math basic algebra work sheets 9 work sheets

Math 090 Week 9 Thursday Review

1. Simplify as much as possible. Leave your answers with only positive exponents.

−3w−2 − 10 + 5−1 − 2−2 (−2x2y3)2(−xyz)3

(3st2)−2(3s4t)

( 10ab2c3

5ab3c2

)−1 ( − 2uv4w−1

u−3v4

)2 ·(u2vw5)

2. Let P(x) = x2 − 1, M(x) = x + 1, and Q(x) = 3x2 + 3x − 1. Find the following. For the divisions, state the domain.

P(x) − Q(x) 2Q(x) + P(x) Q(x) · P(x) Q(x)

P(x)

P(M(x)) P(M(−1))

( P

M

) (x)

( Q

M

) (x)

3. Factor the following.

16x2y2 − 49 2x3 − 6x2 − 20x 54 − 2x3 4x2 − 20xy + 25y2

4. Solve the following.

x2 − 5x − 6 = 0 x2 + 8 = −6x x3 = x

4x2 + 8x + 3 = 0 x3 − 5x2 = 4x − 20 3x3 = 21x2 − 36x

5. A rectangular parking lot has a length 20 ft more than its width. Its area is 2400 ft2. What are the dimensions of the lot?

6. A triangular wall brace has the shape of a right triangle. One of the perpendicular sides is 5 inches long. The other perpendicular side is one less than the length of the hypotenuse. Find the dimensions of the triangular brace.

7. A small rocket was launched vertically upward from ground level with an initial velocity of 128 feet per second. Its height in feet after t seconds can be modeled by the function h(t) = −16t2 + 128t After how many seconds will the rocket hit the ground?

After how many seconds will the rocket reach 220 feet above ground?

How high will the rocket be after 4 seconds?