Honors Algebra 2 Midterm Review Packet

Transcription

1 Honors Algebra 2 Midterm Review Packet This packet contains problems that are similar in content and format to those that you will see on your midterm the week of January 12th. You will be expected to complete a similar amount of work in 1 hour and 40 minutes. Your midterm will be out of 100 points. All questions are worth 2 points unless otherwise noted. The material on this review and the midterm covers Chapters 1-5. Reviewing all tests and quizzes is also recommended. You will be permitted the use of a calculator but there will be absolutely no sharing of calculators allowed. You will be allowed scrap paper, but IT WILL NOT BE COLLECTED. ipads are not permitted in the room during the exam. This means no ipad usage before, during or after the exam. Your exact exam dates and times are as follows: Period 3- January 13th 8:20-10:00am Period 6- January 14th 10:15-11:55am Period 8- January 15th 10:15-11:55am Some study tips and pointers: Find the sections in the book that these problems come from and review the examples and content presented. o Find similar problems in that section and PRACTICE. Practice without guidance from your book, the internet, parents, tutors or friends. Only your knowledge will be available to you at test time. o Practice timing yourself: Learn to solve the problems under pressure. Have a classmate review your work while you review theirs. Give each other study tips... some of the best learning is done when explaining a concept to a peer. Begin reviewing (at least) a week ahead. To realistically do this: Make a schedule. Organize yourself. o Plan time to review and time to practice. o Most importantly, to be realistic, plan free time and breaks as well. If you have any questions while you study over break, e- mail me. I will try to respond as soon as I can, but please be patient. Regardless, we will be reviewing this in detail the week of January 5 th. Merry Christmas, Happy New Year! See you next year, Ms. Solera

2 1) Evaluate the following expression if a = 1, b = 2 and c =!!. 3c 4 a + b 2) Evaluate the following expression if x =!! and y = 2. 3(x + y) 4xy! 3) Write the algebraic expression represented by the product of 4 and the difference of a number and 13. 4) The sum of a number and 17 more than twice the same number is 101. Find the number. 2

3 5) (4 points) Solve the absolute value inequalities. Graph your solutions on a number line.! a. 8x + 5 7! b x 1 < 1 6) Hypoglycemia (low blood sugar) and hyperglycemia (high blood sugar) are potentially dangerous and occur when a person s blood sugar fluctuates by more than 38mg from the normal blood sugar level of 88mg. Write the absolute value inequality to describe blood sugar levels that are potentially dangerous. 7) Cara is making a beaded necklace for a gift. She wants to spend between $20 and $30 on the necklace. The bead store charges $2.50 for large beads (B) and $1.25 for small beads (b). If she buys 3 large beads, how many small beads could she buy to stay within her budget? Write and solve a compound inequality to describe the range of possible beads. 3

4 8) Write the slope- intercept form equation of the line that crosses through (- 8, - 5) (- 3, 10). 9) Write the slope- intercept form equation of the line that crosses through (4, 2) and is perpendicular to y = 2x ) Write the slope- intercept form equation of the line that crosses through (- 6, - 6) and is parallel to y =! x + 8.! 11) Determine the rate of change of the following line:! y +! x = 24!! 4

5 12) (4 points) As an army recruiter, Ms. Cooper is paid a daily salary plus commission. When she recruits 10 people, she earns $100. When she recruits 14 people, she earns $120. a. Write a linear equation to model this situation. b. What is Ms. Cooper s daily salary? c. How much would Ms. Cooper make if she recruited 20 people? d. Graph this linear equation on the grid below. Make sure to include all key points mentioned. 5

6 13) Solve the following systems of equations. Write the ordered triplet that is the solution on the line provided. x + 4z = 7 x 3y = 8 y + z = 1 14) If a system of equations with infinitely many solutions is classified as and occurs when the two lines are. 15) A system of equations with no solution is classified as and occurs when the two lines are. 16) The solution of a system of equations represents the ordered pair/triplet where the lines/planes. 17) The is the point at which income equals cost. 6

7 18) (3 points) Graph the following system of inequalities on the grid provided: 3x + 4y 15 2y + 5x > 12 10y x 19) What are the coordinates of the feasible region in #18? 20) Perform the indicated operation

8 21) Perform the indicated operation ) Evaluate the determinant ) Evaluate the determinant using any method

9 24) Use Cramer s Rule to solve the system of equations. 2x y = 9 x + 2y = 8 25) (4 points) Consider the system of equations: 5x + 3y = 0 4x + 2y = 2 a. Set up the Matrix Equation that would be used to solve the following system of equations b. Find the inverse of the coefficient matrix. For #26-29, solve by factoring. 26) 10x! + 25x = 15 9

10 27) x! + 13 = 17 28) x! 9x = 0 29) 7x + 6 = 20x! 30) Write a quadratic equation in standard form with the following roots 2,!!. For #31-34, simplify. 31) 8 10

11 32) (6 + 5i)(3 2i) 33)!!! 34) (3a)! (7b)! 35) Which value of c would make x! 12x + c a perfect square trinomial? 36) Write the following quadratic equation in vertex form: y = 3x! + 6x 2. 37) Determine the vertex, axis of symmetry and direction of opening of the quadratic equation from #35. 11

12 38) Divide: 3x! 5x! 23x + 24 x 3. 39) (1 point) Is x=3 a solution of the polynomial in #38? 40) If c x = 3x! + 5x! 4, what is the value of 4c 3b? 41) Solve 8x! + 1 = 0 42) Use synthetic substitution to find f 2 if f x = x! 3x! + 5x 3. 12

13 43) (4 points) First, prove that 2x 1 is a factor of 2x! + 15x! + 22x 15. Then find the rest of its factors. 44) List all possible rational zeros of x! + 2x! 23x ) (4 points) Find all zeros of f x = 5x! 29x! + 55x! 28x. 46) Describe the end behavior of a. A 5 th degree polynomial with a negative leading coefficient. b. A 6 th degree polynomial with a positive leading coefficient. 13