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TALLAHASSEE STATEWIDE ALGEBRA II TEAM 1) Match each example with the property it illustrates. A) a • 1 = 1, a 0 a B) If a R and b R,then a b R C) (a + b) + c = c + (a + b) 1) Closure 2) Identity 3) Associative Property 4) Commutative Property 5) Inverse D) a • 1 = a TALLAHASSEE STATEWIDE ALGEBRA II TEAM 1) Match each example with the property it illustrates. A) a • 1 = 1, a 0 a B) If a R and b R,then a b R C) (a + b) + c = c + (a + b) D) a • 1 = a 1) Closure 2) Identity 3) Associative Property 4) Commutative Property 5) Inverse TALLAHASSEE STATEWIDE 2) Let Z1 is 2x +5 = 3 , Z2 is 3x - 1 + 2 > 10 , Z3 is ALGEBRA II TEAM 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. TALLAHASSEE STATEWIDE 2) Let Z1 is 2x +5 = 3 , Z2 is 3x - 1 + 2 > 10 , Z3 is ALGEBRA II TEAM 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. TALLAHASSEE STATEWIDE 3) f(x) = 5x + 3 g(x) = -2x2 + 8x – 2 ALGEBRA II TEAM 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. TALLAHASSEE STATEWIDE 3) f(x) = 5x + 3 g(x) = -2x2 + 8x – 2 ALGEBRA II TEAM h(x) = 3x - 6 + 2 j(x) = 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. x +5 x + 2x -15 2 TALLAHASSEE STATEWIDE ALGEBRA II TEAM 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 . TALLAHASSEE STATEWIDE ALGEBRA II TEAM 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 . TALLAHASSEE STATEWIDE ALGEBRA II TEAM 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 = TALLAHASSEE STATEWIDE -1 . ALGEBRA II TEAM 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 = -1 . TALLAHASSEE STATEWIDE 6) A = C, D 29 58 where i = 5 + 2i 50 + 20i 1 Simplify for x > 1 : 1 + x 1 11+ x ALGEBRA II TEAM B = 7log933 -1 . to C D TALLAHASSEE STATEWIDE 6) A = C, D 29 58 where i = 5 + 2i 50 + 20i 1 Simplify for x > 1 : 1 + x 1 11+ x ALGEBRA II TEAM B = 7log933 -1 . to C D TALLAHASSEE STATEWIDE ALGEBRA II TEAM 7) Solve each equation or problem and assemble the four solutions. i) 6x - 7 3x - 5 5x + 78 + = 4 7 28 x 2x-1 iii) 2 (4 )=8•2 x-5 ii) x +5 - 1 = x 3x 2 + 4x - 6 iv) The remainder for 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. TALLAHASSEE STATEWIDE ALGEBRA II TEAM 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 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. 3x 2 + 4x - 6 x+3 TALLAHASSEE STATEWIDE ALGEBRA II TEAM 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 TALLAHASSEE STATEWIDE ALGEBRA II TEAM 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 TALLAHASSEE STATEWIDE ALGEBRA II TEAM 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. TALLAHASSEE STATEWIDE ALGEBRA II TEAM 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. TALLAHASSEE STATEWIDE ALGEBRA II TEAM 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. TALLAHASSEE STATEWIDE ALGEBRA II TEAM 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. TALLAHASSEE STATEWIDE 11) A) Solve. log2(A – 1) + 1 = log2A C) Solve. C = log3 9 3 3 ALGEBRA II TEAM B) Solve. (log481)(log316) = B D) Find D. 6 TALLAHASSEE STATEWIDE 11) A) Solve. log2(A – 1) + 1 = log2A C) Solve. C = log3 9 3 3 256 ÷ 4 64 = 2D ALGEBRA II TEAM B) Solve. (log481)(log316) = B D) Find D. 6 256 ÷ 4 64 = 2D TALLAHASSEE STATEWIDE 12) A B, C ALGEBRA II TEAM 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 ? TALLAHASSEE STATEWIDE 12) A B, C ALGEBRA II TEAM 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 ? TALLAHASSEE STATEWIDE ALGEBRA II TEAM 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 TALLAHASSEE STATEWIDE 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 ALGEBRA II TEAM TALLAHASSEE STATEWIDE ALGEBRA II TEAM 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 TALLAHASSEE STATEWIDE 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 ALGEBRA II TEAM