Honors Algebra 2 Name You have made the decision to take Honors Algebra 2 for next year. Remember that by enrolling in this course you are making a commitment to excellence in daily work. You will only get out of the course what you put into it. Successful students in Honors Algebra 2 are committed in the following ways Diligently complete homework on a daily basis Seek help from other sources when necessary (internet, fellow student or teacher) Understand concepts rather that just mechanically going through the steps Organized in both notes and presentation of problems on homework Accepts the responsibility of shortcomings Is truly responsible for missed work as a result of absences and school related outings SUMMER ASSIGNMENT The problems in this packet are designed to help you review topics from previous mathematics courses that are important to your success in Honors Algebra 2u. DO ALL THE PROBLEMS WITHOUT THE USE OF A CALCULATOR. Show all the work that leads you to each solution. You may use reference materials to help you but under no circumstances should you help or seek help from another person. I have included links with each problem set that may help if needed. All work should be completed and ready to turn in on the FIRST DAY of school. This packet will count as part of your first quarter grade. If you begin the packet early, be sure to review it in the week prior to the start of school, as you will be given a test on the second day of school to measure your skills. You may email me with any clarifications about these instructions at amoore@trlsd.org. ENJOY YOUR SUMMER!! Mrs. Moore
Exercise Sets A. You should be able to solve multistep equations. B. You should be able to translate word sentences into equations and solve. C. You should be able to solve each equation for the indicated variable. D. You should be familiar with linear equations and functions. E. You should be able to graph linear functions. F. You should be able to simplify exponential expressions. G. You should be able to simplify polynomial expressions. H. You should be able to factor polynomials. I. You should be able to evaluate square root expressions without a calculator J. You should be familiar with the quadratic formula to find solutions. K. You should be able to simplify rational expressions.
Exercise Set A: You should be able to solve multistep equations. Refer to video tutorials at https://youtu.be/ahthbgysz-4 1. 6x + 8 = 2x 2. (5 + 3x) = 4 3. (x 1) = 5(x + 3) 4. 7y (2y + 6) = 5y (3y + 10)
Exercise Set B: You should be able to translate word sentences into equations and solve. Refer to video tutorials https://youtu.be/cqmi93rtszm 1. Find three consecutive even integers whose sum is 222. 2. A number divided by 3 is equal to the number decreased by 14. Find the number. 3. There are one-dollar bills and five-dollar bills in Mr. Rich s wallet. It has 54 bills with a total value of $174. How many ones and how many fives are in the wallet?
Exercise Set C. Literal Equations and Formulas. You should be able to solve each equation for the indicated variable. Refer to video tutorials https://youtu.be/0egumwayp4y 1. ax = a + 2. Solve for a 2. The formula for the area of a triangle is A = base and h is the height. a) Solve the formula for h. 1 bh, where b is the 2 b) Find the height of a triangle if A = 20 ft 2, b = 5 ft 3. If a = 1, then a b =? b 4. 4x + 5y = 25, solve for y.
Exercise Set D: You should be familiar with linear equations and functions Refer to video tutorials https://youtu.be/mfkmsy7i6qw https://youtu.be/uwkgvspwcc8 1. Write each of the linear equations in standard form. a) 3x = y 5 b) 4y 6x = 5 c) y = 2x 1 2. The cost to buy a card is $1.50. Write an equation which expresses the relationship between the total cost (c) and the number (n) of cards bought. 3. Find the value for a. f(x) = 2 5x for f( 2), f ( 1 ), f(3) 2 b. f(x) = 2x 2 + x 2 for f( 2), f(0), f( 1 ) 2 c. Given (x) = 2x 1 and g(x) = x 2, find f(1) + f(2)
Exercise Set E. You should be able to graph linear functions. Refer to video tutorials https://youtu.be/uk7gs3czvp4 https://youtu.be/ltb2-le7ste 1. Graph the following Graph x = 4 Graph y = 3 Graph x = -2 Graph y = -3 2. Graph the following by using the x and y intercept of each equation a. Graph y = x + 1 b. Graph 2x + y = 1 3. Graph Pairs of Linear Functions. Tell whether they are parallel, perpendicular or neither. 4x + 8y = 7 a. { 2x + 4y = 9 4x 2y = 13 b. { 2x 4y = 11 y 4x = 3 c. { y 8x = 5 4. Find the equation in standard form of a line that passes through the point (10, -2) and is parallel to the line 2x + 5y = 3. Graph the line.
F. You should be able to simplify exponential expressions. Refer to video tutorials https://youtu.be/b4msqcjnd3i 1. (3x 4 y) 3 2. a 5 a 5 a 3 3. ( xy 3 x y 2) 3 x 5 y 3 4. x 2 y 2 5. ( 12x 3 y 3 ) 4xy
G. You should be able to simplify polynomials. Refer to video tutorials https://youtu.be/m9rryefxrha https://youtu.be/axv7cqezipy 1. 3x 2 y(xy + 2x 2 ) 2. (x 3)(x 2) 3. (3a + 1)(2a 2 4a + 5) 4. (2x + 8y) 5. (ab 3c)(ab + 3c)
H. You should be able to factor polynomials. Refer to video tutorials https://youtu.be/mxvt9oumkh8 1. Factor each polynomial by using the GCF (greatest common factor), also known as HCF (highest common factor). a. 6a 2 b 2 c 14ab 2 b. 10m 2 2 2. Factor each polynomial a. x(x + 3) 2(x + 3) b. 2(p s) + s(s p) 3. Factor each trinomial a. x 2 3x + 2 n 2 10n 9 a 3 9a 2 + 14a d. 4x 3 12x 2 16x
I. You should be able to evaluate square root expressions without a calculator. Refer to video tutorials https://youtu.be/ef2goqbdv7m a. ± 400 b. ± 1 36 3 c. 27 J. You should be able to find solutions using the quadratic formula: x = b ± Refer to video tutorials https://youtu.be/eevqtpumfou b 2 4ac 2a a. x 2 2x 11 = 0 b. 2 + 2x 12 = 0 c. x 2 + 10 x 3 = 0
K. You should be able to simplify rational expressions. Give restrictions on the variables. Refer to video tutorials https://www.youtube.com/playlist?list=pl8eppkclmloi91ehwgyahtevrbmofbzw4 a. 2a 12 a 2 4a 12 x 5 b. x c. (a 2) 2 a 2 d. k 2 +k 12 5k+20