Algebra 20 Multiple Choice Question Answers

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Question Description

k2 + 3k + 2 = (k2 + k) + 2 ( __________ )

Question 1 options:

Question 2 (5 points)

The following are defined using recursion formulas. Write the first four terms of each sequence.

a1 = 7 and an = an-1 + 5 for n ≥ 2

Question 2 options:

Question 3 (5 points)

Write the first four terms of the following sequence whose general term is given.

an = 3n + 2

Question 3 options:

Question 4 (5 points)

If 20 people are selected at random, find the probability that at least 2 of them have the same birthday.

Question 4 options:

Question 5 (5 points)

Use the Binomial Theorem to expand the following binomial and express the result in simplified form.

(x2 + 2y)4

Question 5 options:

x8+8x6y+24x4y2+32x2y3+16y4x8+8x6y+24x4y2+32x2y3+16y4

x8+8x6y+20x4y2+30x2y3+15y4x8+8x6y+20x4y2+30x2y3+15y4

x8+18x6y+34x4y2+42x2y3+16y4x8+18x6y+34x4y2+42x2y3+16y4

x8+8x6y+14x4y2+22x2y3+26y4x8+8x6y+14x4y2+22x2y3+26y4

Question 6 (5 points)

Consider the statement "2 is a factor of n2 + 3n."

If n = 1, the statement is "2 is a factor of __________."
If n = 2, the statement is "2 is a factor of __________."
If n = 3, the statement is "2 is a factor of __________."
If n = k + 1, the statement before the algebra is simplified is "2 is a factor of __________."
If n = k + 1, the statement after the algebra is simplified is "2 is a factor of __________."

Question 6 options:

4; 15; 28; (k + 1)2 + 3(k + 1); k2 + 5k + 84; 15; 28; (k + 1) + 3(k + 1); k2 + 5k + 8

4; 20; 28; (k + 1)2 + 3(k + 1); k2 + 5k + 74; 20; 28; (k + 1) + 3(k + 1); k2 + 5k + 7

4; 10; 18; (k + 1)2 + 3(k + 1); k2 + 5k + 44; 10; 18; (k + 1) + 3(k + 1); k2 + 5k + 4

4; 15; 18; (k + 1)2 + 3(k + 1); k2 + 5k + 64; 15; 18; (k + 1) + 3(k + 1); k2 + 5k + 6

Question 7 (5 points)

Use the Binomial Theorem to expand the following binomial and express the result in simplified form.

(2x3 - 1)4

Question 7 options:

14x1222x9+14x66x3+114x12-22x9+14x6-6x3+1

16x1232x9+24x68x3+116x12-32x9+24x6-8x3+1

15x1216x9+34x610x3+115x12-16x9+34x6-10x3+1

26x1242x9+34x618x3+126x12-42x9+34x6-18x3+1

Question 8 (5 points)

Write the first four terms of the following sequence whose general term is given.

an = 3n

Question 8 options:

Question 9 (5 points)

Use the formula for the sum of the first n terms of a geometric sequence to solve the following.

Find the sum of the first 11 terms of the geometric sequence: 3, -6, 12, -24 . . .

Question 9 options:

Question 10 (5 points)

A club with ten members is to choose three officers—president, vice president, and secretary-treasurer. If each office is to be held by one person and no person can hold more than one office, in how many ways can those offices be filled?

Question 10 options:

Question 11 (5 points)

Use the Binomial Theorem to find a polynomial expansion for the following function.

f1(x) = (x - 2)4

Question 11 options:

f1(x)=x45x3+14x242x+26f1x=x4-5x3+14x2-42x+26

f1(x)=x416x3+18x222x+18f1x=x4-16x3+18x2-22x+18

f1(x)=x418x3+24x228x+16f1x=x4-18x3+24x2-28x+16

f1(x)=x48x3+24x232x+16f1x=x4-8x3+24x2-32x+16

Question 12 (5 points)

Write the first four terms of the following sequence whose general term is given.

an = (-3)n

Question 12 options:

Question 13 (5 points)

You volunteer to help drive children at a charity event to the zoo, but you can fit only 8 of the 17 children present in your van. How many different groups of 8 children can you drive?

Question 13 options:

Question 14 (5 points)

Write the first six terms of the following arithmetic sequence.

a1 = 5/2, d = - ½

Question 14 options:

Question 15 (5 points)

If two people are selected at random, the probability that they do not have the same birthday (day and month) is 365/365 * 364/365. (Ignore leap years and assume 365 days in a year.)

Question 15 options:

Question 16 (5 points)

Write the first six terms of the following arithmetic sequence.

an = an-1 - 10, a1 = 30

Question 16 options:

Question 17 (5 points)

Find the indicated term of the arithmetic sequence with first term, a1, and common difference, d.

Find a200 when a1 = -40, d = 5

Question 17 options:

Question 18 (5 points)

Write a formula for the general term (the nth term) of each arithmetic sequence. Do not use a recursion formula. Then use the formula for an to find a20, the 20th term of the sequence.

an = an-1 - 10, a1 = 30

Question 18 options:

an = 60 10n; a = 260an = 60 - 10n; a = -260

an = 70 10n; a = 50an = 70 - 10n; a = -50

an = 40 10n; a = 160an = 40 - 10n; a = -160

an = 10 10n; a = 70an = 10 - 10n; a = -70

Question 19 (5 points)

How large a group is needed to give a 0.5 chance of at least two people having the same birthday?

Question 19 options:

Question 20 (5 points)

The following are defined using recursion formulas. Write the first four terms of each sequence.

a1 = 4 and an = 2an-1 + 3 for n ≥ 2

Question 20 options:

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vmohanakumar
School: University of Maryland

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