Algebra 20 Multiple Choice Question Answers

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

Question 1 options:

	k + 5
	k + 1
	k + 3
	k + 2

Question 2 (5 points)

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

a₁ = 7 and a_n = a_n-1 + 5 for n ≥ 2

Question 2 options:

	8, 13, 21, 22
	7, 12, 17, 22
	6, 14, 18, 21
	4, 11, 17, 20

Question 3 (5 points)

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

a_n = 3n + 2

Question 3 options:

	4, 6, 10, 14
	6, 9, 12, 15
	5, 8, 11, 14
	7, 8, 12, 15

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:

	≈ 0.31
	≈ 0.42
	≈ 0.45
	≈ 0.41

Question 5 (5 points)

Saved

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+16y4$x^8+8x^{6}y+24x^4{y}^2+32x^2{y}^3+16y^4$
	x8+8x6y+20x4y2+30x2y3+15y4$x^8+8x^{6}y+20x^4{y}^2+30x^2{y}^3+15y^4$
	x8+18x6y+34x4y2+42x2y3+16y4$x^8+18x^{6}y+34x^4{y}^2+42x^2{y}^3+16y^4$
	x8+8x6y+14x4y2+22x2y3+26y4$x^8+8x^{6}y+14x^4{y}^2+22x^2{y}^3+26y^4$

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 + 8$4;15;28;(k+1{)}^{\mathrm{}}+3(k+1);k^2+5k+8$
	4; 20; 28; (k + 1)2 + 3(k + 1); k2 + 5k + 7$4;20;28;(k+1{)}^{\mathrm{}}+3(k+1);k^2+5k+7$
	4; 10; 18; (k + 1)2 + 3(k + 1); k2 + 5k + 4$4;10;18;(k+1{)}^{\mathrm{}}+3(k+1);k^2+5k+4$
	4; 15; 18; (k + 1)2 + 3(k + 1); k2 + 5k + 6$4;15;18;(k+1{)}^{\mathrm{}}+3(k+1);k^2+5k+6$

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:

	14x12−22x9+14x6−6x3+1$14x^{12}–22x^9+14x^6–6x^3+1$
	16x12−32x9+24x6−8x3+1$16x^{12}–32x^9+24x^6–8x^3+1$
	15x12−16x9+34x6−10x3+1$15x^{12}–16x^9+34x^6–10x^3+1$
	26x12−42x9+34x6−18x3+1$26x^{12}–42x^9+34x^6–18x^3+1$

Question 8 (5 points)

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

a_n = 3ⁿ

Question 8 options:

	3, 9, 27, 81
	4, 10, 23, 91
	5, 9, 17, 31
	4, 10, 22, 41

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:

	1045
	2108
	10478
	2049

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:

	650 ways
	720 ways
	830 ways
	675 ways

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)=x4−5x3+14x2−42x+26$f_1\left(x\right)=x^4–5x^3+14x^2–42x+26$
	f1(x)=x4−16x3+18x2−22x+18$f_1\left(x\right)=x^4–16x^3+18x^2–22x+18$
	f1(x)=x4−18x3+24x2−28x+16$f_1\left(x\right)=x^4–18x^3+24x^2–28x+16$
	f1(x)=x4−8x3+24x2−32x+16$f_1\left(x\right)=x^4–8x^3+24x^2–32x+16$

Question 12 (5 points)

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

a_n = (-3)ⁿ

Question 12 options:

	-4, 9, -25, 31
	-5, 9, -27, 41
	-2, 8, -17, 81
	-3, 9, -27, 81

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:

	32,317 groups
	23,330 groups
	24,310 groups
	25,410 groups

Question 14 (5 points)

Write the first six terms of the following arithmetic sequence.

a₁ = 5/2, d = – ½

Question 14 options:

	3/2, 2, 1/2, 1, 1/4, 0
	7/2, 2, 5/2, 1 ,3/2, 0
	5/2, 2, 3/2, 1, 1/2, 0
	9/2, 2, 5/2, 1, 1/2, 0

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:

	The first person can have any birthday in the year. The second person can have all but one birthday.
	The second person can have any birthday in the year. The first person can have all but one birthday.
	The first person cannot a birthday in the year. The second person can have all but one birthday.
	The first person can have any birthday in the year. The second cannot have all but one birthday.

Question 16 (5 points)

Write the first six terms of the following arithmetic sequence.

a_n = a_n-1 – 10, a₁ = 30

Question 16 options:

	40, 30, 20, 0, -20, -10
	60, 40, 30, 0, -15, -10
	20, 10, 0, 0, -15, -20
	30, 20, 10, 0, -10, -20

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:

	865
	955
	678
	895

Question 18 (5 points)

Write a formula for the general term (the n^th term) of each arithmetic sequence. Do not use a recur