Name________________________________________________ Date _______________________ Period _________ Row _____ Pre Calculus Chapter 10 Test REVIEW Find the indicated sum. Find the sum of the infinite geometric series. 8 4 1 3 9 10) - + + ... 1) ∑ i 2 2 2 i=5 11) -20 - 5 -
Write the first four terms of the sequence defined by the recursion formula. 2) a1 = 3 and an = 2an-1 + 4 for n ≥ 2
5 + ... 4
Express the repeating decimal as a fraction in lowest terms. 2 2 2 2 12) 0.2 = + + + ... 10 100 1,000 10,000
Write a formula for the general term (the nth term) of the arithmetic sequence. Do not use a recursion formula. Then use the formula for an to find the indicated term of the sequence. 3) Find a18; 0, 11, 22, . . .
Use the Binomial Theorem to expand the expression and express the result in simplified form.. 13) (4x + 5)4
Find the indicated sum. 4) Find the sum of the first 70 terms of the arithmetic sequence -4, -14, -24, -34, ...
Evaluate the given binomial coefficient. 296 14) 2 Find the term indicated in the expansion. 15) (3x - 3y) 9; 5th term
Use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum. 41 5) ∑ (-4i + 3) i=1
Solve the problem. 16) Lisa has 4 skirts, 10 blouses, and 3 jackets. How many 3-piece outfits can she put together assuming any piece goes with any other?
Use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of the sequence with the given first term, a1, and common ratio, r. 6) Find a11 when a1 = -2, r = -3.
17) A student must choose 1 of 4 science electives, 1 of 6 social studies electives, and 1 of 4 language electives. How many possible course selections are there?
Find the indicated sum. Use the formula for the sum of the first n terms of a geometric sequence. 3 2 i+1 7) ∑ ( ) 5 i=1
18) A restaurant offers a choice of 5 salads, 9 main courses, and 3 desserts. How many possible 3-course meals are there? 19) How many 3-digit numbers can be formed using the digits 1, 2, 3, 4, 5, 6, 7, 8, 9, and 0? No digit can be used more than once.
Use the formula for the sum of the first n terms of a geometric sequence to solve. 8) Find the sum of the first 13 terms of the geometric sequence: -5, -10, -20, -40, -80, ... .
20) The matching section of an exam has 4 questions and 10 possible answers. In how many different ways can a student answer the 4 questions, if none of the answer choices can be repeated?
Use the formula for the value of an annuity to solve the problem. Round your answer to the nearest dollar. 9) Kurt deposits $200 each month into an account paying annual interest of 5.5% compounded monthly. How much will his account have in it at the end of 10 years?
21) A combination lock has 30 numbers on it. How many different 3-digit lock combinations are possible if no digit can be repeated? 1
Determine whether the problem involves permutations or combinations. Do not solve. 22) A church has 9 bells in its bell tower. Before each church service 3 bells are rung in sequence. No bell is rung more than once. How many sequences are there?
Solve the problem. 28) You are dealt one card from a standard 52-card deck. Find the probability that you are not dealt a 10. 29) A single die is rolled twice. The 36 equally-likely outcomes are shown as follows:
Solve the problem. 23) A hamburger shop sells hamburgers with cheese, relish, lettuce, tomato, onion, mustard, or ketchup. How many different hamburgers can be concocted using any 4 of the extras?
(1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6) (2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6) (3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6) (4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6) (5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6) (6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6)
24) From 10 names on a ballot, a committee of 4 will be elected to attend a political national convention. How many different committees are possible?
Find the probability of getting a sum of 6 or 7. Solve the problem involving probabilities with independent events. 30) A single die is rolled twice. Find the probability of getting a 1 the first time and a 2 the second time.
25) In a student government election, 7 seniors, 2 juniors, and 3 sophomores are running for election. Students elect four at-large senators. In how many ways can this be done? A) 19,958,400
B) 11,880
C) 42
D) 495
26) Ron finds 8 books at a bookstore that he would like to buy, but he can afford only 5 of them. In how many ways can he make his selection? How many ways can he make his selection if he decides that one of the books is a must? Use the theoretical probability formula to solve the problem. Express the probability as a fraction reduced to lowest terms. 27) Use the spinner below to answer the question. Assume that it is equally probable that the pointer will land on any one of the five numbered spaces. If the pointer lands on a borderline, spin again.
Find the probability that the arrow will land on 2 or 4.
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