is less than 1, y is less than 1. iv) Whenx is greater than 1, y is negative. v) Whenx is greater than 1, y is less than 1. a) ii,iii,v b) i,iii c) ii,iii d) i,v e) i,iv,v ( π ) ( ) 3π 27. Evaluate: cos sin 3 4 a) b) c) d) Evaluate the following piecewise defined function at x =2, 4, and 9. { f(x) = a) f(2) = 2,f(4) = 9,f(9) = 7 b) f(2) = 1,f(4) = 9,f(9) = 13 c) f(2) = 2,f(4) = 3,f(9) = 13 d) f(2) = 1,f(4) = 10,f(9) = 20 e) f(2) = 1,f(4) = 3,f(9) = 13 2, if x<4 2x 5, if x 4

7 . 29. Use f(x) =3x 1andg(x) =9 x 2 to evaluate f(g( 3)). a) 91 b) 0 c) 10 d) 1 e) Use the Laws of Logarithms to rewrite the expression below in a form with no logarithm of a product, quotient, or power. ( ) x 9 log a yz 5 a) 9 log a x log a y 5log a z b) 9 log a x log a y +5log a z c) 9 log a x +log a y +5log a z d) 9log a x +log a y +5log a z 9log e) a x log a (5y)log a z 31. Find cos θ, tan θ, and sin θ from the figure below, given a =3,b=4andc =5. a) cos θ = 4 5, tan θ = 3 4, sin θ = 3 5 b) cos θ = 5 4, tan θ = 4 3, sin θ = 5 3 c) cos θ = 5 3, tan θ = 3 4, sin θ = 5 4 c θ a d) cos θ = 3 5, tan θ = 4 3, sin θ = Simplify the following trigonometric expression as much as possible: a) cot x b) sec x c) 1 d) csc x 33. Simplify the following trigonometric expression as much as possible: sin 2 x +cos 2 x +tan 2 x a) tan 2 x b) sec 2 x c) sec x d) sin 2 x b cot x sec x csc x

8 Answer Key - Form A1 1. c 8. a 15. b 22. b 29. d 2. a 9. e 16. b 23. d 30. a 3. b 10. b 17. a 24. a 31. d 4. e 11. a 18. c 25. c 32. c 5. b 12. e 19. e 26. d 33. b 6. c 13. b 20. b 27. a 7. d 14. d 21. d 28. c