Jakarta International School 8 th Grade AG1 Summative Assessment

Transcription

1 Jakarta International School 8 th Grade AG1 Summative Assessment Unit 6: Quadratic Functions Name: Date: Grade: Standard Advanced Highly Advanced Unit 6 Learning Goals NP Green Blue Black Radicals and Radical Equations Polynomial Properties and Operations Classifying Polynomials Adding and Subtracting Polynomials Multiplying Polynomials Factoring Quadratic Expressions Graphing Quadratic Functions Solving Quadratic Equations Factoring and Zero Product Property Quadratic Formula Completing the Square (blue and black only) Applications of Quadratic Functions NP = Not Proficient Green = Standard Level Blue = Advanced Black = Highly Advanced A - All learning goals are met within the topic of study - Accurate, clear, organized, and attentive to detail at all times - Sophisticated understanding shown through communication of higher order thinking B - Most of the learning goals are met within the topic of study - Accurate, clear, organized, and attentive to detail most of the time - Considerable understanding shown through communication of higher order thinking C - Some of the learning goals are met within the topic of study - Accurate, clear, organized, and attentive to detail some of the time - Some understanding shown through communication of higher order thinking D - Few or none of the learning goals are met within the topic of study - Rarely accurate, clear, organized, and attentive to detail - Limited understanding shown through communication of higher order thinking Unit 6 Summative Assessment 1

2 Read all instruction carefully. Choose your level of problems carefully. You must do an entire problem to receive credit. Do not do additional problems until you have completed the requirements of the test. Show all steps of your work and check work carefully. Part I: Polynomial Properties and Operations 1. (ALL) Identify each polynomial by degree AND terms. Variable Expression Degree Number of terms Name 5x 3 2x 23x 3w 2 7w 2 2. (ALL) Simplify the follow expressions completely. Write your answer in Standard Form. a. (x + 3)(-2x + x + 4) b. (2x + 5) 2 3. (GREEN) Simplify (7n 3 + 2n 2! n! 4)! (4n 3! 3n 2 + 8) 3. (BLUE) Solve for k. [-4x 2 + kx 4] [-3x 2 (k+2)x+5] = -x 2 10x 9 (BLACK) Find the values of a and b [2ax 2 (b+5)x 4] [(b+2)x 2 (a-7)x 8]= -x 2 9x + 4 Unit 6 Summative Assessment 2

3 4. (GREEN) Simplify ( 8y 3)( 2y 1) 4. (BLUE) What non-zero integer must be placed in the square so that the simplified product of these two binomials is a binomial? ( 8x+ 4)( 4x+W ) 4. (BLACK) The product of two positive numbers is 15, and the sum of their squares is 85. What is the square of their differences? Unit 6 Summative Assessment 3

4 Part II: Graphing Quadratic Functions 1. (ALL) Match the following functions to the graphs below. For each, give as many reasons as possible to support your choice. A. y = (x + 4)(x - 4) B. y = -x 2-2x + 3 C. y = -x D. y = (x - 5)(x - 5) E. y = x 2 + 2x - 3 F. y = (x + 5)(x + 5) i. Function ii. Function Reason: Reason: iii. Function iv. Function Reason: Reason: Unit 6 Summative Assessment 4

5 For all graphing, give the x-intercept(s), y-intercept, vertex, axis of symmetry and graph the function. Clearly show your work or reasoning for each answer. 2. (GREEN) 2. (BLUE) 2. (BLACK) Graph y = x 2 + 4x 5 Graph y = 4x 2 + 4x + 1 Graph Y = -6x 2 + 5x + 4 x-intercept(s): axis of symmetry: vertex: y-intercept: x-intercept(s): axis of symmetry: vertex: y-intercept: x-intercept(s): axis of symmetry: vertex: y-intercept: Unit 6 Summative Assessment 5

6 Part III: Solving Quadratic Equations 1. (ALL) Solve the following quadratic equations. You must solve one by factoring and one by quadratic formula. You must show all your work. a. 3x 2 2x = 10 b. 3x 2 14x = (GREEN) Solve x 2 5 = -4x 2. (BLUE) Solve for x x 10x 10 = 2. (BLACK) Solve for t = 0 2 t t 3. (GREEN) Solve 3m 2!12m +12 = 0 3. (BLUE) Solve 2x + 10 = x (BLACK) Solve x+ 8 x+ 9 x+ 10 x+ 11 = x+ 7 x+ 8 x+ 9 x+ 10 Unit 6 Summative Assessment 6

7 4. (GREEN) Solve by factoring 4x 2 9 = 0 4. (BLUE) Solve by factoring x 4 29x = 0 4. (BLACK) Write the equation, in standard form, of the quadratic function passing through the points (1, 7), (-1, 5), and (-2, 10). 5. (GREEN) Solve by quadratic formula x = 5x 5. (BLUE) Solve by completing the square show steps 4x 2 + 8x 5 = 0 5. (BLACK) Derive the quadratic formula by solving ax 2 + bx + c = 0 by completing the square. Show your steps clearly! Unit 6 Summative Assessment 7

8 Part IV: Applications of Quadratic Functions 1. (ALL) Use the vertical motion model, h =!16t 2 + vt + s, where: h = height at time t t = time in motion s = starting height v = starting velocity (speed) A diver jumps from a ledge 32 feet above the water with an initial upward velocity of 16 feet per second. A. Graph this situation. B. What is the maximum height reached by the diver before his vertical descent? C. Find the time it takes for the diver to enter the water. 2. (GREEN) Originally a rectangle was 8 meters long and 5 meters wide. When both dimensions were decreased by the same amount, the area of the rectangle 2 decreased by 22 m. Find the dimensions of the new rectangle. 2. (BLUE) An Expanding Circle: When the radius of a circle was increased by 6 inches, the area of the circle increased by 125%. What was the length of the original radius? 2. (BLACK) Let P(x, y) be a point on the graph y = x + 5. Connect P with Q(7, 0). Let a perpendicular from P to the x-axis intersect the x-axis at point R. Restricting the domain of P to 0 x 7, find the maximum area of ΔPRQ. Unit 6 Summative Assessment 8

9 3. (GREEN) The sum of the squares of two consecutive positive integers is 61. Find the integers. 3. (BLUE) The floor of a large parking garage has an area of 400 square meters. The garage is 30 meters longer than it is wide. A. If each car is 2 meters long by 1 meter wide, how many lines of cars, squeezed into the garage from bumper to bumper, will fit in the parking garage? B. How many cars will be in each row? 3. (BLACK) At his usual rate a man rows 15 miles downstream in five hours less than it takes him to return. If he doubles his usual rate, the time downstream is only one hour less than the time upstream. What is the rate of the stream s current? Unit 6 Summative Assessment 9