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Test Booklet Subject: MA, Grade: HS CST High School Algebra II Part 1 Student name: Author: California District: California Released Tests Printed: Wednesday January 15, 2014 CST High School Algebra II Part 1 1 What is the complete solution to the equation |3 − 6x| = 15 ? A B C D x = 2; x = 3 x = −2; x = 3 x = 2; x = −3 x = −2; x = −3 2 What are the possible values of x in |12 − 4x| = 2 ? A B C D x = −2.50 or x = −3.50 −3.50 < x < −2.50 MA:HS 5 A restaurant manager bought 20 packages of bagels. Some packages contained 6 bagels each, and the rest contained 12 bagels each. There were 168 bagels in all. How many packages of 12 bagels did the manager buy? A B C D 6 8 9 12 6 What system of inequalities best represents the graph shown below? 3.5 > x > 2.5 x = 2.50 or x = 3.50 3 For a wedding, Shereda bought several dozen roses and several dozen carnations. The roses cost $15 per dozen, and the carnations cost $8 per dozen. Shereda bought a total of 17 dozen flowers and paid a total of $192. How many roses did she buy? A B C D 6 dozen 7 dozen 8 dozen 9 dozen 4 What is the solution to the system of equations shown below? 2x − y + 3z = 8 x − 6y − z = 0 −6x + 3y − 9z = 24 A B C D Page 1 (0, 4, 4) 1, 4, 10 3 no solution infinitely many solutions A B C D y > −2 and y > x + 1 y > −2 and y < x + 1 y < −2 and y > x + 1 y < −2 and y < x + 1 7 Which point lies in the solution set for the system 2y − x ≥ −6 2y − 3x < −6 A B C D ? (-4, -1) (3, 1) (0, -3) (4,3) Go On CST High School Algebra II Part 1 8 Which system of linear inequalities is represented MA:HS 10 by this graph? A B C D x3 + 7x2 − 7x + 6 − 2x3 + 14x2 − 14x + 12 − 4 2x + 7 x3 + 7x2 − 7x + 6 + 4 2x + 7 polynomial (3x2 + x − 4) (2x − 5) ? A B C D y ≥ 12 x + 3 y ≥ x − 2 y ≥ 2x + 3 y ≤ x − 2 Page 2 6x3 + 13x2 + 3x − 20 6x3 + 13x2 + 3x + 20 12 (−2x2 + 6x + 1) − 2 (4x2 − 3x + 1) = 2x + y ≥ 3 x − y ≥ 2 13 Which A B C D 6x3 − 13x2 − 13x + 20 2x − y ≥ 3 x + y ≤ 2 equations? 2x − 3y = 4 4x + y = −6 represents 6x3 − 13x2 − 13x − 20 A B C D 9 What is the solution to the following system of 4 2x + 7 x3 − 7x2 + 7x − 6 + 11 Which A B C D 4 2x + 7 6x2 − 1 −10x2 − 1 6x2 + 12x − 1 −10x2 + 12x − 1 expression (6y 2 − 2) (6y + 2) ? A B C D is equivalent 36y 2 − 4 36y 3 − 4 36y 2 + 12y 2 + 12y − 4 36y 3 + 12y 2 − 12y − 4 (5,-2) (-2, 5) (-1,-2) (-2,-1) Go On to CST High School Algebra II Part 1 14 What is the volume of the figure below? MA:HS 17 The total area of a rectangle is 4x4 − 9y2 ? Which factors could represent the length times width? A B C D (2x2 − 3y) (2x2 + 3y) (2x2 + 3y) (2x2 + 3y) (2x − 3y) (2x − 3y) (2x + 3y) (2x − 3y) 18 Which product of factors is equivalent to (x + 1)2 − y 2 ? A B C D x3 + 10x2 + 34x + 24 A B C D x3 + 11x2 + 34x + 24 x3 + 10x2 + 24x + 24 3 2 x + 11x + 24x + 24 15 What is (5x3 − 2x) (3x2 + x − 8) ? A B C D 16 3 A B C D 2 15x + 5x − 46x − 2x + 16x 15x6 − 35x3 − 6x2 + 14x 3 (x − 1 + y) (x − 1 − y) (x + 1 + y) (x + 1 − y) tion of 12x2 − 147 ? 15x5 − x4 − 42x3 + 16x 4 (x + 1 − y)2 19 Which expression shows the complete factoriza- 5x3 + 3x2 − x − 8 5 (x + 1 + y)2 (3x − 7) (4x + 2) (4x − 21) (3x + 7) 12 (x − 7) (x + 7) 3 (2x − 7) (2x + 7) 3 8a + c = A B C D Page 3 (2a + c) (2a + c) (2a + c) (2a − c) (4a2 + 2ac + c2 ) (2a − c) (4a2 + 4ac + c2 ) (2a + c) (4a2 − 2ac + c2 ) 20 25x2 − 40xy + 16y 2 A B C D (5x − 4y)2 (5x + 10 − 4y)3 5 (5x − 4y)2 5 (4xy)2 Go On CST High School Algebra II Part 1 x+3 x+5 21 A B x2 + x x2 + 3x −10 C x2 + x + 12 x2 + 3x −10 D x2 + x + 1 x2 + 3x −10 + 6 x2 + 3x − 10 2 24 Which product is equivalent to 4x2 −−x16 ? = A B C D 7x − 9 x2 + 3x −10 22 Which is a simplified form of A B C D MA:HS 3a2 b3 c−2 (a−1 b2 c)3 ? −4 C D 25y 3 18x 25 18xy 7 −4 (x − 2) −4 (x + 2) x2 + 4x x+3 8x−3 15y −5 x2 − 9 x2 + x − 12 = 26 What is the simplest form of ? 