Question 1

Which of the following correctly expresses the Binomial Theorem for expanding $$ (a+b)^n $$?

Accepted Answer

$$ (a+b)^n = \sum_{k=0}^{n} \binom{n}{k} a$$^{n-k}$$ b^k $$

Question 2

What is the coefficient of $$ x^3$  in $$the expansion of $$ (2x+5)^5$ $$?

Accepted Answer

$$ 2000 $$

Question 3

Given the binomial $$ (x-3)^6$ $$, what is the term containing $$ x^4$ $$?

Accepted Answer

Question 4

Which of the following is the correct formula for the $$ k -th $$term in the expansion of $$ (a+b)^n $$?

Accepted Answer

$$ \binom{n}{k} a$$^{n-k}$$ b^k $$

Question 5

Find the constant term in the expansion of $$ (2x - \frac{1}{x})^8$ .$$

Accepted Answer

$$ 560 $$

Question 6

A chemist is mixing two solutions, one with concentration $$ a $$ and the other with $$ b . If $$the total mixture is modeled by $$ (a+b)^4$ $$, what is the coefficient of the $$ a^2$b^2$$ $ term?

Accepted Answer

$$ 6 $$

Question 7

Which of the following is the correct value for $$ \binom{7}{3} $$?

Accepted Answer

$$ 35 $$

Question 8

In the expansion of $$ (x+2)^5$ $$, what is the sum of the coefficients?

Accepted Answer

Question 9

Which term in the expansion of $$ (3x-2)^7$ $$ contains $$ x^4$ $$? (Give the full term.)

Accepted Answer

Question 10

A medical researcher is modeling the probability of a genetic trait using $$ (p+q)^6$ $$, where $$ p  is $$the probability of having the trait. What is the probability of exactly 2 individuals having the trait in a group of 6, if $$ p=0.3 $$ and $$ q=0.7 $$? (Use the binomial probability formula.)

Accepted Answer

$$ 0.302 $$

Question 11

Which of the following is NOT a property of binomial coefficients $$ \binom{n}{k} $$?

Accepted Answer

$$ \binom{n}{k} = n \cdot \binom{n-1}{k} $$

Question 12

If $$ (x+y)^n  is $$expanded, what is the sum of all the coefficients?

Accepted Answer

$$ 2^n $$

Question 13

Find the middle term in the expansion of $$ (x-1)^8$ .$$

Accepted Answer

$$ 56x^4$ $$

Question 14

Which of the following best describes the pattern of exponents in the expansion of $$ (a+b)^n $$?

Accepted Answer

The exponent of $$ a $$ decreases by 1 and the exponent of $$ b $$ increases by 1 in each successive term.

Question 15

In the expansion of $$ (2x-3)^5$ $$, what is the coefficient of $$ x^2$ $$?

Accepted Answer

Question 16

A business is modeling profit using $$ (p+q)^4$ $$, where $$ p  is $$the probability of profit and $$ q  is $$the probability of loss. What is the probability of exactly 3 profits in 4 trials if $$ p=0.6 $$?

Accepted Answer

Expanding Binomials Using the Binomial Theorem

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