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TALLAHASSEE STATEWIDE
ALGEBRA II TEAM ROUND – CONDENSED TEST
1/14/2017
1) Match each example with the property it illustrates.
A) a •
1
= 1, a  0
a
1) Closure
2) Identity
3) Associative Property
4) Commutative Property
5) Inverse
B) If a  R and b  R,then a  b R
C) (a + b) + c = c + (a + b)
D) a • 1 = a
2) Let Z1 is 2x +5 = 3 , Z2 is 3x - 1 + 2 > 10 , Z3 is
x+4
 1 , and Z 4 is x 4 = 256
x+4
A = the sum of the solutions for Z1
{B} = {solutions for Z1} ∩ {Real solutions for Z4}
{C} = {solutions for Z1} U {solutions for Z3}
D = the sum of the smallest positive integer solution for Z2 and the largest Real integer
solution for Z4.
3) f(x) = 5x + 3
g(x) = -2x2 + 8x – 2
h(x) = 3x - 6 + 2
j(x) =
x +5
x + 2x -15
2
A = the sum of the solutions for g(x)
B = the solutions where h(f(x)) = 44
C = j(f(x)) when simplified, where defined
D = the maximum point, (x, y), for g(x). This answer is an ordered pair.
4) Find A and B so that the solutions to x2 + 10x + 29 = 0 in the form A + Bi and A - Bi,
where i =
-1 , B > 0, and A is a positive integer.
Find C and D so that the quadratic equation in the form x2 + Cx + D = 0 has one solution
-6 + 3i 5 , where i =
-1 .
1
TALLAHASSEE STATEWIDE
ALGEBRA II TEAM ROUND – CONDENSED TEST
1/14/2017
5) Venkat is reading the book, “War and Peace”, for fun. The product of the facing pages
Venkat is on is 15,750. Assume these page numbers are consecutive Natural Numbers and
the book’s page numbers are numbered consecutively beginning with page one. What are the
page numbers?
A = the larger of the page numbers
B = the smaller of the page numbers
C = the units digit for 2375 + 6451 + 9347 + 42123
D = the most simplified version of i2017 + i1999 + i42 + i-2 where i =
29
58

where i =
5 + 2i 50 + 20i
6) A =
C, D
1
Simplify for x > 1 : 1 + x
1
11+ x
B = 7log933
-1 .
to
-1 .
C
D
7) Solve each equation or problem and assemble the four solutions.
i)
6x - 7 3x - 5 5x + 78
+
=
4
7
28
iii) 2x(42x-1) = 8 • 2x-5
ii)
x +5 - 1 = x
iv) The remainder for
3x 2 + 4x - 6
x+3
A = the largest of the answers for parts i, ii, iii, and iv.
B = the second largest of the answers for parts i, ii, iii, and iv.
C = the third largest of the answers for parts i, ii, iii, and iv.
D = the smallest of the answers for parts i, ii, iii, and iv.
8) A = the positive solution of 2x2 + 2x – 2 = x – x2
B = [log3(log283)]2
C = the sum of the first six triangular numbers if the first triangular number is one.
-1
3 2
D = the determinant of 

 4 2
2
TALLAHASSEE STATEWIDE
ALGEBRA II TEAM ROUND – CONDENSED TEST
1/14/2017
9) At the M & N Ranch, Jessica is planning to build a corral for Enrie’s cows using a fence for
the three sides of the corral and the Cao River as the fourth side. The side parallel to the river
will be y feet long and the two sides perpendicular to the river will each be x feet long. The
total perimeter of the fence will be 900 feet.
A : Write an equation expressing y in terms of x.
B : Write a polynomial, in descending powers of x, for the area of the corral in square
feet.
C = the maximum area of the corral in square feet.
D = the value(s) of x that make the area of the corral equal to zero.
10) Find the ordered pair (A, B) that satisfies the system of equations :
6 7
- =8
A B
15 14
= 21
A B
The polynomial P(x) = x3 + Cx2 + Dx + 10 has factors x + 1 and x – 1. Find the values of
C and D.
11) A) Solve. log2(A – 1) + 1 = log2A
C) Solve. C = log3
9
3
3
B) Solve. (log481)(log316) = B
D) Find D.
3
6
256 ÷ 4 64 = 2D
TALLAHASSEE STATEWIDE
ALGEBRA II TEAM ROUND – CONDENSED TEST
12) A
B, C
1/14/2017
Solve the following if D and E are digits : (DD)E = DEED where DD is a two digit
number and DEED is a four digit number. A = DEED
There are 2 trees in a garden (trees "B" and "C") and on the both trees are some
birds. The birds of tree B say to the birds of tree C that if one of you comes to our
tree, then our population will be the double of yours.
Then the birds of tree C tell to the birds of tree B that if one of you comes here,
then our population will be equal to that of yours.
Now answer : How many birds are in each tree? Let B = the number of birds in
tree B and C = the number of birds in tree C.
D
Michael has 9 red socks, 5 white socks, and 8 blue socks in his dresser drawer.
What is the minimum numbers of socks he must draw out, one at a time to
guarantee he will have 5 socks of the same color ?
13) Given x2 – 2x < 8.
A = the largest integer solution
B = the smallest integer solution
Given 2x3 – x2 - 18x + 9 = 0.
C = the sum of the roots
D = the sum of the roots taken two at a time
14) A = 16708 written as a base ten number.
B = The Arabic number for the Roman numeral DCCXLVI.
C = The binary (base 2) numeral for the base ten numeral 57.
x +1
D = the value of f(g(23)) if f(x) = 2x – 1 and g(x) =
2
4
TALLAHASSEE STATEWIDE
ALGEBRA II TEAM ROUND – CONDENSED TEST
5
1/14/2017