The Algebra Ace

Polynomials

5

What is the vertex of: 

f(x)=2x^2-8x+7

(2,-1)

10

Sketch a graph of 

f(x)=x(x+3)(x-1)(x-4)

Graphs vary.

15

Solve: 

2x^6-3x^4-18x^2+27=0

+-sqrt(6)/2, +-sqrt(3), +-isqrt(3)

20

Solve: 

5x^4-19x^2-4=0

+-(isqrt(5))/5, +-2

25

Solve: 

x^3+8x^2+14x+4=0

-2, -3+-sqrt(7)

Exp./Logs

5

Solve: 

-10e^(x+10)=-30

ln(3)-10

10

Solve: 

16^(3x+2)=64^(-2x)

-1/3

15

 Solve: 

log_8(x)+log_8(x+2)=1

2

20

Solve: 

-10+3(x-1)^(2/3)=38

-63, 65

25

Solve: 

sqrt(5x-1)-3=sqrt(2x-4)

2, 10

Rationals

5

Simplify: 

(5x^2+10x-15)/(25x-25)*(5x+10)/(4)

((x+3)(x+2))/4

10

Simplify: 

2/(x-4)+2/(x-6)

(4(x-5))/((x-6)(x-4))

15

Solve: 

(x+1)/x^2=1/x+1

+-1

20

Solve: 

(x-5)/(2x^2)=(x-6)/(6x^2)+(2)/(3x^2)

13/2

25

Solve: 

x/(x^2-2x+1)-1/(x-1)=1

0,2

Trig.

5

Convert into degrees: 

-(10pi)/3

-600^o

10

Determine the amplitude, period, and any shifts for: 

-3sin(4theta-pi)+5

a=3, period=pi/2, HS=pi/4, VS=5

15

Solve the triangle: 

B=58^o, C=44^o, b=33

A=78^o, c=27, a=38.1

20

Solve the triangle: 

a=10, b=18, c=25

A=19.4^o, B=36.7^o, C=123.9^o

25

Solve: 

3cos(theta)-1-cos^2(theta)=cos^2(theta)

2pi, pi/3, (5pi)/3

Probability

5

In a swim final of 8 competitors, what is the probability of correctly guessing the podium finish?

1/336 or 0.003

10

If you toss a coin 12 times, what is the probability of getting 5 heads?

.193

15

A spinner has 5 equally sized regions: red, yellow, blue, green, and purple. If the spinner is spun twice, what is the probability of getting the same color on both spins?

0.20

20

In a bag of M&M's, there are 12 blue, 10 black, 8 green, 7 yellow, and 9 orange. If you grab a handful of 5 M&M's, what is the probability of getting one of each color?

0.044

25

Weights of bananas are normally distributed with an average of 0.25 lbs and standard deviation of 0.04 lbs. What is the probability that in a bunch of 7 bananas, at least 3 weigh 0.3 lbs or more?

0.030

Conics

5

Which conic sections have foci?

Parabolas, Hyperbolas, and Ellipses

10

Sketch a graph: 

((x-1)^2)/9-((y+3)^2)/16=1

Graphs vary.

15

Write an equation for the ellipse:

V: (-2,8), (-2, -14), CV: (7, -3), (-11, -3)

((x+2)^2)/81+((y+3)^2)/121=1

20

Solve: 

-3x^2+2y^2-13x+3y-13=0; x+y+3=0

(-2,-1)

25

Solve: 

6x+6y-3z=3; -5x+4y+4z=-25; -3x+y+2z=-11

(1, -2, -3)