Pure Mathematics 20 Unit 1. Systems of Equations and Linear Inequalities

Transcription

1 Pure Mathematics 0 Unit Sstems of Equations and Linear Inequalities. Eploring Ordered Pairs and Solutions. Pages 4-: ALL. Solving Sstems of Linear Equations Graphicall Pages -:,, 4, 7, 7, 9,, 7, 9,,,, 7, 44. Solving Sstems of Linear Equations b Substitution. Pages -7: 9, 0, 4, 9,, 6 abc, 8, 9 b, 0, 6, 7, 47. Solving Sstems of Linear Equations b Elimination. Pages 8-40:,, 7, 8, 0,, 9, 7,,, 44, 46, 48, 8, Solving Sstems of Linear Equations ( Variables) Pages 44-46: 7, 8,,,,, 44, 7. Eploring Non-Linear Sstems with a Graphing Calculator. Page 47: All 8. Reviewing Linear Inequalities in One Variable. Pages 6-64: 4, 8,, 6,, 4, 47, 0,, 6, 9 9. Graphing Inequalities in the Coordinate Plane Pages 68-7: All 0. Graphing Linear Inequalities in Two Variables. Page 7:,, 6,,,, 4, 9,, 7, 4, 4. Review. Pages -4: All Pages 94-9: 0 (multiples of ) ***SEE DATE ON COURSE OUTLINE*** Evaluation Summar. Describe the steps ou would use to solve a sstem b elimination and the steps for substitution. Which method do ou prefer? Eplain wh.. Naomi invested $000, part at 8% per annum and the rest at 0% per annum. In one ear, the two parts earned equal amounts of interest. How much did Naomi invest at each rate?

2 Pure Mathematics 0 Unit Quadratic Functions. Eploring Transformations (Absolute Value Function) Worksheet. Transformations of Quadratic Functions. () Pages 09-:,, 0, -9,,, 4. Transformations of Quadratic Functions. () Pages 8-:,, 0,, 4,,, 6, 0, 4,, 9, 8, Writing Equations of Quadratic Functions. Pages 09-: 48,, 4, 6, 60-66, 69 Pages 8-: 46, 47, 48,, 4, 60, 6, 66, 70, 7, 7, 77, 78, 80. Completing the square. () a Page : 4 odd and worksheet 6. Completing the square. () a Page : 44 6 and worksheet. 7. Maimums and minimums; zeros using Page : calculators. 8. Problems. () (formula, number, geometric Page 9: 74 and revenue) Pages -4: 7-78, Problems. () Worksheet 0. Review. Page 44: -6 odd, 6-64 all ***SEE DATE ON COURSE OUTLINE*** Evaluation Summar. Given the quadratic function s ( + t ) u, describe how ou would find each of the following and then state the: a) direction of opening b) coordinates of the verte c) equation of the ais of smmetr d) domain and range e) maimum or minimum value. For +, describe and illustrate the steps to complete the square and obtain the verte.. Vehicles Incorporated currentl sells an average of 0 compact cars each week at a price of $6400 each. The sales department wants to increase the price, but the marketing department predicts that for ever $00 increase, sales will fall b one car. If the dealer cost (cost to the dealer) for each car is $4000, what price will maimize profits for Vehicles Incorporated?

3 Pure Mathematics 0 Unit Quadratic and Polnomial Equations. Solving quadratic equations b graphing. Pages -6:,, 7, 8,, 4,, 7, 9, 6, 4,, 6, 4, 4, 4,, 4,. Solving quadratic equations b factoring. Factoring Review Worksheet Pages 60-6:,, 7,, 4, 7, 6, 4, 44, 47, 49,, 60, 6, 6, 66, 70, 7, 80, 86, 89 Pages 78-80:,,, 6,, 6, 7, 8,, 9, b ± b 4 ac. The quadratic formula., 4, 7, 47,,, 6, 64, 70, 77, 8 a Pages 7-7: 7, 6, 6, 66 a, c, 67 a, c, The discriminant b 4ac. Pages 89-90:,,,,,,, 7, 8,, 4,, 4, 47, 4 a. The remainder theorem. Pages 0-0: 7, 9, 9,, 40, 4, 44, 47, 48,,,, The factor theorem. Pages 09-:,, 7, 8, 4,,,, 7,,, 7, 9, 6, 6, 66, 67, 69, 8a, 8 7. Solving polnomial equations. Pages 9-:,,, 4,, 6, 7, 8,,, 8, 4, 4, 46, 49, 78, 84, 9, Review. Page : (omit - 4 and 7-7 ) ***SEE DATE ON COURSE OUTLINE*** Evaluation Summar a. Given an eample for each situation. Include the equation being solved, the function being graphed, and draw a graph illustrating solution(s), verte and -intercept. i) two solutions ii) one solution iii) no solution b. Eplain how the graph relates to the solution(s).. Use the Remainder Theorem to find k if P()4 + k 6 and P() ( + ) has a remainder of. a. Use the Factor Theorem to find one factor of P() b. Use our answer from part a) to algebraicall find all solutions of In our solution, include the full factored form of the given polnomial equation.

