Brunswick High School has reinstated a summer math curriculum for students Algebra 1, Geometry, and Algebra 2 for the school year.

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1 Brunswick High School has reinstated a summer math curriculum for students Algebra 1, Geometry, and Algebra 2 for the school year. Goal The goal of the summer math program is to help students retain the concepts they learned, which are either lost or reduced over the summer months. Math skills require use in order to be mastered and retained. The topics that were included are chosen because they contain the skills necessary and important to the curriculum. With this in mind, it is our goal that students participating in this program will maintain critical math concepts over the summer months. Instructions The review assignments will be due by the first day of school for a homework grade. Students will be given an opportunity to score their work and ask questions. Assessments will be used to allow students to demonstrate their knowledge of the material they worked on over the summer months. The assessments will be taken for a grade in the first quarter in the form of a single test. Resources Students are allowed to form study groups and receive assistance from peers and parents, but it is understood that each student should do his or her own work and is responsible for understanding the topics on his or her own. Digital resources are also allowed as there are many online math tutorials that are available. Each section has a website that you can go to for additional help. Other websites you may find useful include: purplemath.com khanacademy.org

2 Summer Review For Students Moving from Honors Geometry To Honors Algebra 2

3 Part One: Linear Equations Graph each line using a table of values. 1. Solve for y 7x y = -7-7x -7x Subtract 7x from each side -y = -7x 7 y = 7x + 7 Multiply or divide each term by Pick 3 numbers for x and plug them into the equation to find y. X Y (1) + 7 = 14 7(0) + 7 = 7 7(-1) + 7 = 0 3. Plot the points on a graph then draw the line. Special Case Lines The slope of a horizontal line is 0. The equation of a horizontal line is y = c. The slope of a vertical line is undefined. The equation of a vertical line is x = c.

4 Finding x and y intercepts of a line. To find the x intercept make y = 0. To find the y intercept make x = 0. 5x 3y = 10 x-intercept (y = 0) y-intercept (x = 0) 5x 3(0) = 10 5(0) 3y = 10 5x = 10-3y = 10 x = 2 y = -10/3 x-intercept (2, 0) y-intercept (0, - 3 1/3) Slope: Rise over Run Slope Formula: m y = y x x

5 Writing Equations of Lines Slope-intercept for of an equation: y = mx + b where m is the slope and b is the y-intercept Example 1: Write an equation of a line with a slope of 2 through the point (-3, 4) in slopeintercept form. m = 2 and (x, y) = (-3, 4) y = mx + b Answer: y = 2x = 2(-3) + b 4 = -6 + b 10 = b Example 2: Write an equation of a line through the points (1, -5) and (3, -7). m = y 2 y 1 = = -2 = -1 x 2 x m = -1 and (1, -5) = (x, y) y = mx + b Solution: y = -x = -1(1) + b -5 = -1 + b -4 = b

6 Part Two: Solving Linear Equations Part Three: Solving Systems of Equations Solve a system of equations by GRAPHING.

7 Solve each system of equations by SUBSTITUTION. Solve each system of equations by ELIMINATION. Part Four: Radicals Simplifying Radicals and Radical Expressions SIMPLIFYING RADICALS (perfect squares: 1, 4, 9, 16, 25, 36, 49 )

8 Honors Algebra 2 Summer Math ADDING AND SUBTRACTING RADICALS To add or subtract square roots, they have to have the same radicand (number under the radical) =9 5 You may have to simplify the radicals first = = = = 14 2 MULTIPLYING/DISTRIBUTING RADICALS To multiply square roots, you multiply the coefficients together and the radicands together. Always simplify your final answer = = = = 30 3 Distribute each expression = = = = = = = = = DIVIDING BY RADICALS/RATIONALIZING THE DENOMINATOR In order for a fraction to be simplified, the expression in the denominator cannot have a radical in it. Rationalizing the denominator is a procedure for making that happen.

9 Part Five: Factoring Factoring is the opposite of multiplication (distribution) and FOILing. You should always start by factoring out the Greatest Common Factor (GCF). It is the biggest number/letter that is a multiple of all the terms. Example: Factor by the GCF Example: Factoring a trinomial with an x 2 leading.

10 Example: Factoring a trinomial with a 3x 2 leading. Example: Difference of squares. Part Six: Quadratic Equations We will look at 2 methods for solving a quadratic equation. A. Factoring B. The Quadratic Formula

11 Method A: Solving by Factoring (This method does not apply to every equation as some expressions are not factorable) Method B: Solve by Quadratic Formula The quadratic formula is a method for solving quadratic equations that will work for all cases.