Download Review for the 1 st Sem Final

Review for the 1 st Sem Final for Algebra 2C
Chapter 1
Evaluate the expression
#1.
-6 + 3(-3 + 7)2
#1.
16 ÷ (2 + 6) • 10
#2.
5(n2 + n) – 3(n2 – 2n)
#3.
4(-3x + 1) = -10(x – 4) – 14x
#4.
Solve for P: I = Prt
Simplify the expression
#2.
12(n – 3) + 4(n – 13)
Solve the equation
#3.
2(x + 6) = -2(x – 4)
Solve for the given variable
#4.
Solve for h: V = 1/3 πr2h
Solve
#5.
You are working on a project in woodshop. You have a wooden rod that is 72
inches long. You need to cut the rod so that one piece is 6 inches longer than the other
piece. How long should each piece be?
#5.
You have 480 feet of fencing to enclose a rectangle garden. You want the length
of the garden to be 30 feet greater than the width. Find the length and width of the garden
if you use all of the fencing.
Solve and graph the inequalities.
#6.
-16 ≤ 3x – 4 ≤ 2
#6.
-5 ≤ -n – 6 ≤ 0
#7.
| 10 – 4x | = 2
#7.
| 8x + 1 | = 23
#8.
| 4n – 12 | > 16
#8.
| 4x + 10 | < 20
Chapter 2
Graph the function
#9.
y=x–3
#9.
y = 2x + 7
Find the Slope of the line passing through the given points
#10.
(1,- 4), (2,6)
#10.
(4,2), (-18,1)
Tell whether the lines are parallel or perpendicular
#11.
Line 1: through (-1,9) and (-6,-6)
Line 2: through (-7,-23) and (0,-2)
#11.
Line 1: through (4,-3) and (-8,1)
Line 2: through (5,11) and (8,20)
Graph the equations
#12.
5x – 6y = -2
#12.
3x + 0.2y = 2
#13.
x = -10
#13.
y=¾
Write the equation of the line that passes through the given points.
#14.
(2,0), (4,-6)
#14.
(-5,9), (-4,7)
The variables x and y vary directly. Find x when y = -5
#15.
x = 6, y = 3
#15.
x = -5, y = -1
#16.
2x + 3y > 4
#17.
f(x) = {x + 6
{ -2/3 x – 3
#18.
y = - | x +2 | + 11
Graph the inequality
#16.
9x – 2y ≤ -18
Graph the functions
#17.
f(x) = { 2x
{ -x + 3
if x ≥ 1
if x < 1
Graph the function
#18.
y=|x|+9
if x ≤ -3
if x > -3
Chapter 3
Solve the system of equations
#19.
7x – 4y = -3
2x + 5y = -7
#19.
3x + 2y = 6
-6x – 3y = - 6
#20.
-9x + 6y = 0
-121x + 8y = 0
#20.
6x – y = -2
-18x + 3y = 4
#21.
y > -3x
x ≤ 5y
Graph the system of equations
#21.
y ≥ -4
y < -2x + 10
Find the minimum and maximum value of the objective function subject to the given
constraints.
#22.
Objective function
C = 2x + 3y
#22.
Constraints
x≥0
y≥0
x+y≤9
Objective function
C = x + 4y
Constraints
x≥2
x≤5
y≥1
y≤6
Sketch the graph of the equation
#23.
x+y+z=7
#23.
x + 6y + 4z = 12
Solve the system using the substitution method
#24.
x + 2y + 5z = - 1
2x – y + z = 2
3x + 4y -4z = 14
#24.
3x + 2y – z = 8
-3x + 4y + 5z = -14
x – 3y + 4z = -14
Chapter 4
Perform the indicted operation
#25.
 1  4  3 5 
  7 2  +   5 2

 

#25.
 3 5 
 0  1 

 2  7
 4 9 


#26.
 7  7
 2  4
2
+ 4


 5  6
 1 3 
#26.
 7 1 0 
4  1  7 
3
-2 


8  6  2
 3  5 5
Solve for x and y
#27.
 2x  8
  10  9 =


y
 6
 10  9


Find the product
1  4  4  1
#28. 