4 Pure Mathematics 0 Unit 4 Functions. Operations with Functions Pages 47-0: 4, 6, 0, 6, 4, 7, 44, 4,, 60, 6, 68, 70. Composition of Functions Pages 6-9:,, 0,, 6,, 4,,, 6, 44, 4,, 60, 6, 7, 7, 78. Inverse of a Function Pages 68-70:,, 6, 7,,, 6, 4-47, 48, 67, 69, 74, 8, 89, 9, Graphing Polnomial Functions Pages 7-7: All. Solving b Graphing All Tpes Worksheet Questions with asterisks * should be solved algebraicall (and solutions confirmed graphicall). 6. Polnomial Equations and Inequalities Pages 8-8: -8, 9,, -6, 9, 0,, 4, 4, 4*, 47*, 49,, *, 4*, *, 6*, Absolute Value Equations and Inequalities Pages 96-98: *, 4*, 6*, *, 6*, 0*,, 4, 4, 46,, 6, 6, 78, 80, 8, 96, 0, 04, Rational Equations and Inequalities Pages 09-: -,, 0,,, 4, 49*, 0*, *, 6*, 70*, 77, 79, 89, 9, 0*, *, 9 9. Radical Equations and Inequalities Pages -6:,,, 6, 4*, 6*, *, 7, 44, 4, 48*, *, *, 68, 7, 7, 7, 8, 8, 8*, 4 0. Review Pages 0-: 40*, 4*, 4*, 4*, 60*, 6*, 64*, 6*, 66*, 67*, and all other questions. Page : *, *, 6*, 7*, 8*, 9*, and all other questions. ***SEE DATE ON COURSE OUTLINE***

5 The students should be able to solve the following equations and inequalities algebraicall and graphicall: absolute value equations (single absolute value onl) radical equations (up to radicals with one being simple e.g. ) rational equations polnomial equations polnomial inequalities (this includes quadratic inequalities) The students should be able to solve the following inequalities graphicall onl: absolute value inequalities radical inequalities rational inequalities Evaluation Summar. Summarize the features of linear, quadratic, cubic, quartic and quintic functions in a table using the following headings. Name, degree, general form, end behavior if a is positive, end behavior if a is negative and greatest number of turning points possible.. In the method used to solve a radical equation, both sides of the equation are squared to remove the radicals. Eplain wh radicals are isolated before both sides are squared.. Make a list of the operations that can be applied to two functions to define new functions. Make up functions of our own, and use these to demonstrate each point in our list. 4. In our own words, describe the difference between a) f(g()) and g(f()) b) fg() and f(g())

6 Pure Mathematics 0 Unit Reasoning. Inductive Reasoning, Conjectures and Countereamples Pages 40-4: -6, -, 8, 9,, Pages 4-46: -0. Connecting words Page 4-6: -7,,, 6, 7, 8, 4,, 6,, 6-9, 40, 4, 6, 7, 8, 60, 6. If-Then statements Pages 6-6: - 4. Deductive Reasoning (and Direct Proofs) Page 49: -4, 6, 7 Page 7: -9. Congruent Triangles Pages 64-6: All Page 8:,,, 6 6. Geometric Proofs Pages 89-9: -0, 6, 7, 9, 8 7. Review. Pages 76-78: 4-0 Page 79: -9 ***SEE DATE ON COURSE OUTLINE*** Evaluation Summar. Eplain what is meant b the converse of an If... then statement. Illustrate our eplanation with an eample of a true statement that has a true converse, and a true statement that has a false converse.. Eplain what is meant b the contrapositive of an If... then statement. Illustrate our eplanation with an eample. Use our eample to eplain wh the contrapositive has the same meaning as the original statement.

