Determine if the sequence is arithmetic or geometric - find

Question

This Exam consist of four parts as follows.

Part A: Communication

Part B: Knowledge & Understanding

Part C: Application

Part D: TIPS

Part (A) Communication:

Place only your answer in the space Provided.

1. Evaluate.

a) 2³ x 4^-2 x 2⁰   a)________________

b) 81^1/2 + 8^1/3 - 32^4/5  b)________________

2. Simplify.

a) (b^{2m +3n}) / (b^{m - n}) a)________________

b) (2x^-2)²(3x⁴)^-3 b)________________

c) a^-2b c^3-d / a^-3b c^2d - 1 c)________________

3. Determine if the sequence is arithmetic or geometric. 4, 12, 36,........

4. Concert 2400 and -1350 to radian measure

5. Find the value(s) of k so that the function f(x) = 9x² + kx + 4 has no x-intercept.

6. Simplify. (x²-x-6) / (x²-4)

7. Solve for x, X² - 81 = 0

8. What is the domain and range of the function f(x) = -2x - 4

Part B: Knowledge & Understanding:

Answer the following questions in the space provided. Complete solutions are required and all the answers should be expressed in their simplest form.

1. How much will $7500 be worth if it is invested now for 10 years at 6%/a, compounded monthly?

2. Solve for x, where tan x = -1, where 0

3. Find the sum of the series, -77 - 70 - 63 - ............+252

4. For f(x) = 2/3(x - 5), determine f^-1(12) - f^-1(4) / (12 - 4)

5. Given f = {(1,2), (2, 5), (3, 7), (4, 8)}, list the ordered pairs that belongs to the function, y = -2f(3x - 6) + 1

6. For the relation y = -4x² - 6x - 5.

a) Write the relation in vertex form
b) determine if the relation has minimum or maximum.

9. Given f = {(1, 1), (2, 2), (3, 3), (4, 4)}, determine the new ordered pair of point that belongs to y = -2f(1/2x - 1) - 1 and explain the transformation in order.

Part C: Applications:

1. Solve for x.

a) 2sin²x = 1 - sinx, 0≤x≤2π

b) sinx - cos²x - 1 = 0, 0≤x≤360⁰

2. Tara and Tobey are planning to buy a home in three years. They would like to accumulate enough money for a $30 000 down payment. They will deposit the same sum of money at the end of each month in an account that pays 6%/a, compounded monthly.

(a) Draw a time line to represent the annuity.

(b) Write the series that represents the annuity.

(c) Determine the monthly deposit required to meet their goal.

Part D: Thinking Inquiry Problem Solving.

Prove each identity.

a) (cos2x - sin2x)/(cos2x + sinxcosx) = 1 - tanx   b) cosxtan³x = sinxtan²x

2. A relation is defined by g (x) = -x² + 6x - 4

(a) Determine the equation of g^-1(x).

(b) Graph g (x) & g^-1(x)

(c) State the domain and range of g (x) and g^-1(x)

(d) Which relation, g (x) or g^-1(x), is a function? Explain.