Mother

*The numbers are a lot smaller than the letters on my paper, if that helps*

Evaluate the expressions below

1. 9C3

2. 20C3

3. 9P2

4. 70P3

1. Use mathematical induction to prove the formula

3+6+9+...+3n=(3n(n+1)) / (2)

2. Use the Binomial Theorem to expand and simplify (2a-5b)^(4)

Find lim h-0 (f(x+h) - f(x)) / (h)

f(x) = 5-6x^2

A. -2x

B. 12x

C. -12x

D. The limit does not exist.

Find first differences for the sequence in order from a1 to a5. Determine whether or not the series is quadratic or not.

-1, -3, -1, 5, 15

A. 2, 2, 6, 10; not quadratic

B. 2, 2, 6, 10; quadratic

C. -2, 2, 6, 10; not quadratic

D. -2, 2, 6, 10; quadratic

Which of the following shows the best next step to prove the following by mathematical induction? 3^n > n * 2^n, n≥1.

(1 and 2 below are the steps given, I need to find the 3rd step.)

1. When n=1, the formula is valid because

3^1 > 1 * 2^1

3>2

2. Assuming that

3^k > k * 2^k

A. You must show that

3^(k+1) > k + 1 * 2^(k+1)

B. You must show that

3^(k+1) > k*2^(k+1)

C. You must show that

4^k >k * 3^k

D. You must show that

3^(k+1) > (k+1)26(k+1)

Find a quadratic model for the sequence.

-4, -4, -3, -1, 2

A. y = 0.5x2 - 0.5x - 4

B. y = 0.5x2 - 1.5x - 3

C. y = 4.5x2 - 21.5x+21

D. y = -4.5x2 + 21.4x - 21

Find first differences for the sequence in order from a1 to a5. Determine whether or not the series is quadratic or not.

-1, -3, -1, 5, 15

A. 2, 2, 6, 10; not quadratic

B. 2, 2, 6, 10; quadratic

C. -2, 2, 6, 10; not quadratic

D. -2, 2, 6, 10; quadratic

Sketch the curve represented by the parametric equations. Then

eliminate the parameter and write the corresponding rectangular equation whose

graph represents the curve.

1. x=r^(2) - 6

y = t/2 t - 1

2. x = √(r^(2) + 2)

y = t/4

3. x= 2 + 3 cosθ

y = 2 sinθ

Sketch the curve represented by the parametric equations. Then

eliminate the parameter and write the corresponding rectangular equation whose

graph represents the curve.

1. x=r^(2) - 6

y = t/2 t - 1

2. x = √(r^(2) + 2)

y = t/4

3. x= 2 + 3 cosθ

y = 2 sinθ

Solve the system of equations at the right algebraically by the method of substitution.Then verify your results by using a graphing utility.

x^(2) + 2y^(2) - 4x+ 6y - 5 = 0

x + y + 5 = 0

(a) Determine the number of degrees the axis must be rotated to eliminate the -term

of the conic x^(2) +6xy +y^(2) - 6 = 0

(b) Graph the conic in part (a) and use a graphing utility to confirm your result

Find the standard form of the equation of the hyperbola with vertices (0, ±3) and asymptotes y = ±3/2x

For the polar equation r=8cos3θ, find the maximum value of lrl and any zeros of

r. Verify your answers numerically

Given: r = (4)/(-2-cosΘ)

What type of conic does this represent?

A. Circle

B. Ellipse

C. Hyperbola

D. Parabola

r=4/(-2-6sinθ)

What type of directrix does this conic have?

A. Vertical

B. Horizontal

C. Oblique

D. This conic does not have a directrix.

r=4/(-2-6sinθ)

What is the distance between the pole and the directrix?

r=4/(-2-6sinθ)

What is the eccentricity of the function?

Use matrices to solve the system of equations

1. 2x + y + 2z = 4

2x + 2y = 5

2x - y + 6z = 2

2. 2x + 3y + z = 10

2x - 3y - 3z = 22

4x - 2y + 3z = -2

Solve the system by elimination

x - 4y - z = 3

2x - 5y + z = 0

3x - 3y + 2z = -1

Solve the system by elimination

2x + 5y = -11

5x - y = 19