7 Pure Mathematics 0 Unit 6 The Circle. Introduction Preview Worksheet (Theorems and Vocabular) Page 8 All. Chord Properties Pages : -0, -6, 0. Angles in a Circle. Pages 4-44: -6, 8, 4. Cclic Quadrilaterals. Pages 49-4: -6, 8,,. Tangents to a Circle Pages 4-4: -4, 6, 8-6. Angles and Polgons. Pages 44-44: -4,, 8,, 4, 7, 0,, 6, 9, Review Pages : Omit 9, Pages 448: Omit 4-6 ***SEE DATE ON COURSE OUTLINE*** Formal Proof Opening Statement: Consisting of what is given and what is to be proved. Bod of the Proof: Statements with corresponding reasons. Closing Statement: Conclusion of proof. ie. Hence or therefore. Required Proofs. Perpendicular bisector of a chord contains the centre of the circle.. Angle inscribed in a semicircle is a right angle.. Tangent segments to a circle from an eternal point are congruent. NB: Trigonometric ratios can be used to justif proofs, in addition to circle properties.

8 Pure Mathematics 0 Unit 7 Coordinate Geometr and Trigonometr. Getting Started Worksheet Coordinate Geometr Preview. Connecting Coordinate Geometr and Plane Geometr Pages :,,, 4, 8,, 6, 0,, 4. Distances Between Points and Lines Pages :, 4, 7,,, 8, 0, 9,,, 6, 9, 4, 47,, 6 4. The Equation of a Circle. Page 48-48:,, 7, 8,, 6, 0,, 4, 7-6, 8, 40, 44, 0,. Intersections of Lines and Circles Pages :,, 8, 0, 9,, 4,, 7, 9,,, 9, 4, 4, 47,, 4,, 7, 6, 6, 67, 8, Review Pages 6-7: - Page 8: - ***SEE DATE ON COURSE OUTLINE*** Evaluation Summar. Eplain in detail the process that ou would follow to determine the equation of the tangent line to a circle at a given point on the circle. Use the circle define b ( ) + ( + ) 8 and the point (, 4 ) to illustrate our eplanation.. A circle centre O, is defined b + r. The point P(a,b) is outside the circle. T is the point of contact on the circle of a tangent from P. Find the lengths of OT, OP and the length of the tangent PT.

9 Pure Mathematics 0 Unit 8 Finance. Unit Prices and Echange Rates Page 4: All Page 6: All. Earning Income Pages 0 : - 9. Net Income Pages 6 7: 6, 7,,, 9, 0,, 0,, 4. Interest and Annuities Page 4-4: 4 8 even, 9 4. TVM Solver Worksheet and Pages Consumer Credit / Balancing a Budget Pages 6: 0 Pages 6-66: 0, 7. Housing Costs Pages 60 6: even,, 8. Review Page 7: 9 ***SEE DATE ON COURSE OUTLINE***

10 Pure Math 0 AP Course Sllabus All material below is in addition to the regular Pure Math 0 Curriculum. Unit Sstems of Equations (and Inequalities) Matrices ( 4 RREF on paper) Matrices ( Solving using multiplicative inverse) eg Cramer s rule Non-linear sstems (algebraicall) eg or, Sstems of Inequalities (. in tetbook) Unit Quadratic Functions Transformations of all tpes of functions (etensive preview of Pure math 0 transformations is appropriate here) Challenge problems (old math contest questions) Focus on Ma / Min (optimization) questions. Unit Quadratic and Polnomial Equations Tougher word problems (lots to choose from in tetbook for this chapter) Comple/Imaginar Numbers

11 Unit 4 Functions and Inequalities Everthing algebraic! (solve for cases rather than checking) Equations single and double (radical, rational and absolute value) mied tpe Inequalities single and double (radical, rational and absolute value) Unit Logic and Reasoning Tougher Venn diagrams (requiring sstems of equations) Indirect Proofs Lots of tougher proofs to assign from tetbook in this chapter. Unit 6 Circles Tougher questions material mainl the same. Sector area and Arc Length Complete the square to change circle from general to Unit 7 Coordinate Geometr Tougher proofs Ambiguous case of Sine Law.( if not done in 0AP) Unit 8 Finance Business vs. Personal Financial Statements Risk vs. Reward