Mid-Term Review1) What is the Law of Sines formula?

2) What is the Law of Cosines formula?

3) Find x. 4

8

x

62°

4) What is the inverse of f(x) = 6x – 7?

5) An arithmetic sequence has a3 = -6 and a11 = 50. Find a1.

6) Write recursive and explicit formulas for the sequence in #7.

7) Rewrite the equation in vertex form: y = 2x2 – 8x + 7.What is the vertex?

8) If sin θ = and sec θ < 0, what is cot θ?

9) What is the formula for projectile motion?

10) A projectile is shot straight up from a height of 48 ft with an initial velocity of 32 feet per second.

a) What is the rocket’s maximum height?

b) When will the rocket hit the ground?

2

3

11) Let f(x) = x2 and g(x) =

a) Find f(g(x)) and give its domain.

b) Find g(f(x)) and give its domain.

c) Find g(g(x)) and give its domain.

12) Give the domain and range of in interval notation.

1

3x

2

100( )

4h x

x

13) Factor:

a) 6x2 – 7x + 3

b) 125x3 – 8y3

c) 81x4y6 – 9z10

14) Solve for x using the quadratic formula

(Oh, no! What is that again?)

2x2 + 7x = 6

15) Simplify

5 648x y z