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M115 (Beginning Algebra, Fall 2015)
Final Exam
You must show work. Insufficient/inadequate work receives no credit.
Solve the equation.
9
1
1 7
1) x + x = 2x + + x
8
8
4 8
Name:
2) 0.7(5x + 15) = 2.3 - (x + 3)
1)
2)
Solve the problem.
3) Midtown Antiques collects 4.5% sales tax on all sales. If total sales including tax are $
1615.24, find the portion that is the tax. Round to the nearest cent if necessary.
Solve the inequality using interval notation.
4) -5(4y + 3) < -25y + 25
3)
4)
Solve using the addition and multiplication principles.
2
5) (2x - 1) < 2
3
5)
Write an equation in slope-intercept form of the line satisfying the given conditions.
6) Through (-2, -5), parallel to 2x + 3y = -22
7) Through (-9, -6), perpendicular to -6x + 7y = 96
6)
7)
1
Find the equation for the graph.
8)
8)
Graph the equation.
9) 3x - y = 3
9)
Find an equation of the line containing the given pair of points. Write your final answer as a linear function in
slope-intercept form.
10) (6, -6) and (-1, 2)
10)
Simplify. Do not use negative exponents in your answer.
-4
x 6 y4
11)
wz 5
11)
Divide.
12) ( 4 m 2 + 11 m - 45 ) ÷ (m + 5 )
12)
2
13)
-4x3 - 16x2 - 7x + 20
-2x - 5
13)
Find the x-intercepts for the graph of the equation.
14) y = x2 - x - 42
14)
List all numbers for which the rational expression undefined.
x2 - 4
15)
x2 + 3x - 54
Simplify, if possible.
t3 + 64
16)
t3 - 4t2 + 16t
16)
Multiply and, if possible, simplify.
3x + 9 4x2 + 8x + 4
·
17)
x+1
x2 - 9
Solve.
15)
17)
18) One maid can clean the house three times faster than another. Working together they can
clean the entire house in 3 hours. How long would it take the faster maid cleaning alone?
3
18)
Solve the problem.
19) Fred bicycles 6 km/h slower than Samantha. In the time it takes Fred to bicycle 24 km,
Samantha travels 36 km. How fast does Fred bicycle?
Solve. If no solution exists, state this.
-40
= -3
20) x +
x
21)
19)
20)
y
y
y
+
=
2
2
2
y - 7y + 10 y - 4 y - 3y - 10
21)
Solve using the substitution method.
22) 5x - 2y = -1
x + 4y = 35
22)
Solve using the elimination method.
23) 8x - 7y = 7
-4x - 3y = 3
23)
4
Solve the problem.
24) The total sales made by a salesperson was $24,000 after 3 months and $72,000 after 23
months. Predict the total sales after 32 months.
1. Find the equation of the line in slope intercept form: S = mt + b
2. Predict the total sales after 42 months.
5
24)