EOC MATH 3 REVIEW 3

Rational Equations

100

Given the function. What value(s) of x is the function undefined?

f(x)=(3x)/(x^2+4x-5)

A. x = 0, 1, -5 B. x = 0

C. x = 2, 3     D. x = 1, -5

Answer: D

200

Solve:

1/(x-8)-1=7/(x-8)

x=2

300

Given 6/r+4/(r-4)=1

a) What two values of r are undefined?

b) Solution(s)?

a) r is undefined at 0 and 4

b) r = 2, 12

400

Given the equation:

2/(x-1)=4/(x+1)-2/(x+3)

a) What are the restrictions on x?

b) Solutions?

a) x = -1, -3, 1

b) No Solution

500

Solve

x/(2x+2)=(-2x)/(4x+4)+(2x-3)/(x+1)

x=3

Solving Equations

100

Solve: 

Round to the nearest hundredth.

3^(2x+3)=(sqrt3)^(x+4)

x=-0.67

200

Solve for x:

Round to nearest thousandth

3*2^(7x)=48

x=0.571

300

Solve for x:

log_2(2x-5)=5

x = 18.5

400

Given 

f(x)=3Absx-1 and g(x)=0.03x^3-x+1

find when f(x)=g(x)

X= -0.986, 0.501 and 11.288

500

What is the solution to 

8(2^(x+3))=48

_{A. x = log2}(3) B. x = 3 - log₂(6) C. x=-3 + log₂(6)

Answer: C

Simplify/Factoring

100

Factor

x^3-5x^2+3x-15

(x^2+3)(x-5)

200

Factor

x^3+2x^2-9x-18

(x+2)(x+3)(x-3)

300

Factor

x^3-x^2-6x

x(x-3)(x+2)

400

Simplify by factoring

(x^3-2x^2-9x-18)/(x^3-x^2-6x)

(x+3)/x

500

The expression (x+4) is a factor of x²+kx-20. What is the value of K?

K =-1

Miscellaneous 1

100

What is the largest real number solution to the polynomial:

p(x) = (x-5)(3x+5)(x^2-7x+15)

x=5

200

Nancy can paint a fence in 3hrs. It takes Ben 4hrs to do the same job. If they work together, how many hours should it take?

1.7 hours

300

The graph of which function has an amplitude of 2 and a period of 4pi.

A. y=2sin(1/2x)

B. y=2sin(4x)

ANS. A

400

Find the x coordinate of the center of the circle

4x^2+4y^2-4x+2y-1=0

x=1/2

500

Given the interval (4,10], list the following functions from least to greatest.

f(x) = 2^x

g(x) = 2x

h(x) = x^2

g(x), h(x), f(x)

Miscellaneous 2

100

Let

p(x) =x^5-x^4+8x^2-9x+30

Evaluate p(-2)

p(-2) = 32

200

Find the area of a sector with an arc length of 40cm and a radius of 12cm.

area=240cm²

300

A polynomial eq. with real coefficients has roots at x=+/-1 and x=2i. What is the minimum degree of the polynomial equation?

4 roots

400

Find the inverse

f(x)=-1/(x+1) 

f(x) = -1/x-1

500

Given the Following Solve for A, B, and C

(2x+1)/(x-3)+(4x+6)/(2x-5)=(Ax^2+Bx+C)/((x-3)(2x-5)

A = 8, B = -14, C = -23