THE CITY COLLEGE OF NEW YORK
PRECALCULUS
MATH 19500 - BC
SPRING 2016
EXAM 1
First and Last Name:
Time Allowed: 60 minutes
Materials Allowed: Black writing utensil (preferable pencil), and eraser.
Forbidden Materials: Calculators, and Phones. No electronics.
Problem Points Earned
1
2
3
4
5
6
EC
TOTAL
/ 90
PERCENT
%
1
2
Problem 1 (+5 each). Choose exactly 2 of the 3 expressions below. Draw the indicated set on a
real number line. Remember to label enough points to make your drawing clear. X-out the part
you do not want graded.
(a) [−1, 1) ∩ [0, 10]
(b) (−∞, 3) ∪ [5, +∞)
(c) [0, 2] ∩ [1, 3]
3
Problem 2 (+5 each). Choose exactly 2 of the 3 expressions below. Preform the indicated operation and simplify completely. X-out the problem you don’t want graded.
(a)
1
2
−
=
x + 1 (x + 1)2
(b)
x+1
2
+
=
x2 − 1 x − 1
(c)
x
2
− =
x−1 x
4
Problem 3 (+5 each). Choose exactly 2 of the 3 expressions below. Preform the indicated operation and simplify completely. X-out the problem you don’t want graded.
(a)
x2 − 4 x2 − 1
·
=
x−1 x−2
(b)
x + 1 x2 + 2x + 1
÷
=
x
x−1
(c)
x
2
÷ =
x−1 x
5
Problem 4 (+10 each). Choose exactly 2 of the 3 expressions below. Simplify the following
expressions and rationalize each denominator. X-out the problem you don’t want graded.
√
2− 5
√ =
(a)
3 2
x2 − y
(b) p
√ =
x− y
(c)
xy
√ =
1− 2
6
Problem 5 (+10 each). Choose exactly 2 of the 3 expressions below. Solve the given equation for
all real x. If no real x solve the given equation, then explain why. X-out the problem you don’t
want graded.
(a) x2 − 6x = −9
(b) |2x − 1| = 4
(c)
√
x−1+
√
x=1
7
Problem 6 (+10 each). Choose exactly 2 of the 3 expressions below. Solve the given equation for
all real x. Write your final answer in interval notation. If no real x solve the given equation, then
explain why. Feel free to use drawings to help you. X-out the problem you don’t want graded.
(a) −6x < −9
(b) x2 − 6x + 9 > 0
(c)
x
>3
x+1
8
Extra Credit (+2 Each). Only attempt if you have plenty of time and you have checked your
answers. The extra credit is not worth as much as one problem part in the exam.
E1. Evaluate the sum 1 + 2 + 3 + 4 + 5 + 6 + · · · + 998 + 999 + 1000
E2. What number when you add one to it then take the square root of the resultant number yields
the initial number? (Solve for the number in terms of radicals). This number goes by the name of
the golden ratio.