Pre-alculus Midterm Exam Review Name:. Which of the following is an arithmetic sequence?,, 8,,, b),, 6, 0,, c), 9,, 9, 6, d), 0, 6,, 7, e), 8,, 8,,. What is a rule for the nth term of the arithmetic sequence with a 8 = and a =? a n b) a n 8 c) a n d) a n 7 e) a n. What is the common ratio of an infinite geometric series whose sum is and the first term is a = 6? b) c). Find the sum of the series: k k d) e) 96 b) 7 c) 98 d) 87 e) 00. What is the sum of the series: +.8 +.08 + 0.68 +.? b) 7. c) 8 d) 0 e) does not converge 6. What is S for the arithmetic series +. +. +.6 +.8 +? b) 0 c) d) 7.6 e) 60 7. What is the twelfth term of the sequence of a geometric sequence; -6, 8, -..,88,66 b) -,88,66 c),06,88 d) -,06,88 e) - 8. How to do you write the series + 6 + 8 + 0 using sigma notation? k b) k c) k d) k e) k k k k k k 9. How do you write the series + 6 + 9 +. using sigma notation? n n. n b). c). d) n. e). n n n n n n 0. Which series is represented by k k k? + 0 + b) 0 + + 6 c) + 7 + d) 0 + + 8 e) 0 + +. What is the common ratio of the sequence,,,,...? 00 0. b) c) d) e) 6
. What is S 6 for the geometric series 0. 0.7 +. 6.7 +? 60.7 b). c) d) 9 e) 00. What is the common difference of the sequence,., 6, 7.,? b). c) d) e).. An infinite geometric series has a sum of 00 and a common ratio. Which is the first term of this series? 0 b) 60 c) 80 d) 00 e) 80. How many distinguishable permutations of the letters in ABANA are there? 60 b) 0 c) 80 d) 60 e) 70 6. How many distinguishable permutations of the letters in STORE are there? b) c) 60 d) 0 e) 7. In an activity club with students, the offices of president, vice president, secretary, and treasurer will be filled. In how many ways can the offices be filled? b) 7 c) 96 d) 0,66 e),0 8. In how many ways can a 9 person committee be chosen from a group of people? 9 b) c) 0 d) 60,80 e) 79,8,600 9. What is the coefficient of x in the expansion of (x + ) 7? b) 0 c) d) 9 e) 8 0. What is the coefficient of x in the expansion of (x )? 6 b) 7 c) 08 d) 70 e) 60. A movie theater sells sizes of popcorn (small, medium, and large) with choices of toppings (no butter, butter, extra butter). How many possible ways can a bag of popcorn be purchased? b) c) 9 d) 7 e) 8. In how many ways can 0 runners finish a race first, second, or third? b) 0 c) 00 d) 70 e) 000. How many possible license plates can be issued with two letters followed by three numbers? (Letters and digits may be repeated),000 b) 67,600 c) 0,000 d) 676,000 e) None of these
. In how many ways can cards be chosen from a standard deck of cards? 6 b) 0 c),600 d),00 e),600. A musician has songs she can play at an open mic night. How many different ways can she play of them? b) 0 c) 0 d) 60 e) 0 6. A printer has 8 colors of ink, but can only pick to use on a pamphlet that he is printing. How many different color combinations can he choose? b) 6 c) 0 d) 6 e) 0,0 7. A math class is made up of boys and 0 girls. How many ways can the teacher choose one boy and one girl to solve a problem for the class? b) c) 0 d) e) 8. Which of the following sets represents the shaded region in the Venn Diagram? A B A B b) A B c) A' B d) A B ' e) B 9. You are forming a 7-member committee from 0 men and women. The committee must consist of men and women. How many different 7-member committees are possible? 60060 b) 868600 c) 7 d) 980 e) None of these 0. A fair coin is flipped three times. What is the probability of obtaining three tails? 0. b) 0.67 c) 0. d) 0.0 e) 0.7. A fair coin is flipped 6 times. What is the probability of obtaining at least heads? 0. b) 0.89 c) 0. d) 0.09 e) none of these. If P(A) = 0.6, P(B) = 0., and P(A or B) = 0.8, what is P(A and B)? 0. b) 0. c) 0. d) 0. e) 0.. A card is randomly selected from a standard deck of cards. What is the probability that it is a or an ace? 0. b) 0.08 c) 0. d) 0.06 e) 0.08. What is the probability of or fewer successes for a binomial experiment consisting of 8 trials with the probability of 0.7 of success on each trial? 0. b) 0. c) 0. d) 0.69 e) 0.77
