Placement Exam For Level C Worksheet - Summer High School Program, 2015
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42015 Summer High School Program
Placement Exam for Level C
NAME: ______________________
Multiple Choice: Indicate your answer in the box to the right of each question.
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1. Evaluate −3��
− ( 20 − ��
) when �� = −2
(a) 20
(b) -10
(c) 28
(d) -12
(e) None of these
1.
3
5
2. The coefficient of ����
�� in ( �� + �� + �� )
(a) 15
(b) 20
(c) 25
(d) 30
(e) None of these
2.
��
��+3
3. Solve for ��: 4
= 2
+ 9
(b) log
3
(c) log
3
(d) log
9
(a) 0
(e) None of these
2
4
2
3.
√ 5
4. If sin �� + cos �� =
then sin 2�� equals
2
1
√ 5
1
1
(b) −
(d) −
(a)
(c)
(e) None of these
4.
4
4
2
2
5. Compute the tens digit of 1! + 2! + 3! + ⋯ + 2015!
(a) 1
(b) 3
(c) 9
(d) 0
(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.
8. If 2 cos ��, 3 sin ��, 4 tan �� form a geometric sequence (in that order), find sin ��
2
3
5
8
(a)
(b)
(c)
(d)
(e) None of these
3
4
6
9
8.
9. In a circle of radius �� a chord of length 24 splits the perpendicular diameter into segments whose
lengths are in a ratio of 1:9. Compute ��.
(a) 8 √ 13
(d) 10 √ 10
(b) 20
(c) 15
(e) None of these
9.
1 of 4
Page
New York Math Circle
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