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Unformatted text preview: Mathematics 1 1 2 'EXAM I Name: Instructor: Date: February 22, 2005
1. There are 11 problems on the exam
2. No graphing or programmable calculators are allowed. Scientiﬁc calculators are allowed
but are not needed.
3. Give exact answers (fractions, square roots, etc.). Decimal approximations may not
receive full credit.
. . . . 33 2
4. Please do not Simpllfy unless expllutly told so. Answers such as :r = ills—L6 are okay.
Answers such as 3x+4=7x2 require more simpliﬁcation.
5. No notes or books are allowed.
6. Use only the scratch paper provided.
7. Show your work and make your methods clear. Unjustiﬁed answers will receive no credit.
8. For each problem put your ﬁnal answer inside the box. Score E
P — H
H
O H
O H
O O H H
O H
D
H
o H
O H
H
H
N TOTAL POINTS 1. (10 points) Set an equation to ﬁnd the sum of the ﬁrst hundred terms of a geometric sequence where the . . . 1
second term 15 a2 = 3 and the common ratlo IS 7" = LEAVE THE EXPRESSION SO THAT IT CAN BE EVALUATED WITH A CALCULA
TOR, BUT YOU DO NOT NEED TO EVALUAT‘E THE EXPRESSION. 2. (10 points) Solve the inequality. Write the answer in interval notation.
2
1c — 8:5 — 9 IE <0 3. (10 points) Find all real solutions of the equation 11$" + 3162 ~ 1 = 0 4. (10 points) Find the equation of the line tangent to the circle x2 + 312 = 25 at the point
(—3,4). Write your answer in slopeintercept form. 5. (6 points). The endpoints of a line segment .71? are A(4,1) and B(10,3) as shown in the
ﬁrst graph below. Use the following three graph papers to sketch the reﬂection of AB about a) yaxis b) xaxis c) origin points. Include the coordinates of the end 10 10 10 10 6. (6 points )
Rewrite the sum using sigma notation. 1 2 3 4 49 ~+—+—+—+ .... ..+— 10 102 103 104 7. (10 points) The points P(—4, 3) and Q(8, 7) are the endpoints of a diameter of a circle.
Find the equation of the circle passing through these points. 8. (10 points) Sally runs 2 mph faster than Pat throughout a 4 mile race. If Sally ﬁnishes
6 minutes ahead of Pat, What was Sally’s time for the race? Write your answer in minutes. 9. (6 points) Solve for r in terms of h. Simplify as much as possible. 27T’I‘2 + 27rrh = 201r 10 10. (10 points) Solve the inequality and specify the answer using interval notation. [213—3
4 1:4 11 11. (4 points each ) For the following problems simplify as much as possible. (Give an exact answer using radicals,
not a decimal approximation.) a) Perform the indicated operations and simplify as much as possible. 4x/2_4—8\/5_4+\/6 in I
b) Carry out the indicated operation and simplify as much as possible. 1 1
2+h m
h c) Rewrite the expression using rational exponents instead of radicals. 12 HS SCRATCH 13 ...
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 Spring '08
 Carlson
 Algebra

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