. A spinner has equal regions numbered through. What is the probability that the spinner will stop on an even number or a multiple of? b) c) 9 7 d) e) 6. What is the probability that in a family of seven children exactly two are girls? Assume a boy and a girl are equally likely. 7 8 7 b) 6 c) 8 d) 7 e) 7 7. A fair coin is tossed 0 times. What is the probability of obtaining at least six heads? 0.00 b) 0.60 c) 0.88 d) 0.79 e) 0.770 8. Events A and B are independent, P(A) = 0., P(B) = 0.6, what is P(A and B)? 0. b) 0. c) 0. d) 0.8 e). 9. Events A and B are dependent, P(A) = 60%, and P(B A) = 0%. What is P(A and B)? 0% b) 8% c) % d) 0% e) 90% 0. Five cards are dealt from a well-shuffled deck of playing cards. The expression 0 0 represents the probability of: one red king or two red kings b) one jack or two black tens c) one black jack and two black tens d) at least two black queens e) two red kings and two black jacks. A bag contains 6 red marbles, blue marbles, and 7 green marbles. If marbles are randomly selected (without replacement) from the bag, what is the probability that they are all blue?.008 b).00 c).0066 d) 0. e).007. High school students were surveyed about lunch. % of all students bring a lunch from home. The remaining students buy a school lunch. The school lunch offers pizza, grilled cheese, and tacos. Of the students who buy lunch, 0% like pizza, % like tacos, and the remaining 8% like grilled cheese. If a student was picked at random what is the probability that a student buys a grilled cheese at school? % b) % c) 8% d) % e) 00% For numbers, refer to the ellipse represented by x y. Find the coordinates of the center.. 6 9 (, ) b) (, ) c) (, ) d) (, ) e) (, ). Find the coordinates of the foci. 7, b) (, ), (, ) c), 7 d) (, ), (, 8) e) (, ), (6, )
. Find the coordinates of the vertices and co-vertices. (, ), (, 6), (, ), (, ) b) (, ), (, ), (, ), (, ) c) (, ), (, ), (, ), (, ) d) (, ), (, ), (, ), (, 6) e) Ellipses don t have co-vertices 6. Find the coordinates of the foci for the hyperbola y x. 0, b) 0, 6 c),0 d) 6,0 e) None of these 7. Write the standard form of the equation of the hyperbola for which the transverse axis is units long and vertical and the conjugate axis is units long. x y b) y x.. c) y x d) x y.. e) y x. 8. What is the directrix of the parabola with equation x = 8y? x = 7 b) x = 8 c) y = 7 d) y = 7 e) y = 8 9. Determine the orientation of the parabola: focus (0, ), directrix y = up b) down c) left d) right e) none 0. Which of the following is equivalent to 7? 8 b) 0 c) d) 0 e) 7. Which of the following is equivalent to 0? 6 b) 7 6 c) d) e) 8. What is the arc length of a sector with a radius of cm and a central angle of 0?.7 cm b).8 cm c). cm d) cm e) 00 cm. What is the area of a sector with a radius of 0 cm and a central angle of? 8 0.08 cm b).6 cm c) 8.7cm d). cm e) 8.8 cm
. If (6, ) is a point on the terminal side of an angle θ in standard position, what is the value of sin θ? 0 b) c) 0 d) 0 e). The number of degrees in one revolution is: b) π c) π d) 80 e) 60 6. The tangent and cosine functions are both negative in which quadrant? I b) II c) III d) IV e) none 7. What is the value of tan when cos = in quadrant? b) c) d) e) 8. Using a reference angle, sin 7 =? sin 7 b) sin 6 c) sin 7 d) sin 6 e) sin 7 9. Find the exact value of csc tan. b) c) d) e) 60. If cot x = where 0 x π find cos x. b) c) d) e) 6. An airplane is at an elevation of,000 ft and approaches the airport with an angle of descent of 0. What is the distance between the airport and the point on the ground directly below the plane?,.99 ft b) 8,069.7 ft c) 86,8.7 ft d) 0,.9 ft e),90.69 ft 6. If cos and, which of the following is true? sin b) tan c) tan d) cot e) sin