 
3  2  x 3 
#29.
 x 4  1
 2 3 2 


 5 8 1 
Solve for x, if the determinant is -77
#27.
 3x  2  4 0   16  2
 1 8  +  7  8 =  y
0 
 

 
#28.
  6  2   1 4
 x
3   5 3

#29.
 8 x 9
12 3 9 


 3 13 4
Solve for x, if the determinant is 441
Solve the system using Cramer’s rule
#30.
x + 7y = - 3
3x – 5y = 17
#30.
9x + 2y = 7
4x – 3y = 42
Solve the matrix equation by using the inverse matrix
#31.
 5  13
 3 1
X = 
0


5 

  4 0
#31.
5  1
17 20
8 2  X = 26 20




Use the inverse matrix to solve the linear system
#32.
3x + y = 8
5x + 2y = 11
#32.
2x + 7y = - 53
x + 3y = - 22
Chapter 5
Graph the quadratic function. Label the vertex and axis of symmetry
y = 2x2 – 12x + 19
#33.
y = -2(x + 3)2 – 4
#34.
2x2 + 7x + 3
#34.
3x2 + 17x + 10
#35.
49 – 100x2
#35.
25b2 – 60b + 36
#36.
2y2 – 4y – 8 = -y2 + y
#33.
Factor
Solve the equation
#36.
5p2 – 25 = 4p2 + 24
Simplify the expression
#37.
#38.
___
√175
_____
√ 18/13
#38.
____
√ 605
_____
√ 45/32
#37.
Solve the equation
#39.
x2 = 90
#39.
2x2 + 5 = 41
#40.
5(x – 7)2 = 135
#40.
-3(x + 2)2 = -18
#41.
2x2 + 9 = - 41
#41.
5x2 + 18 = 3
#42.
( -1 – i) + (9 – 3i)
(5 + i)(8 + i)
#43.
(2 – 9i)(9 – 6i)
3+i
3–i
#44.
2 + 5i
5 + 2i
Add or Subtract
#42.
( -4 + 7i) + (- 4 – 6i)
Multiply
#43.
Divide
#44.
Write the quadratic function in vertex form
#45.
y = x2 – 6x + 11
#45.
y = x2 + 16x + 14
Solve the equation
#46.
x2 + 14 = 10x
#46.
x2 = 8x - 35
#47.
-2u2 + 5 = 3u2 – 10u
#47.
11m2 – 1 = 7m2 +2
#48.
y > -3x2 + 5x – 4
Graph the inequality
#48.
y ≤ -x2 + x + 6
Write a quadratic function in vertex form whose graph has the given vertex and passes
through the given point.
#49.
Vertex: (2,-1)
Point: (4,3)
#49.
Vertex: (- 4,6)
Point: ( - 1,9)
Chapter 6
Simplify the expression
#50.
(x2y2) – 1
#50.
-3x- 4y0
#51.
y 10 • 20x14
2x3
xy6
#51.
12xy • 7x5y2
7x4
4y
Use synthetic substitution to evaluate the polynomial function for the given value of x
#52.
f(x) = -4x3 + 3x – 5 ; x = 4
#52.
f(x) = 3x5 – 2x2 + x ; x = 5
Describe the ending behavior of the graph of the polynomial function by completing the
statement; f(x) → ____ as x → - ∞ and f(x) → ______ as x → + ∞.
#53.
f(x) = 3x6 – x – 4
#53.
f(x) = x7 – 3x3 + 2x
#54.
(6x2 – 19x + 5) – (19x2 – 4x + 9)
#55.
(2x + 5)(3x3 – x2 + x)
#56.
3x3 – 2x2 – 9x + 6
#57.
x3 + 8x2 = -16x
#58.
16x4 – 1
Add or Subtract
#54.
(10x3 – 4x2 + 3x) + (x3 – x2 + 1)
Multiply
#55.
(x + 8)(x2 – 7x – 3)
Factor completely
#56.
2x3 – 5x2 + 18x – 45
Solve the equations
#57.
x3 + 27 = 0
Factor completely
#58.
32x6 – 2x2
Factor completely
#59.
x3 – 8
#59.
x3 + 64
(x4 – 6x3 – 40x + 33) ÷ (x – 7)
#60.
(4x4 + 5x3 + 2x - 1) ÷ (x + 1)
Divide
#60.
Given one zero of the polynomial find the remaining zero
#61.
f(x) = 4x3 + 9x2 – 52x + 15; one zero is -5
#61.
f(x) = 5x3 – 27x2 – 17x - 6; one zero is 6
Find all the zero of the function
#62.
f(x) = x3 + x2 – 2x – 2
#62.
f(x) = x3 + 9x2 – 4x – 36