Algebra Math
sjsaaorabi
FinalMAth96.pdf
Final Exam Name___________________________________ Silva Math 96 Spring 2020
YOU MUST SHOW ALL WORK AND BOX YOUR ANSWERS FOR CREDIT. WORK ALONE. Solve the absolute value inequality. Write your answer in interval notation.
1) |2x - 12 |> 2
Solve the compound inequality. Graph the solution set. Write your answer in interval notation.
2) -4x > -8 and x + 4 > 3
Solve the three-part inequality. Write your answer in interval notation.
3) -1 < 3x + 2 < 14
Solve the absolute value equation. 4) 4x + 9 = 2x + 7
Solve the compound inequality. 5) 3( x + 4 ) ≥ 0 or 4 ( x + 4 ) ≤ 4
Solve the inequality. Graph the solution set and write your answer in interval notation.
6) |5k + 8| > -6
Solve the inequality graphically. Write your answer in interval notation .
7) x + 3 ≥ 1
x-8 -6 -4 -2 2
y
8
6
4
2
x-8 -6 -4 -2 2
y
8
6
4
2
1
Graph the system of inequalities. 8) 2x + 8y ≥ -4
y < - 3 2 x + 6
x-10 -8 -6 -4 -2 2 4 6 8 10
y 10
8
6
4
2
-2
-4
-6
-8
-10
x-10 -8 -6 -4 -2 2 4 6 8 10
y 10
8
6
4
2
-2
-4
-6
-8
-10
Find the determinant of the given matrix. 9) 10 5
0 -4
Use Cramer's rule to solve the system of linear equations.
10) 6x + 5y = -12 2x - 2y = -4
Write a system that models the situation. Then solve the system using any method. Must show work for credit.
11)A vendor sells hot dogs, bags of potato chips, and soft drinks. A customer buys 3 hot dogs, 4 bags of potato chips, and 5 soft drinks for $14.00. The price of a hot dog is $0.25 more than the price of a bag of potato chips. The cost of a soft drink is $1.25 less than the price of two hot dogs. Find the cost of each item.
Use row reduced echelon form to solve the system. 12) x + y + z = 3
x - y + 4z = 11 5x + y + z = -9
2
Find the domain of f. Write your answer in interval notation.
13) f(x) = 13 - 9x
If possible, simplify the expression. If any variables exist, assume that they are positive.
14) 2x + 6 32x + 6 8x
Match to the equivalent expression. 15) 100-1/2
A) 1 1000
B) 1 10
C) 1 100
D) 1 10
Write the expression in standard form. 16) (5 + 8i) - (-3 + i)
Simplify the expression. Assume that all variables are positive.
17) 5 t 5
z10
Solve the equation. 18) 3x + 1 = 3 + x - 4
Write the expression in standard form.
19) 3 + 3i 5 + 3i
3
Write the equation in vertex form. 20) y = x2 + 5x + 2
The graph of ax2 + bx + c is given. Use this graph to solve ax2 + bx + c = 0, if possible.
21)
x-5 5 10
y 50 40 30 20 10
-10 -20 -30 -40 -50
x-5 5 10
y 50 40 30 20 10
-10 -20 -30 -40 -50
Solve the equation. Write complex solutions in standard form.
22) 4x2 + 5x + 5 = 0
Graph the quadratic function by its properties.
23) f(x) = 1 3 x2 - 2x + 3
x
y
x
y
Solve the equation. Find all real solutions. 24) 2(x - 1)2 + 11(x - 1) + 12 = 0
Solve the problem. 25) The length of a table is 12 inches more than its
width. If the area of the table is 2668 square inches, what is its length?
4
Solve the equation. 26) log9 (x - 3) + log9 (x - 3) = 1
27) Alice invests $12,000 at age 25 from the signing bonus of her new job. She hopes the investments will be workth $20,000 when she turns 40. If the interest compunds continuously, approximately what rate of growth will she need to achieve her goal?
28) Graph, on the same coordinate system, the inverse of the one- to- one funciton shown.
x-4 -3 -2 -1 1 2 3 4
y
4
3
2
1
-1
-2
-3
-4(-4, -4)
(-3, 1) (0, 2)
(2, 4)
x-4 -3 -2 -1 1 2 3 4
y
4
3
2
1
-1
-2
-3
-4(-4, -4)
(-3, 1) (0, 2)
(2, 4)
Solve the equation. 29) 7x - 1 = 17 (Round to the nearest
hundredth.)
30) 3x2=81
Find f-1(x). 31) f(x) = 4x3 + 7
Simplify the expression, if possible.
32) log2 5 1 4
5
Find the center and radius of the circle. 33) x2 + 4x + y2 = 5
Use the graph to determine the equation of the ellipse. 34)
x-10 -5 5 10
y 10
5
-5
-10
x-10 -5 5 10
y 10
5
-5
-10
Graph the parabola. 35) x = y2 - 4
x-10 -5 5 10
y 10
5
-5
-10
x-10 -5 5 10
y 10
5
-5
-10
Graph the equation. 36) 36y2 - 9x2 = 324
x-10 -5 5 10
y 10
5
-5
-10
x-10 -5 5 10
y 10
5
-5
-10
Match the function with its corresponding graph 37) A. f(x) = |x| B. f(x) = x
C. f(x) = x2 D. f(x) = 2x E. f(x) = log x F. f(x) = x I. II.
x-2 -1 1 2
y 2 1
-1 -2
x-2 -1 1 2
y 2 1
-1 -2
x-2 -1 1 2
y 2 1
-1 -2
x-2 -1 1 2
y 2 1
-1 -2
III. IV.
x-2 -1 1 2
y 2 1
-1 -2
x-2 -1 1 2
y 2 1
-1 -2
x-2 -1 1 2
y 2 1
-1 -2
x-2 -1 1 2
y 2 1
-1 -2
V. Vi.
x-2 -1 1 2
y 2 1
-1 -2
x-2 -1 1 2
y 2 1
-1 -2
x-2 -1 1 2
y 2 1
-1 -2
x-2 -1 1 2
y 2 1
-1 -2
6
