Montini Catholic High School Algebra I Concepts

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1 Montini Catholic High School Algebra I Concepts All students enrolled in Plane Geometry, Geometry, Honors Geometry, Modern Algebra II and Algebra II for the fall of 018 will take a diagnostic exam the first week of school to assess their retention of basic Algebra I concepts that are necessary to be successful in their next math course. When the student is given the results, they will also be given remediation work for any concepts the student struggled with. This packet covers the same concepts that are on the diagnostic exam. If done properly, this will hopefully alleviate the need for any remediation in the fall. As you go through each topic, check your answer. If you are having difficulty: Watch videos from last years math class Use your notes or teacher handouts from last years math class Videos via Studystorm app (a free app already on their ipads) Videos, examples, and practice problems via khanacademy.org (a free website) Search the internet for the concept Use books from your local library Additionally, you continue to have access to your schoology course with all materials from this past year. Concepts covered: A. Operations with negative numbers Operations with fractions Simplify numerical expression (including negatives and fractions) B. Absolute value Simplify radicals C. Simplify algebraic expression (order of operations, like terms, laws exponents ) Evaluate an algebraic expression D. Solve linear equations of one variable Solve systems of linear equations E. Factor expressions of one variable F. Find x-intercepts and y-intercepts Graph linear equations G. Translating verbal statements into mathematical statements H. Quadratics: graphs (including finding the vertex and intercepts) and solving ALL QUESTIONS ARE INTENDED TO BE COMPLETED WITHOUT A CALCULATOR All fractions should be left in improper form: a b Answers are at the end of the packet

$A. operations with negatives & fractions / simplify numerical expressions Evaluate (Write the value of each expression) 1. 36 1 13 =. -4 11 = 3. 14 4. 1 1 4 5. 18 3 6. 4 30 5 8 7. 7 3 5 35 8. 3 1 9.$

2 A. operations with negatives & fractions / simplify numerical expressions Evaluate (Write the value of each expression) = = For help go to: Pre-Algebra app: Fractions and Mixed Numbers o Multiplying and Reducing Fractions (all videos) o Dividing Fractions (all videos) o Adding/Subtracting Fractions Like Denominators (all videos) o Adding/Subtracting Fractions Unlike Denominators (all videos) o Multiplying and Dividing with Mixed Numbers (all videos) o Addition and Subtraction with Mixed Numbers (all videos) o Complex Fractions and Order of Operations (all videos) OR Khanacademy.org: Pre-algebra o Negative numbers Adding and subtracting negative numbers Multiplying and dividing negative numbers o Fractions Adding and subtracting fractions with unlike denominators Adding and subtracting mixed numbers Multiplying fractions

3 B. Absolute Value and Radicals Simplify each of the following For help go to: Algebra app : Radical Expressions and Equations o Simplifying Radical Expressions (all videos) o Adding and Subtracting Radical Expressions (all videos) o Multiplying and Distributing Radical Expressions (all videos) o Dividing Radicals and Rationalizing the Denominator (all videos) OR Khanacademy.org: Absolute value (example video & practice) Simplifying square roots (algebra video & practice) Rationalizing the denominator (algebra video, worked example video, & practice)

4 C. Simplify & Evaluate Algebraic Expressions Simplify #5-30 Evaluate #31-39 x y 3x y 6. x x y 3x 4y x 3 x 4x 8. x y3x y x x y 30. 3xy xy 31. if a 3& b, then 5a 4b 3. if m & p, then 4m p 33. 3b d if d 3& b, then if a 3& b, then a 4b if a & c, then 6 a 4 b 36. if k 1& g, then 3 k 4g 37. if a & b 3, then a 1 4b 38. 3x y if x & y 6, then x 3 y if m & b, then 9m 3b For help go to: Algebra app: o Pre-Algebra: Simplifying Expressions and Combining Like Terms (all videos) OR khanacademy.org: Simplifying exrepssions Combining like terms exponent rules, exponent properties evaluating an expression

5 D. Solve linear equations of one variable & Solve linear system of equations Solve each equation or system of equations 40. x 3 5 a d 1 4d 43. 3b 4b c c r 6r 46. b1 b3 4 x 3 x 1 4x y3 y x x a k x 1 x x x

6 55. x y 4 x y x y 1 5x x 3y 5 3x y xy4 7x 3y x 6y 4 9xy x4y 3 9x6y 6

7 For help with #40-54 go to: Pre-Algebra app: Solving Equations and Inequalities o Solving Equations one variable terms (all videos) Algebra app: Solving Equations o Solving Single-Step Equations (all videos) o Solving Two-Step Equations (all videos) o Solving Multi-Step Equations (all videos) o Solving Equations with a Variable on Both Sides (all videos) OR khanacademy.org: Linear equations 1,, 3, 4 Solve absolute value equations Absolute value equations with one solution Absolute value equation with two solutions For help with #55-60 go to: Algebra app: Systems of Linear Equations o Solving a System of Linear Equations in Two Variables (all videos) OR Khanacademy.org: System of linear equations Solving system of equations by elimination Solving linear systems by substitution Systems of equations by substitution (practice)

