Elizabeth City State University
Elizabeth City, North Carolina27909
2014
STATE REGIONAL MATHEMATICS CONTEST
Level I
TEST BOOKLET
Directions:
Each problem in this test is followed by five suggested answers. When
you have decided which of the suggested answer is correct, shade the
corresponding circle on the answer sheet.
Sample question:
A) 6
54 – 48 =
B) 7
C) 16
D) 12
E) None of these
Sample answer:
B C D E
Answer A is marked since the difference between 54 and 48 is 6.
You will have 80 minutes to work on the 40 questions in this test booklet.
Page 1
Elizabeth City State University
Regional Math Contest - 2014
Level I/ Algebra I
1. If r {3,6} and s {1, 2} , the largest value of 3r - s is:
A) 16
B) 19
C) 7
D) 10
E) None of these
2. If a is any real number, for what value(s) of b does the equation x  a  b have NO
solutions?
A) all b < 0
B) Only b = -1
C) Only b = 0
D) All b 
E) None of these
3. Given that r ≠ 0 and r = 5w = 7a, find the value of r - w in terms of a.
A) a/7
B) 7a/5
C) 3a
D) 28a/5
E) None of these
4. Solve the following for x:
A) 3 - c
B) 3  c
2
C)
c
3
2
D)
c
6
2
E) None of these
2x + c = 6.
Page 2
5. Given  x  a 2  x 2  a , solve for x.
A) x = a
B) x  0
C)
a 1
x
2
D)
a2  1
x
2
E) None of these
6.
x2  y2
x y
x # 7 = 3, then which of the following is a possible value of x?
-10
-7
-4
3
None of these
The operation # is defined as: x # y 
If
A)
B)
C)
D)
E)
7. A wire x inches long is bent into the shape of a circle. Express the area of the circle (in
square inches) in terms of x.
A) 3.52 
B) x 2
2
C) x 2
4
D) x 2
4
E) None of these
8. If x2 + y2 = 25 and x2 - y2 = 7 then x4 - y4 = ?
A) 7
B) 14
C) 49
D) 175
E) None of these
Page 3
9. If the three points (-2, -1), (x, 2) and (8, 14) are collinear, the the value of x is:
A) 1
B) 1.5
C) 2
D) 3
E) None of these
10. Which of the following polynomials below is identical to the polynomial (x2 - 1)(x2 - 4)?
A) x4 + 4
B) x4 - 5x2 + 4
C) (x2 + 1)(x2 + 4)
D) (x2 + x - 2)(x2 - x - 2)
E) None of these
11.
m 2  at
, find the expression for t.
z
A)
pz  m 2
t
a
2
B)
m  pz
t
a
C)
pz
t
 m2
a
D)
m2
t  apz 
a
E) None of these
Given p 
12. Solve for x, given:
A) x = 1
B) x = -1
C) x = -2
D) x = -3
E) None of these
y=x-1
and
y = 2x + 1
Page 4
13. If the ratio of the legs of a right triangle is 4/3, and the hypotenuse is 25 cm, what is the
area of the triangle?
A) 625 2 cm2
B)
4
44 cm2
9
C) 25 2 cm2
D) 300 cm2
E) None of these
14. Think of a 2-digit number, and call it "N." Double it and add 12. Then divide that sum
by two and subtract your original number, N. What is the result?
A) 6
B) N
C) 12
D) N + 6
E) None of these
15. If
x  3 9 , then what does x2 equal to?
A) 3 81
B) 3
C) 9 3 9
D) 9 3
E) None of these
16.
if x  1
3x
Suppose that the function f is defined such that f ( x)  
2
( x  1) if x  1
If a is negative then f(1 - a) =
A) (2 - a)2
B) a2
C) 3 - 3a
D) 3a
E) (a - 1)2
Page 5
17. A line contains (2, -7) and (-4, 2). Which statement is not true?
A) The line has y-intercept -4
B)
11 

The line contains  1,  
2

C) The line is parallel to 3x - 2y = 6
D) The line is perpendicular to 3y - 2x = 4
E) No portion of the graph of the line lies in the first quadrant
18. Two polynomials in x are of degrees r and s, respectively. One of the polynomials is
multiplied by the cube of the other. Which of the following could be the degree of the
product?
A) 3r + s
B) r3 + s
C) r + s2
D) 3rs
E) None of these
19. Which of the following sets does NOT represent a function?
I.
 x, y  | y  2 x  1
II.
III.
IV.
V.
A)
B)
C)
D)
E)
20. If
A)
B)
C)
D)
E)
 x, y  | x
2
 y 2  10, y  0
 3,1 ,  4,1 ,  5, 2  ,  6, 2  ,  7,3
 x, y  | y  2  1
 x, y  | x  y  2, x  0
x
2
2
I
II
III
IV
V
x + y = 11 and
91
11
136
59
None of these
xy = 15, find the value of x2 + y2.
Page 6
21. The difference of two numbers is 2. If the difference of their squares is 18, what is their
sum?
A) 20
B) a number between 10 and 16
C) a number between 5 and 8
D) this value can not be determined
E) None of these
22. Two fair dice are rolled. What is the probability that the difference of the squares of the
numbers is divisible by three?
A) 1/3
B) 11/18
C) 1/2
D) 5/9
E) None of these
23.
Given f ( x ) 
x 1
, which expression is equivalent to f(1-x)?
x 1
A)
x
x2
B) x  2
1 x
C) 4  4 x  x 2
x 1
D) x  1
x2  1
E) none of these
24.
The equation
A)
B)
C)
D)
E)
x3
1
has 2 solutions. Their product is:

