FEBRUARY REGIONAL
ALGEBRA I INDIVIDUAL
1) Solve. 6x + 33 + 5x = 11(x + 3)
A) -3
B) ø
C) all Real numbers
D) 3
E) NOTA
2) If you chose two Real numbers, A and B, then either A > B, A < B, or A = B, is an example of
which property?
A) commutative
B) symmetric
D) trichotomy
C) transitive
E) NOTA
3) Write using symbols. Seven less than the product of four and x is divided by the quantity one
added to the product of four and x.
A)
4x - 7
1+ 4x
B)
4x - 7
+ 4x
1
C)
7 - 4x
1+ 4x
D)
7 - 4x
+ 4x
1
E) NOTA
4) Doug Upp must shovel a pile containing 100 ft3 of dirt into his dump truck. With each scoop, he
1 3
moves
ft of dirt from the pile to the dump truck. How much dirt is left in the pile after x
6
scoops?
A) 100 +
1
x
6
B) 100 -
1
x
6
C) 100
1
x
6
D) 99
5) Solve for x. 2(3x – 7) – (2x + 5) = -7(x + 10) + 5(4x – 7) – 17x
A) ∅
6) Solve for x.
B) -
43
8
C) -
43
4
D) -12
E) NOTA
x + A 6x + 4A
=
B
C
A) 4AB – AC
D)
B) AC – 4AB
4AB - AC
C - 6B
C)
E) NOTA
1
4AB - AC
6B - C
5
x
6
E) NOTA
FEBRUARY REGIONAL
ALGEBRA I INDIVIDUAL
7) Which of these inequalities is graphed on this number line?
-6
A) x - 1 < 7
8
B) x - 1 ≤ 7
D) x - 1 ≥ 7
C) x - 1 > 7
E) NOTA
8) All of the 20 members of the Deer Lake girls basketball teams are either 13 years old, or 63
inches tall, or both. Fifteen of the girls are 13 years old while twelve of the girls are 63 inches tall.
How many of the girls are either 13 years old or 63 inches tall, but not both?
A) 27
B) 13
C) 8
D) 7
E) NOTA
9) Given A = {1, 2} and B = {a, b, c}, find A X B.
A) 2abc
B) 3a + 3b + 3c
C) {(a, 1), (b, 1), (c, 1), (a, 2), (b, 2), (c, 2)}
D) {(1, a), (1, b), (1, c), (2, a), (2, b), (2, c)}
E) NOTA
10) Solve. 3 x - 4 + 6 x - 4 + 18 = 0
A) ∅
B) all Real numbers
C) {2, 6}
D) {-2, -6}
E) NOTA
11) Solve 2x +1 ≥ 11 . Then, find the sum of the integers that make up its solution.
A) -1
B) 5
C) 6
D) ∞
E) NOTA
12) Solve for x, then find the product of the solutions.
A) 4
B) 2
13) Find the rate of change for
A)
8
3
B)
3
8
C)
4
5
3 5x - 6 = 81
D) −
693
25
E) NOTA
D) −
8
3
E) NOTA
x y
- =2.
8 3
C) −
3
8
2
FEBRUARY REGIONAL
ALGEBRA I INDIVIDUAL
14) Jessica is taking a taxi from the airport to the Cao Hotel. It costs her $2 just to get into the
taxi, a cents for the first mile and b cents for each additional sixth of a mile. The hotel is x miles
from the airport. How much is Jessica’s fare in cents if x > 1?
A) 200 + a + 6b(x – 1)
B) 200 + a +
1
b ( x - 1)
6
C) 200 + a + 6bx
D) 200 + a +
1
bx
6
E) NOTA
15) Currently, Ronnie is 26 years older than Steve. Twenty-nine years ago, Ronnie was twice as
old as Steve. Find the sum of their present ages.
A) 136
B) 81
C) 55
D) 26
E) NOTA
16) What is the name given to the degree of the polynomial 6xy – 2x + 3y?
A) trinomial
1 1
+
3 4
17) Simplify.
1 1
+
2 6
B) quadratic
A)
7
8
C) linear
B) 1
C)
D) cubic
8
7
E) NOTA
D) 12
E) NOTA
18) Ilya decided to use Cramer’s Rule to solve a system of equations in two variables. In order to
find the variables x and y (respectively), he set up the following matrices :
 12 7 3 12 


 5 -1 , 4 5 
 3 7 3 7 


 4 -1 4 -1 
Which of these is the system of equations Ilya is trying to solve?
A) 3x + 12y = 7
4x + 5y = -1
B) 3x + 7y = 12
4x - y = 5
D) 12x + 7y = 3
5x - y = 4
C) 7x + 3y = 12
-x + 4y = 5
E) NOTA
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FEBRUARY REGIONAL
ALGEBRA I INDIVIDUAL
19) What is the range of the figure at the right?
A) ∞
B) -2 < x < 2
C) y > 2
D) y < 2
E) NOTA
20) The square of the sum of the first and third of four consecutive even integers is 3600. Find
the greatest of the four integers.
A) 3602
B) 602
C) 306
D) 34
E) NOTA
21) (2x – 3)(x2 + 5x – 6) = Ax3 + Bx2 + Cx + D. Find A + B – C + D.
A) 0
B) 36
C) 40
D) 54
E) NOTA
22) When factored completely, one of the factors of x3 + 4x2 – 9x – 36 is ….
A) x – 6
B) x – 4
C) x – 3
D) x – 2
E) NOTA
23) Evaluate if m = -8, n = 4, and p = 2. n2 – m2 + p3n2 ÷ m2.
A) -46
B) -10
C) 1.25
D) 82
E) NOTA
24) Andy just won $20,000 in the Pokemon Sweepstakes! He invested part of the money into an
account that made a profit of 8% and the remainder into an account that lost 12% of that part of
the investment. Andy lost $800 overall for both investments. How much money did Andy
initially invest in the account that made the profit of 8%?
A) $16,000
B) $12,000
E) NOTA
C) $8000
D) $4000
25) (5x – 7y)2 = Ax2 + Bxy + Cy2. Find A + B + C.
A) -70
B) 4
C) 74
D) 144
4
E) NOTA
FEBRUARY REGIONAL
ALGEBRA I INDIVIDUAL
26) Neha has a pool and deck outside of his house.
The pool is square in shape measuring (x + 2) on
each side. The deck is rectangular in shape and its
dimensions, including the pool, are (x + 5) by
x+5
(2x – 3). Find the area of the deck alone (shaded
part of the picture).
A) 2x2 + 7x – 15
B) x2 + 11x + 11
C) x2 + 4x + 4
D) x2 + 3x – 19
x+2
2x – 3
E) NOTA
27) The Math Club raised money to go to the February Regional by having a car wash. They
charged $5 for each car and $8 for each truck. They washed a total of 63 vehicles and made $402.
How much money did the Math Club make by washing the trucks?
A) $232
B) $170
C) $34
D) $29
E) NOTA
28) Which of the following is an example of a quadratic binomial?
A) 3x4 + 7x2
B) x4 – 2x2 + 3
D) 2x2 + 2x + 2
C) 4x2 – 5
E) NOTA
29) Which of the following is the equation of a line perpendicular to y = -5.
A) 4x = 9
B) 4x + y = 9
D) y = 9
C) x – 5y = 9
E) NOTA
5
FEBRUARY REGIONAL
ALGEBRA I INDIVIDUAL
30) Which of the following does not represent a function?
A)
B)
X
Y
C)
D)
E) NOTA
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