8 E. Factor expressions of one variable Factor x y 4xy 6. 1a b 30ab 4a b 63. x 7x m 18m y 3y b 5b x 13x d 5d p 8p v 1va 4a 71. x y 16 For help go to: Algebra app: Factoring o Review of the Methods of Factoring (all videos) o Factoring Complicated Expressions (all videos) OR Khanacademy.org: Greatest common factor (video and practice) Factor polynomials: common factor Factor quadratics intro Factoring quadratics as Factoring quadratics: leading coefficient = 1 Factor quadratics by grouping Factoring quadratics: common factor + grouping More examples of factoring quadratics

9 F. Find intercepts, linear graphs Write the intercepts of each equation and then sketch the graph 73. yx x3y x4y x3y x 3y x y

10 For help go to: Algebra app: Linear Equations and Their Graphs o Intercepts of Linear Equations (all videos) o Graphing Lines Using Intercepts (all videos) OR Khanacademy.org: Intro to intercepts Intercepts from an equation x-intercept of a line intercepts of lines review graphing lines graph from linear standard form graphing a linear equation For each of the following graphs write the intercepts and the equation (in the form Ax+By=C) equation: equation: equation:

11 equation: equation: equation: For help go to: Algebra app: Linear Equations and Their Graphs o Finding the Equation of a Graphed Line (all videos) OR Khanacademy.org Intercepts from a graph Slope-intercept equation from graph Convert linear equations to standard form Linear equations in any form

12 G. Translating verbal statements into mathematical statements less than a number n 86. the sum of 5 and y more than twice a number n less than the sum of b and more than the product of and x 90. a number q decreased by a number m is more than times a number r is greater than quotient of 10 and b 94. the difference of twice x and is increased by the product of 4 and n 96. the product of 8 and the sum of 1 and y For help, go to: Pre-Algebra app: Solving Equations and Inequalities o Translating Words into Equations OR khanacademy.org: writing expressions with variables

13 H. Quadratics (vertex, intercepts, graph) solve Graph each quadratic, list the vertex and intercepts 97. y x y x y x x 3 Vertex: x-intercept(s): y-intercept: Vertex: x-intercept(s): y-intercept: Vertex: x-intercept(s): y-intercept: 100. y x x y x 5 x y x 1 x 6 Vertex: x-intercept(s): y-intercept: Vertex: x-intercept(s): y-intercept: Vertex: x-intercept(s): y-intercept:

14 Solve 103. x x x 4x x x 13x x 3x x 1x x 16x x 50x 4 0 For help with #97-10, go to: Algebra app: Quadratic Equations and Functions o Graphing Quadratic Equations (all videos) o Vertical and Horizontal Shifts of Quadratic Graphs (all videos) o The Vertex and Axis of Symmetry (all videos) OR Khanacademy.org: Vertex and axis of symmetry of a parabola Graphing quadratics: vertex form Graph quadratics: vertex form Graphing quadratics: standard form Graph quadratics: standard form Graphing quadratics in factored form Graph quadratics: factored form Graph quadratics all forms Forms & features of quadratic functions For help with # , go to: Algebra app: Quadratic Equations and Functions o Solving Quadratic Equations by Factoring (all videos) o Solving Quadratic Equations Using Square Roots (all videos) o The Quadratic Formula (all videos) OR Khanacademy.org Solving quadratics by factoring Using the quadratic formula

15 ANSWERS: ¼ x 5y 5 6 y 6. 4x xy 4y 7. x x x 5xy y 9. x y x no solution 47. 1,8 1, , , 56., 5 57., xy 3x y 6. 6abab 5b 4a , 59., x4 x m5m y5 y 66. b1b x3 x d 1d p p 70. 3v a 71. x6 x y49y x-int,0 y-int 0,3 74. x-int 3,0 y-int 0, 55. 3, , 3

16 75. x-int 8,0 y-int 0, x-int,0 y-int 10 0, x-int 15,0 4 y-int 0, x-int 4,0 y-int 0, 79. x-int none y-int 0,5 equation: y x-int 81. x-int 0,0 y-int 0, 0 equation: y x 8. x-int,0 y-int 83. x-int,0 y-int 0, 1 equation: x y 84. x-int6,0 y-int 85. n y , 0 y-int none equation: x 3 n 88. 0,3 equation: 3x y 6 0, 6 equation: x y 6 b x q m r b n y 94. x 7

17 97. vertex: 1, vertex: 3,5 4,0, 1,0 0, 3 none 0, vertex:, 100. vertex:, ,0,,0 0, 3,0,,0 3 0, 4

18 101. vertex: 1, vertex: 3,0, 5,0 0, , 1,0, 6,0 0, ,8 108., , no real solutions 110., ,6 9

What students need to know for PRE-CALCULUS Students expecting to take Pre-Calculus should demonstrate the ability to:

What students need to know for PRE-CALCULUS 2014-2015 Students expecting to take Pre-Calculus should demonstrate the ability to: General: keep an organized notebook take good notes complete homework every