Math 110 Final

Which of (x+1), (x+2), and (x+3) are factors of 3x4 +8x3 +x2 −8x−4?

Only (x+1) and (x+2)

Which of (x−3), (x−2), and (x+2) are factors of x^4 −x^3 −11x^2 +9x+18?

Only (x−3) and (x−2)

Find the domain of the function f (x) = (square root) 2x − (2/x)

[-1,0) and (1,oo)

Solve the rational inequality: (x^2+5x-6)/(x-3) > 0

[-6,1) and (3,oo)

A coed indoor soccer team has 7 boys and 5 girls. How many ways can the coach choose a starting team of 3 boys and 3 girls?

between 300 and 400

f(x)= absolute value of x

even function

f(x)= a^x

exponential function graph (opposite of logarithmic function, positive and moves more negative)

f(x)= 1/x

hyperbola

f(x)= square root of x

hyperbola

If a=ln6 and b=ln42, then b−a=

ln7

f(x)= log(x)

logarithmic function

f(x)=x^3

odd function

A coed indoor soccer team has 6 boys and 7 girls. How many ways can the coach choose a starting team of 3 boys and 3 girls?

over 600

f(x)= x^2

parabola

solve the system of equations for x 2x+y+3z =−2 x+y+2z =0 2x+y+4z =−1

x=-3

Find the asymptotes of the hyperbola 36y2 − 100x2 = 9.

y= plus or minus 5/3x

Solve the system of equations: 2x+y+3z =−2 x+y+2z =0 2x+y+4z =−1

y=1

Solve the oblique asymptote: (4x^2+4x+1)/(x+2)

y=4x-4

Find the asymptotes of the hyperbola 4y^2 − 25x^2 = 9.

y=±5/2x

Solve the rational inequality: (4/(x+2)) > 2

(-2,0)

Solve the rational inequality: (4-x)/(x+3) > 0

(-3,4)

domain of (x^2+1)/2x^2+x-6)

(-oo,-2) , (-2,3/2) , (3/2,oo)

Solve the oblique asymptote: (x+1)(x-4)/2x

(1/2)x-(3/2)

Solve the equation e^5x = 2 for x.

(ln2)/5

What is the domain of the function defined by the equation y=(3x^2-1)/(x^2-9)

(−∞, −3) ∪ (−3, 3) ∪ (3, ∞)

The polynomial 2x^3 + x^2 − 2 x − 1 has three rational zeros. Find the three zeros and compute their sum.

-(1/2)

Find the constant term in the expansion of (x^3-1/x^2)^5

-10

Given that 2 and 3 are zeros of the polynomial p(x) = x^4 −2x^3 −7x^2 +8x+12, find the sum of the other two zeros.

-3

Given that 1 and -1 are zeros of the polynomial p(x) = x^4 +5x^3 +5x^2 −5x−6, find the sum of the other two zeros.

-5

Find the coefficient of x^6 in (x^2 − 2)^4.

-8

Five people randomly choose integers between 1 and 10, inclusive. What is the probability that at least two of them chose the same number to the nearest tenth?

.7

Four people randomly choose one of 5 colors. The probability that at least two of them choose the same color is closest to

.8

If x is the solution to 4^(5x−1) = 64^x, then x is between

0 and 1

Three people randomly choose one of eight flavors of ice cream. The probability that at least two of them choose the same flavor is closest to

0.33

If x^1000 + x^55 +1 is divided by x + 1, then the remainder is

1

A pair of fair dice is rolled. What is the probability that the sum of the numbers is even?

1/2

What is the probability of rolling either a five or a six with a pair of fair dice?

1/4

How many different seven letter passwords can be formed using 4 A's, 2B's, and 1 C?

105

How many years would it take an amount of money to double if it is invested at 10% compounded continuously?

10ln(2)

How many years would it take an amount of money to quadruple if it is invested at 10% compounded continuously?

10ln4

Find the infinite geometric sum 25+5+1+ 1/5 + 1/25 ···. The sum is

125/4

Find the coefficient of x^4 in (x^2 − 1)^6.

15

log5 30 is between

2 and 3

How many different 3-letter passwords can be made from the word DONKEYS if each letter can appear just once in a password.

210

Given x = 1−i is a solution to x^4 −6x^3 +11x^2 −10x+2 = 0. The real solutions to this equation are 2± √b where b=

3

Use properties of logarithms to find the exact value of the expression log5 2 • log2 125 .

3

Find the constant term in the expansion of (x^4-1/x^3)^7

35

How many years would it take an amount of money to triple if it is invested at 5% compounded continuously?

3ln2

If b and c are real numbers so that the polynomial x2 +bx+c has 2−2i as a zero, find b+c.

4

If b and c are real numbers so that the polynomial x2 +bx+c has −1+i as a zero, find b+c.

4

How many different four-person committees can be formed from a group of 12 people?

495

A pair of fair dice is rolled. What is the probability that the sum of the numbers five or less?

5/18

Find log6(4square root 3) + log6(9square root 2).

5/2

Find the arithmetic sum 3 + 6 + 9 + .... + 6,000 .

6,003,000

find the inverse of (2x+1)/(3x-1) then g(5)

6/13

log4 25 · log5 49 · log7 16

8

How many different 4-letter passwords can be made from the word DONKEYS if each letter can appear just once in a password.

840

(26x-12)/(8x^2-2x-3) = (A/4X-3) + (B/2x+1)

A=3