Pre-Calculus 12 Practice Exam 1 MULTIPLE-CHOICE (Calculator permitted )

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1 Pre-Calculus 1 Practice Exam 1 MULTIPLE-CHOICE (Calculator permitted ) 1. Determine the smallest zero for = sinθ + in the interval θ In high school a shot put is thrown out of a circle with a radius of. feet. A curved wooden stopboard is placed in an arc around part of this circle. The central angle is 6.. Determine the length of the curved stopboar. On Oct. 010 the tide at New Westminster reached a maximum height of 10.8 feet at midnight. At 9 am the tide reached the next minimum height of.8 feet. Assuming the relationship is sinusoidal what was the height of the tide at 7 am? 6.1 ft 6. ft 8.7 ft 9.9 ft + 1. Solve 7 = x.. ft.0 ft. ft.0 ft The population in a particular communit is increasing at an annual rate of 6.%. Assume this trend will continue. In how man ears will the present population of grow to 000? In a stud which compared the ph of urine and tears the following data was collecte On average how man times more alkaline are tears than urine? 7. A restaurant offers a selection of different sandwiches different soups and different flavours of juice. In how man different was can a person select one item from each categor? Determine the th term in the expansion of x x 16x 18x 110x 9. A famil of 6 ( parents and children) sit in a row at a theatre. A parent must sit at either end with the children between them. In how man was can the famil be seated? From a standard deck of cards how man -card hands can be formed containing at least clubs? A hocke team has plaed 10 games and has a record of wins losses and ties. In how man was could this have happened if after the first games the team s record was wins and a loss? When the polnomial P(x) is divided b x + the remainder is. Which point must be on the graph corresponding to the function = P(x)? ( ) ( 0) ( ) ( ) 1. Determine the range of the rational function graphed below. all reals ( 0][8 ) ( ]( ) ( 1)( 10][8 )

2 1. The graph = f (x) is stretched horizontall b a factor of 1. Determine the equation of the transformed graph. 1 1 = f ( x) = f ( x) = f ( x) = f ( x) MULTIPLE-CHOICE (Calculator NOT permitted) 1. The students at a graduation dinner are separated into groups to be seated at 10 different tables. The order in which these 10 groups will approach the buffet is to be determined randoml. In how man was can this order be determined? 0. A point with an x value of lies on the circle with equation x + =. This point also lies on the terminal arm of θ in standard position. Determine the value of sec θ. 1. The graph of = sinb( x c) + 1 Determine a value of is shown below C P ( x ) 16. Consider the graph of = cos Which statement is false? I II III IV 7. Determine all restrictions for the expression tan x cos x 1 cos x 0 sin x 0cos x 1 cos x 1 cos x 0cos x Solve cos x = 0 x < Solve sin x = cos x x Determine an expression for all angles coterminal with a standard position angle measuring 10. Express our answer in radians. + n 6 + n + n 6 + n 19. Determine the exact value of tan 7. Simplif cscθ sinθ secθ cosθ cot θ cot θ tan θ tan θ. Solve x 1 = 8 x+ 1 x = x = 1 x = x = x 6. Express log 10 in terms of log xor log log x 1 log log x 10 log log x 1+ log log x 10 + log

3 7. Evaluate log Bart and Arnie presented separate solutions to the statement Write log x + log as a single log 9 1. The graph of = f (x) is shown below. Which graph represents the graph of = f x +? ( ( )) Which statement is true? Onl Bart is correct The are both wrong Onl Arnie is correct The are both correct 9. Which statement must be true for f ( x) = log 1 x when x > x1? f x ) > f ( ) f x ) > 0 f ( x ) 0 ( 1 x ( x ) f ( x1 ( 1 < ( x ) > 0 f ( x1) < f > ) f 0 0. For which graph is the relation and its inverse both functions?. Consider the following transformations on the graph of = f (x) Which transformations will have no effect on the zeros of the original graph of = f (x)? I and II onl II and IV onl II and III onl III and IV onl. The graph of = f (x) as shown below is transformed to x = f ( ). Determine all invariant points. ( 0 ) ( 1 1) ( 1) ( 11 ) and ( 1)

4 P lies on the graph of = f (x). Which point must lie on the graph 1 1 = f x +?. The point ( 6) ( 7 ) ( ) ( 1 ) ( ). Which of the following functions are polnomial functions? 9. Given f ( x) = x + and g ( x) = x + x 1 determine the value of ( g( ) ) f The graphs of = f (x) and = g(x) are shown below. Which graph represents = f ( x) + g( x)? III onl IV onl I and IV onl II and III onl 6. Which sketch best represents the graph of = ax bx + cx + if a < 0? 7. Which three expressions are factors of = 9x 6x x + 16? I II III onl I II IV onl I III IV onl II III IV onl 1. As a furniture salesperson Chacci gets a % commission on all his weekl sales above $000. Which row in the table shows the composite function that will determine his commission if x represents his weekl sales? 8. When x kx + k x 1is divided b x the remainder is 1. Determine all values of k. k = 17 k = k = k = 8

5 . Consider the graphs of the functions f ( x) = x and g ( x) = f ( x). Which row describes the domain and range of g (x)?. Prove algebraicall. ( marks) tanθ ( 1 tanθ ) cos sinθ θ 1 = 1+ tanθ. The graph of = f (x) is shown below.. Given the graph of = f (x) as shown determine the graph of = f (x) Sketch the graph of = f ( x) ( marks). Use the graphs of = f (x) and = g(x) shown to sketch the graph of = f ( x) g( x). Label enough points to get an accurate representation of the graph. ( marks) WRITTEN-RESPONSE QUESTIONS (Calculator NOT permitted). Determine the range of the function = x WRITTEN-RESPONSE QUESTIONS (Calculator permitted) 1. Solve algebraicall over the set of real numbers giving exact values where possible. ( marks) sin θ + sinθ = 1 1. Solve algebraicall: ( ) + log ( 1 x) 1 log1 x 1 =. Justif the validit of each solution ( marks). Consider the graphs of x g ( x) = x 9 x x 6 f ( x) = and x 9 Use our knowledge of rational functions to outline the similarities and differences between these two graphs. You will be evaluated on the concepts expressed the organization and accurac of our work and our use of language. ( marks)

6 Answers MULTIPLE-CHOICE 1. d 1. c. a. b. b 1. b. b. c. b 1. d. a 6. a. c 1. c 6. a 7. c. b 16. b 7. c 8. c 6. d 17. b 8. d 9. c 7. c 18. d 9. a 0. a 8. a 19. a 0. a 1. d 9. b 0. a 1. d. d 10. c 1. d. c. a 11. c. d. b. b.. WRITTEN-RESPONSE (Calculator permitted) 1. WRITTEN-RESPONSE (No calculators) 1...