5x3 y + 20x2 y 2 + 20xy 3 5xy A B C D (x + 2)2 (x + 2y)2 x2 + y 2 x2 + 4y 2 2x2 − 10x x2 + 8x + 16 27 Page 4 · A 1 B x C x + 4 D xx −+33 23 What is 20x ÷ 27y 2 32y 3 81x 32 81xy 7 4 (x + 2) 25 3a5 b3 c5 3ab c5 3 b2 c5 3 ab3 c5 A B 4 (x − 2) A 8x (x + 4)(x − 5) B 2x + 4 (x + 4)(x −+ 5) C 8x (x + 4)(x + 5) D 2x + 4 x2 + 20 · 4x + 16 x2 − 25 = Go On CST High School Algebra II Part 1 4(x + y) 5x2 y 3 28 A − B −2x − 2y 10 = 31 Which of the following complex numbers is represented by the point on the graph below? 4 x2 y 3 4 x2 y 3 C − D ÷ MA:HS 4(x + y) x2 y 3 (x − y) 4(x + y)2 5x2 y 3 √ −1 , which point shows the location of 5 − 2i on the plane? 29 If i = A B C D 4 + 3i 4 − 3i 3 − 4i 3 + 4i 32 If i = A B C D point A point B point C √ Page 5 −1 , then 4i (6i) = 48 24 -24 -48 point D 30 If i = −1 , what is the value of i4 ? A B C D A B C D √ i -i 1 33 What is an equivalent form of 3 +2 i ? A B C D 3−i 4 3−i 5 4−i 4 4−i 5 -1 Go On CST High School Algebra II Part 1 MA:HS 34 What is the product of the complex numbers 38 What are the solutions to the equation x2 + 2x + (3 + i) and (3 − i) ? 2 = 0? A B C D A B C D 8 10 9–i 10 – 6 i √ −1 and a and b are non-zero real = numbers, what is a +1 bi ? 35 If i A B C D 39 What are the solutions to the equation 1 + 1 x2 = 3 x 3 2 + B x = 3 + a + bi a2 − b2 C x = a − bi a2 − b2 D x = 3 + − −8 − 3i −8 − i 2 − i 2 − 3i (12 − 5i) and (−3 + 4i) ? 9–i 15 − 9i 3 2 ? √ a − bi a2 + b2 37 What is the sum of the complex numbers Page 6 x = −1 + i; x = −1 − i √ √ x = −1 + 2 2; x = −1 − 2 2 A x = (−5 + i) ? A B C D x = 0; x = −2i a + bi a2 + b2 36 Which expression represents (−3 − 2 i) A B C D x = 0; x = −2 + √ 5 5 3 ; x = − 2 2 2 √ √ 5 5 ; x = 3 − 2 2 √ √ 13 ; x = 23 − 213 2 √ √ 13 13 ; x = 3 − 2 2 40 There are two numbers with the following properties. 1) The second number is 3 more than the first number. 2) The product of the two numbers is 9 more than their sum. Which of the following represents possible values of these two numbers? A B C D −6, −3 −4, −1 −1, 4 −3, 6 −16 + 63i 9 − 9i Go On CST High School Algebra II Part 1 41 Jenny is solving the equation x2 − 8x = 9 by completing the square. What number should be added to both sides of the equation to complete the square? A B C D 2 4 8 16 MA:HS 45 Which of the following sentences is true about the graphs of y = 3 (x − 5)2 y = 3 (x + 5)2 + 1 ? + 1 and A Their vertices are maximums. B The graphs have the same shape with different vertices. C The graphs have different shapes with different vertices. D One graph has a vertex that is a maximum, 42 Two consecutive positive integers have the property that one integer times twice the other equals 612. What is the sum of these two integers? while the other graph has a vertex that is a minimum. 46 What are the x -intercepts of the graph of y = A B C D 33 35 37 39 43 What are the solutions to the equation x2 − 6x + 12x2 − 5x − 2 ? A 1 and 16 B −1 and 16 C 23 and − 14 D − 23 and 14 5 = −8 ? A B C D 2 and 3 2i and 3i 3 + 2 · 3 and 3 − 2 · 3 3 + 2i and 3 − 2i 44 Which of the following most accurately describes the translation of the graph y = (x + 3)2 − 2 to the graph of y = (x − 2)2 + 2 ? A B C D Page 7 up 4 and 5 to the right down 2 and 2 to the right down 2 and 3 to the left up 4 and 2 to the left Go On CST High School Algebra II Part 1 MA:HS 47 Which is the graph of y = −2 (x − 1)2 + 1 ? A C B D 48 Which ordered pair is the vertex of f (x) = x2 + 6x + 5 ? A B C D Page 8 (−3, −4) (−2, −3) (−1, 0) (0, −5) STOP