Download CHAPTER 1 - wvhs.wlwv.k12.or.us

Final Review Semester 1
Name:_____________________
Period_________
Advanced Algebra
CHAPTER 1
Identify the property shown
1. 3 · x = x · 3
2. 2(r + w) = 2r + 2w
4. 15x(1) = 15x
5. 2r + (3r + 4r) = (2r + 3r) + 4r
3. 3a + 0 = 3a
Name the sets of numbers to which each number belongs.
6. 34
7. -525
8. .875
Evaluate the each expression. (PEMDAS)
10. 14 + (6 ÷ 2)
11. [18 – (6 + 4)] ÷ 2
12. 8(4² ÷ 8 – 32)
13.
9. √30
6  9  3  15
82
Evaluate each expressions when a = 8, b = -3, c = 4 and d = - ½ .
14. 5(6c – 8b + 10d)
15. (b – c)² + 4a
16. d(a + c)
17. b – c + 4 ÷ d
Simplify each expression.
18. 8(3a – b) + 4(2b – a)
19. 4(10g + 80h) – 20(10h – 5g)
20. 40s + 18t – 5t + 11s
21. 50(3a – b) -20(b – 2a)
Solve each Equation. Check your solution.
22. 4m + 2 = 18
23. -3b + 10 = -15 + 2b
24. -5x = 3x – 24
Evaluate each expression if w = -4, x = 2, y = ½ , and z = -6.
25. | 2x – 8 |
26. | 6 + z | - | -7 |
27. | wz | - | xy |
28. 12 - | 10x – 10y |
Solve each equation. Check your solutions.
29. | x + 15 | = 37
30. | t – 4 | - 5 = 0
31. | 3x – 1 | = 2x + 11
32. | 16 – 3x | = 4x – 12
Solve the inequality then graph the solution set on a number line.
33. 3a + 7 ≤ 16
34. 4(5x + 7) < 13
35. 2z < -9 + 5z
36. -3 ≤ x + 4 ≤ 8
37. 2x – 5 > 1 or 2x – 5 < -1
0
0
0
0
0
38. | 2x – 9 | ≤ 7
0
39. | x + 2 | > 1
0
CHAPTER 2
Determine whether the relation or equation is a function.
1. {(6, 3), (2, 1), (-2, 3)}
2. {(-5, 2), (2, 4), (1, 1), (-5, -2)}
3. {(2, 3), (2, 4), (2, 6)}
4.
y
1
1
Evaluate the function.
5. f(x) = | x | Find f(-5)
6. f(x) = x² - x – 1 Find f(1) – f(3)
7. f(x) = 2(x² - 4) + 1 Find f(0)
8. f(x) = 3x – 4 Find f(2) + f(-8)
Graph the equation.
9. –2y = 4x + 2
10. 6x = -12y + 48
y
y
2
1
2
1
Find the slope of the line that passes through each pair of points. Then tell whether the line rises, falls, is
horizontal, or is vertical.
11. (-6, -3), (6, 7)
12. (5.5, -5.5), (11.5, -7.5)
13. (-3, 24), (-3, -41)
Tell whether the lines are parallel, perpendicular, or neither.
14. Line 1: through (3, 2) and (1, 5)
15. Line 1: through (-3, -1) and (4, -8)
Line 2: through (-1, 6) and (2, 8)
Line 2: through (5, 3) and (4, 2)
16. Line 1: through (-2, 1) and (-5, 3)
Line 2: through (0, 3) and (3, 5)
17. Line 1 through: (0, 6) and (-5, 0)
Line 2 through: (-4, 4) and (2, -1)
Write an equation in slope-intercept form for the line that satisfies each set of conditions.
18. Slope of 3, passes through (-6, 9)
19. Passes through (3, -8) and (-3, 2)
20. Passes through (-1, 2), parallel to the graph of y = 3x + 6.
21. Passes through (3, 2), perpendicular to the graph of 2y = 3x + 4
Graph the inequality.
22. y < 3x – 5
y
2
23. x > y – 1
24. y + 2x  4
y
1
2
y
1
1
1
CHAPTER 3
Graph the linear system and tell how many solutions it has. If there is exactly one solution, find it graphically.
x y  4
1)
2)
x y  2
y
y  2x  1
3)
2 y  6x
y
1
1
1
1
1
Solve using substitution.
 3x  4 y  1
5)
x  2y  1
Solve using elimination.
6)
2 y  4 x  10
y
1
4)
y  x2
3x  3 y  6
7)
4x  2 y  7
6 x  2 y  11
4x  y  6
 2x  3 y  8
x  5 y  4
Graph the following system of linear inequalities. Clearly identify the solution.
8)
x  2y  4
9)
 3x  y  1
y
1
1
Solve the linear system of 3 variables.
10)
x  5 z  13
z  2
2x  3y  6
y
1
2 x  4 y  3z  0
x  4y  8
1
Perform the indicated operation(s), if possible.
1 

0
2


(8)  2  7 


4
2 


11)
1
12)  9

 5
 4
0 6  2   3 5
  3 4     1 8

1
5
 
 


 6 0 3 6 
7   1 4 7
3  2 5 8
 1 2  4 1 


 4 3 0  1
13)  

14) 
Solve the matrix equation for x and y.
1 1 3 2   5

   
16) 2  1 4  1  y

   
3 0 2  x  2 
 2 x 0   4 0
15) 


 4  y  4 1
Evaluate the determinant.
  3  1
17) 

  7  2
a b 
18) 

c d 
19)
 1 2 1 
2
0 0

 3  4 2
Find the inverse.
 7  4

 5 3 
20) 
 3  1

 5 2 
21) 
Write the matrix equation that corresponds to the linear system.
15) 2x + 3y = 6
16) y = 8
3x + y = -1
3x + y = 1
Use an inverse matrix to solve the linear system.
18)
 3x  4 y  1
x  2y  1
19)
17) 3x + 4y + z = 16
2x + 3y – z = 2
x+ y +z=1
9 x  5 y  43
 2 x  2 y  22
CHAPTER 4
Graph the quadratic function. Label the vertex and axis of symmetry.
1. y = x² + 3x – 4
2. y = (x + 3)² - 4
3. y = (x + 1)(x – 4)
Factor the trinomial. If the trinomial cannot be factored, say so.
4. x² +8x + 15
5. m² - 9m + 20
6. 6x² + 5x – 6
7. 9a² - 56a + 12
8. n² - 49
9. 4x² - 4x – 35
Solve the equation for x.
10. x² + 10x + 21 = 0
11. 3x² - 24x – 27 = 0
12. x² - 8x = -15
Simplify the expression.
13.
32
14.
125
15. 3 27  3
16.
15  3
17.
81
125
18.
16
25
Solve the equation
19. x² = 144
20. 2x² = 200
21. 7x² = 175
22. x² = -16
23. 6x² = -216
24. 4(x + 5)² = -8
Write the expression as a complex number in standard form.
25. (3 + 5i) + (2 + i)
26. (9 – 2i)(9 + 2i)
27.
2i
4i