Placement Exam For Level B - Summer High School Program, 2015

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2015 Summer High School Program
Placement Exam for Level B
NAME: ______________________
Multiple Choice: Indicate your answer in the box to the right of each question.
3
4
1. Evaluate −3��
− ( 20 − ��
) when �� = −2
(a) 20
(b) -10
(c) 28
(d) -12
(e) None of these
1.
2. Which day of the week comes 60 days after Tuesday?
(a) Wednesday (b) Thursday
(c) Friday
(d) Saturday
(e) Sunday
2.
2
9
7
1
�� +
�� = −3 and
�� −
�� = 2, what is the value of 4�� − 8��?
3. If
5
5
5
5
24
(a) 20
(b) 24
(c) -16
(d) −
(e) None of these
5
3.
245
4. What is the remainder when 2
is divided by 11?
(a) 4
(b) 6
(c) 8
(d) 10
(e) None of these
4.
5. Troy writes down the number 1. Each minute, Troy writes down a number 1 more than twice the
previously written number. Of all the numbers Troy writes, which is closest to 1000?
(a) 977
(b) 997
(c) 1017
(d) 1023
(e) None of these
5.
4
3
2
6. How many distinct positive factors does 2
3
4
have?
(a) 21
(b) 27
(c) 45
(d) 60
(e) None of these
6.
��
��
2
7. If the roots of �� = ��
− 5�� + 2 are �� and ��, compute the value of
+
.
��
��
29
20
21
(a) −
(b)
(c)
(d) 7
(e) None of these
10
7
2
7.
2
2
8. If ( �� + �� )
= 49 and ( �� + �� )
= 9, how many possible values can �� − �� take?
(a) 1
(b) 2
(c) 4
(d) Infinitely many
(e) None of these
8.
2
9. Compute the number of intersections of the graphs of �� = | ��
− 1 | and �� = �� + 1
(a) 0
(b) 1
(c) 2
(d) 3
(e) None of these
9.
1 of 4
Page
New York Math Circle

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