math basic algebra work sheets 9 work sheets

Week 15 TR GW Review for Final

1. Solve.

5 − (8 + 3x) = 2x + 6 2x + 1

3 −x− 14 = 1 5(2x− 3) = 6(x− 1) + 4x

V = LWH for L A = 1 2 h(b + B) for b 2|3x− 7| = 8

|4x + 2|− 7 = −3 |3x + 1| = |x + 2| x2 − 8x + 16 = 0 x2 + 2x = 8

6x2 = −9x − 4x2 + 36 = 0 6x2 + 7x = 3

2. Solve the following inequalities.

6x + 3

−4 < −3 5 − (6 − 4x) ≥ 2x− 7

8 ≤ 3x− 1 < 14 |3x + 4| ≤ 2

3. Solve the following system of equations.

9x−y = −4 − 5x + 2y = −2 5x− 4y = 2 y = x + 4 x + 6y = 26 − 10x + 8y = 7

4. A jar contains dimes and quarters. There are 36 coins, and they total $5.70. Find the number of dimes and the number of quarters in the jar.

5. A regulation National Hockey League rectangular ice rink has perimeter 570 ft. The length of the rink is 30 ft longer than twice the width. What are the dimensions of an NHL ice rink?

6. A rectangular picture frame has a length that is 2 inches longer than its width. The area is 48 in2. Find the dimensions of the frame.

7. Write an equation of the line that satisfies the conditions listed. Also, graph each.

a. slope is −4 3

and passes through (2, 7)

b. Passes through the points (2,−5) and (1, 4)

c. Passes through (7,−1) and is parallel to 4x−y = 3

d. Passes through (4, 3) and is perpendicular to 2x− 5y = 7.

8. Graph the following linear functions. Find and label the slope and x and y-intercepts.

y = 1

4 x− 2 3x− 4y = 12 −

2

5 + 5 = y

9. Simplify the following. Leave your answers with positive exponents only.

2−1 + 4−1 + 50 (5m−3)2(m4)−3 3x3y10

x2y6z

(−3x4y3)(4x−2y5)

( 2x3y5

z2

)−2 (x5yz6)

10. Find the domain of each rational function below and simplify.

R(x) = x2 − 9

x2 + 7x + 12 r(x) =

x2 + 2x

x2 −x− 6

11. Perform the operation and simplify if possible.

6

5a + 10 +

7

6a + 12

1

x + 1 −

2

x2 − 1 (2y + 3)2

5y ·

15y3

4y2 − 9

x2 −x− 6 x− 6

÷ x2 + 2x− 15

x2 − 6x

3

x + 2

4

x − 7