2
x4
6
7
10
12
None of these
Page 7
25. The length of a rectangular pen is one more than twice it width. If both dimensions are
increased by 5 units, which expression gives the resulting increase in area?
A) 15x + 30
B) 16x + 30
C) 2x2 + 11x + 30
D) 2x2 + 16x + 30
E) None of these
26. When a polynomial P(x) is divided by x - 2, the quotient is 3x2 - x - 5 and the remainder is
-1. Then P(1) equals
A) 2
B) 3
C) 4
D) 7
E) None of these
27. For all positive integers x, let x# be defined as the sum of the integers from 1 to x,
inclusive. Which of the following equals 6# - 5# ?
A) 1#
B) 2#
C) 3#
D) 5#
E) None of these
28.
The coefficient of c2d2 in the expansion of
A)
B)
C)
D)
E)

28
56
64
70
256
29. If (x + 3) is a factor of x3 - 2kx + k2, then k is:
A) 3
B) -3 or 9
C) 3 or -9
D) -3
E) None of these
Page 8
c d

8
is:
30. Find the equation of a line parallel to 3x - 5y = 15 that intersects the line y = x at x =
3.
A)
5
y  x2
3
B)
5
y   x 8
3
C)
3
6
y  x
5
5
D)
3
y  x3
5
E) y  3x  6
31. The display on a digital clock reads 6:38. What will the clock display twenty-seven digit
changes later?
A) 7:01
B) 7:03
C) 7:05
D) 7:07
E) None of these
32. Find real numbers k and p such that x 2  7 2   x  7 2  2 p ( x  7)  k  x  7 2 .
A) k = 7, p = 2
B) k = 2, p = 7
C) k = 1, p = 3
D) k = 2, p = 14
E) k = 2, p = 2
33. If 2 x  15 , then determine the value of
A) 15 2
B) 9 15
C) 45
D) 30 3
E) 75
0.6  8 x .
Page 9
34. Suppose p and q are distinct primes. Which of the following statements are true?
I. p + q is never prime.
II. pq has exactly 4 positive integer factors.
III. The least common multiple of p and q is 1.
A) I only
B) II only
C) III only
D) I and II
E) II and III
35. Find all values of x satisfying the following conditions:
y1 = 7x, y2 = (4x + 1), and y2 exceeds y1 by 2.
A)  1 
 
3
B)  1 
 
11 
C)  1 
 
 3
D)  1 
 
 11 
E)  1 
 
 11 
36. If
A)
B)
C)
D)
E)
f ( x  1)  x 2  3 x  5 , then find f(x).
x2 + 3x + 4
x2 + x + 3
x2 + 2x + 4
x2 - x + 2
x2 - 2x + 2
Page 10
37. Factor and simplify the algebraic expression:
A)
 x  5
B)
 x  5 5  x  6
C)
1
6
5
  x  5
6
5
5
( x  6)
6
5
( x  6)
 x  5
E)
  x  5
1
6
 x  5
D)
5
 x  5
1
5
none of these
38. The hot water faucet in a bathtub can fill the tub in H minutes, the cold water faucet in C
minutes. If I first turn on the hot water faucet, and then, a minute later, turn on the cold
water faucet as well, how many minutes will it take to fill the tub?
A) H  (C  1)
2
B) H (C  1)
CH
C)
HC
CH
D)
HC
1
CH
E) H (C  1)
CH
39. Find the next two numbers in this sequence: 245, 125, 65, 35, ...
A) ..., 20, 12.5, ...
B) ..., 20, 10, ...
C) ..., 25, 15, ...
D) ..., 25, 20, ...
E) None of these
Page 11
40. Which of the following is not a rational number?
A)
1.777...
B)  9.123123123...2
C)
D)
E)
1.5129


1
5 3

2 1
2

2
2
3 8
Page 12
Answer Key
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
35.
36.
37.
38.
39.
40.
B
A
D
C
E
E
D
D
E
B
B
C
E
A
C
B
C
A
E
A
E
E
A
C
A
A
C
D
C
C
A
B
C
B
C
B
C
B
A
D
Page 13