MATH 1010 Final Exam
University of Utah
April 30, 2010
Instructor: Knaeble
Name:
ID number:
• There are 20 problems, each worth five points, for a maximum score of 100 points. There is
also a 5-point extra credit problem.
• You are not allowed to get help from your textbook, class notes, calculators, other students,
or any other form of outside aid. If you have questions, please ask your instructor. You may
not talk with other students during the exam.
• To be considered for partial credit you must show your work.
• Where appropriate, clearly indicate your final answer by circling it.
Question
Points
1
Score
Question
Points
5
11
5
2
5
12
5
3
5
13
5
4
5
14
5
5
5
15
5
6
5
16
5
7
5
17
5
8
5
18
5
9
5
19
5
10
5
20
5
Total:
50
Total:
50
1
Score
1. 5 points Simplify:
(1 + 2)2
3−1
4 2
2. 5 points Which two values of x satisfy the equation?
|7 − 2x| = 15
Page 2
3. 5 points Write an equation for the line.
4
3
y
2
1
–4
–3
–2
–1
0
1
2
3
4
x
–1
–2
–3
–4
1
4. 5 points A line through (2, 3) has slope m = . Write an equation for this line.
2
Page 3
5. 5 points Find the domain of the function:
f (x) =
x+2
x2 − 1
6. 5 points Simplify. [Hint: you may want to factor first]
x2 − 4
x+2
· 2
x − 2 x + 4x + 4
Page 4
7. 5 points Solve the following system of linear equations:
2x + 3y = 4
−4x + y = 6
8. 5 points Solve the following equation:
x2 − 1 = −6x
Page 5
9. 5 points Multiply and then simplify:
(3x2 + x + 2)(x2 + 2x + 1).
10. 5 points Find each number that, when added to its reciprocal, gives
Page 6
10
.
3
11. 5 points Train A leaves the station at 12:00 noon traveling straight west at 70 miles per hour.
Train B leaves the station at 1:00 pm traveling straight west at 60 miles per hour. At what
time will they be 100 miles apart? Show your work.
Page 7
12. 5 points Find the solution(s) to the equation:
√
5x + 15 = x + 3
13. 5 points Simplify the expression:
√
3
x2
Page 8
6
14. 5 points Consider the functions f (x) = x + 3 and g(x) = x2 and compute the following:
1. f ◦ g(1)
2. g ◦ f (1)
15. 5 points The equation x2 − x + 1 = 0 has no real solutions. What are the complex (or
imaginary) solutions?
Page 9
16. 5 points A ball falls according to the equation p(t) = −16t2 − 16t + 96. When will it hit the
ground? In other words, for what positive t will p(t) equal zero?
17. 5 points Sketch the graph of the equation x = y 2 . Label at least three points.
5
y
0
-5
0
5
x
-5
Page 10
18. 5 points Compute the following logarithms:
(a) log4 (64)
(b) log2 (0.5)
(c) log6 (4) + log6 (9)
19. 5 points Sketch the graph of y = 2x . Label at least three points.
5
y
0
-5
0
5
x
-5
Page 11
20. 5 points Solve for x:
3x = 9100 .
21. 5 points (bonus) Which number is bigger: 21010 or 10102 ? Briefly explain your reasoning.
Page 12