SAMPLE. Chapter 1: Basic Skills. Chapter 2: Systems of Linear Equations. Chapter 3: Analytic Geometry. Chapter 4: Polynomials
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1 Overview... 3 Chapter : Basic Skills. Order of Operations lgebraic Epressions Equations.... Simple Linear Equations... 5 Chapter : Sstems of Linear Equations. Graphing Sstems of Linear Equations.... Solving b Substitution....3 Solving b Elimination Possible Solutions... 3 Chapter 3: naltic Geometr 3. Length of a Line Segment Midpoint of a Line Segment Equation of a Circle Medians and Centroids Perpendicular Bisectors and Circumcentres ltitudes and Orthocentres Classifing ing Shapes : Polnomials. Epanding and Factoring Factorization TrinoS tion of Trinomials () Chapter : Polnomials.3 Factorization of TSof Trinomials () Perfect-square Trinomials and Differences of Squares Factorization Strateg Chapter 5: Graphs of Quadratic Relations 5. Properties of Quadratic Relations Finding Zeros Transformations of Quadratic Relations () Transformations of Quadratic Relations () Modelling Quadratic Relations... 9 Complete MathSmart (Grade ) ISBN:
2 Chapter 6: Solving Quadratic Equations 6. Standard Form to Factored Form Partial Factoring Completing the Square The Quadratic Formula Nature of Roots... 3 Chapter 7: Triangles and Trigonometr 7. Congruent and Similar Triangles Solving Problems on Similar Triangles The Primar Trigonometric Ratios () The Primar Trigonometric Ratios () Solving Problems Modelled b Right Triangles... Chapter : cute Triangle Trigonometr. The Sine Law Solving Problems Using the Sine Law The Cosine Law......M Solving Porblems Using the Cosine Law ppling the Sine Law and the Cosine Law... 7 iew... M... Cumulative Review Hand Reference... 9 nswers......ṡ ISBN: Complete MathSmart (Grade ) 5
3 5 Graphs of Quadratic Relations Parabola: a graph of a quadratic relation that is shaped like the letter U is of smmetr: a line that divides a parabola into two equal halves Verte: the highest or lowest point of a parabola 5. Properties of Quadratic Relations Identif and check the representations of quadratic relations second differences are constant but not shows a parabola Parabola -intercept -intercept C E opens upward verte ais of smmetr B D F Graph the quadratic relations. = B = Complete MathSmart (Grade ) ISBN:
4 Graph the quadratic relations. Write the ke characteristics of each in the table. C = D = intercept(s) - - E = - ( ) F = ( + ) = = = - ( ) = ( + ) + (, )(, ) = - - -intercept (, ) Direction of Opening is of Smmetr = Verte (, ) Ma./Min. Value = ISBN: Complete MathSmart (Grade )
5 Chapter 5 Graphs of Quadratic Relations Sketch the parabolas with the given characteristics. G verte: (-3,) -intercept: (,) B B -intercept: (.5,) -intercept: (,-6) C D nswer the questions without graphing. H = + 7 no -intercepts opens upward -intercepts: (,), (-,) ma. value: 3 a. What is the direction of opening? os b. What is the -intercept? I = a. What is the direction of opening? C D Standard Form of Quadratic Relations = a + b + c direction of opening a >, upward a <, downward (,) -intercept e.g. = + = - + (,) b. Will there be a maimum value or a minimum value? J = -( ) Epand and rewrite in the form: = a + b + c. a. What is the direction of opening? b. What is the -intercept? Complete MathSmart (Grade ) ISBN:
6 Circle T for true and F for false. K The ais of smmetr is alwas the -ais. L The verte alwas lies on the ais of smmetr. M parabola with no -intercepts and with a positive -intercept alwas opens upward. N ll parabolas have -intercepts. O Consider = a + b + c. Stud each scenario and answer the questions. P Q a. If it is an equation of a parabola, then a cannot be. b. If a is negative, the parabola will open downward. c. c is the -intercept. The graph shows the path made b Steven s dive. a. Check the equation that represents the graph where represents the horizontal distance and represents the water depth. + MP =. + B =. C = -. b. What was the maimum water depth Steven reached? The graph shows the water arch Karen s garden hose made while she watered her plants. a. Check the equation that represents the graph where represents the horizontal distance and represents the height. = + 5 B = -.5 C = b. How far awa was Karen from the plants? ISBN: Complete MathSmart (Grade ) 3
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) Simplif: z z z 6 6 z 6 z 6 ) Simplif: 9 9 0 ) Simplif: a a a 0 a a ) Simplif: 0 0 ) Simplif: 9 9 6) Evaluate: / 6 6 6 ) Rationalize: ) Rationalize: 6 6 0 6 9) Which of the following are polnomials? None
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