Advanced Algebra - Semester 1 Review

Chapters 1 and 3

1.

2. Not possible, Dimensions don’t match

3.

4.

5. Not possible, Inner dimensions don’t match

6.

7.

8. Yes. When you multiply A and B, if you get the identity matrix they are inverses.

9. 3X5

10. a. MN

b. 2X3

11.

12.

13.

Chapter 4

1.

2.

3.

4.

5.

6.

7.

8. -

9.

10.

11.

12.

13.

14.

15.

16.

Chapter 5

1. a. down

b. (6, 8)

c. x = 6

d. Max at y = 8

e. 2

2. y = 2(x-1)² + 7 is wider. The larger the IaI is, the narrower the graph.

3. a. (-15, -185)

b. y = (x+15)² – 185

c. Min at y = -185

4. y = -9

5. x = -3, x = 1

6. a. x = -4, x = .5

b. x = -8, x = 3

c. x = -4, x = 6

d. x = -1, x = 7/3

7. a. x = 7.5, x = -1

b.

c.

d.

8. a. 2 real rational

b. 1 real rational

c. 2 complex

9. 0

10. x = -4, x = 2

11. y = -2x² – 12x – 12

Chapter 7

1. K = 500

2. y = 28

3. y = 67.5

4. a. Common points: (-1, -1), (0, 0), (1, 1), cubic shape, rotational symmetry

b. Common points: (-1, 1), (0, 0), (1, 1), parabola, line symmetry

5. A. 2, B. 3, C. 4, D. 1

6. a.

b.

c.

d.

e.

f.

g.

h.

i.

j.

k.

l. 5

m.

n.

7. a. 32

b. 81

c.

8. a.

b.

c.

10. a. x = 4

b. x = 9

c. x = 204

d. x = 12

e. x = 125

f. x =

g. y = 4

h. x = 2

Chapter 8

1. A. 3, B. 2, C. 1, D. 4

2. Zeros: x = -3, 1(multiple root), 4. Degree: 4. y = (x+3)(x-1)²(x-4)

3. A. DNE, DNE, A, B, D

B. DNE, B, D, A, C

4. a. x = 0, -1, 4

b. x = -5, -4

c. x = 0, -3, 4

d. x = 1, 4

e. x = 2i, 1

f. x =

g. x =

h. x =

5. x = -3, 1, 2

6. (x-4)(x+1)(x-2)

7. x = 0 (Triple root), x = -2 (Double root)

8. a. 28x⁵

b. x(x-1)(x+1)

c. x(x+1)

9. a.

b.

c.

d.

e.

f.

g.

h.

i.

j.

10. a. x cannot be 0, x =

b. x cannot be -5, 2, No solution.