MPM2D+HW

**MPM2D Homework - 2012-2013**
=Date= ||= =Class Topics and Summary Notes= || =**Handouts/Homework**= || 1. graphing quadratics and applications of quadratics 2. trigonometry of right angle triangles and oblique triangles This semester quizzes will count as one test - drop lowest quiz score Review of multiplying and factoring quadratics - where we left off || p 256 # 2 b,d,e, 3, 7d,f 14, 16, 18 p 258 # 3 b,c,f, 6a, 7, 8, 10a, 12a, Quiz on this next class || Graphing quadratic functions - called parabolas. First method (but not the best) is with a table of values, which is today's assignment || 4 graphs on one page p 167 # 3,4 p 172 # 1,2 || y = -x²+ 5x - 4 - if you sketch all three of them, what's the same? what's different? - can you predict where the parabola will be located and whether it will open up or down? - the goal will be to sketch a graph without using a table of values, but for now we use a table || 3 graphs on one page, use x-values from -5 to 5 and y-values from -30 to 30 y = ( x+2)² y = x²- 4x - 3 y = - x²- 6x - 4 || Based on the homework, is there an EASIER way to get the same general shape? We could find the x and y intercepts (just like we did with lines) - we learned that today! If we can write a quadratic function in the form y = (x+a)(x+b), we can find the x-intercepts. However, there may be zero, one, or two x-intercepts; there will always be a y-intercept. If we can factor the quadratic, we can solve for where the quadratic equals zero. The next question will be "what can we do it the quadratic cannot be factored?" || Finish the three sample problems then find x and y-intercepts for: 1. y = x²+ 2x - 3 2. y = -x²+ 5x - 4 3. y = x ² - x - 6 4. y = -(x-3)² Sketch each parabola || We will continue sketching parabolas by finding intercepts - now with harder problems. How to sketch y = 2x²+ x - 3? Can we factor this expression? Yes. Can we solve for the x and y-intercepts? Yes. Then it is almost the same as the problems we just finished. If you need a bit of help, you can [|look here] or search for Soving Quadratic Equations by Factoring You should be equally familiar with A=1 quadratics and A not equal to 1 quadratics || Sketch these parabolas after finding the intercepts y = 3x²+ 5x + 2 y = 2x²+ 3x - 9 y = 3x²+ 4x - 7 y = 4x² - 25 || We finished with a quiz on the work from the previous class ||  || Now we need to show that y = (x+2)² and y = x² + 4x + 4 are the same Using the attached worksheet, we can NOW FIND 4 important points on the parabola: the x-intercepts, the y-intercept, and the vertex. And then graph. You can use [|fooplot.com] to check your graphing. || Do questions 2-5 on the quiz next class on sketching parabolas with A not equal to 1 || Test next Thursday **- everything through next class.** given y = x²+ 6x + 8, find the intercepts, the axis of symmetry, and the vertex. given y = (x - 2)² - 9, find standard form, the intercepts and vertex. Use Fooplot.com to check your work. You will see BOTH of these questions on next Thursday's test! New concept - can we work with vertex form if A is not equal to 1? Of course, but it is a bit harder. || do all of part 1 and a,c of part 2
 * =Today's=
 * Jan 29 || Exam Review and feedback - overview of second semester curriculum
 * Jan 29 || Exam Review and feedback - overview of second semester curriculum
 * Jan 31 || Quiz 1 - multiplying and factoring quadratics
 * Feb 4 || consider the parabolas y = x² and y = x²+ 2x - 3 and
 * Feb 6 || Quiz 2 - graphing parabolas by making a table of values
 * Feb 8 || Quiz3 - graphing parabolas by finding x and y intercepts
 * Snow Day || If you did not do the Feb 8 work yet, you should. Tomorrow's quiz will cover that material. ||  ||
 * Feb 12 || We did the work from Friday, Feb 8: sketching parabolas where A not equal to 1.
 * Feb 14 || Start by expanding perfect squares like (x+2)² and (x-3)² - do 10 of these.
 * Feb 20 || Quiz at the end of today's class
 * Take up work from factoring - Feb 8 - quiz on this at the end of class.**
 * Review the work from last class - handout on factored form and vertex form**
 * New work - writing quadratic functions in Vertex Form - handout** || complete the [[file:vertexPart2.pdf|handout and p 270]] # 3,4 ||
 * Feb 22 || Problems on converting between standard form and vertex form.

2a should have -8 not -7

we have done || Sample questions that were done in class: 1. find the intercepts and vertex for y = x²- 8x + 12; then sketch the parabola 2. a quadratic function has A=3, x-intercepts at -4/3 and 2, and a y-intercept at -8; find the factored form and the standard form of the function and then sketch the parabola 3. write y = -2 x²+ 3x + 5 in factored form and then use the intercepts and value of A to sketch the parabola 4. for the quadratic function y = 2(x - 3)² - 8, write the function in standard form, then factor to find the x-intercepts, then sketch the parabola. ||  || When finished, students began working on a handout for transformations of parabolas. Using fooplot.com, students are trying to find out how the shape and location of the graph changes as the values of A, B or C change in standard form, factored form, or vertex form. || || The goal of our work in transformations is to see the effect of changing the values of a, h, and k in y = a**(x -** h**)² +** k Last chance for students to redo their quadratics test Solving for x-intercepts in quadratics that cannot be factored 1. finding the intercepts for y = (x+3)² - 4 the standard form is y = x ² + 6x + 5, which factors easily and gives x = -1 and x = -5 2. what about y = (x+1)² - 5? the standard form is y = x² + 2x - 4, which cannot be factored. Using fooplot, we can show that there are two x-ints, but both are decimals, not whole numbers. SO... we use the Quadratic Formula to solve for the x-intercepts Note that the ± simplifies two formulas into one, since all parts other than the + or - are identical.
 * Feb 26 || Review of quadratic functions - including factoring quadratics, sketching parabolas, finding the vertex form of the quadratic, converting between factored form, standard form, and vertex form. Some test questions will ask you to find points (intercepts and vertex) and then graph, while other questions will give you a graph and ask you to find one or more forms of the quadratic function.
 * Feb 28 || Test on quadratic functions - whole class.
 * Mar 4 || Work on quadratic transformations handout - the goal of our work today is to accurately locate the vertex, y-intercept, and direction of opening for a quadratic function given in vertex form. We will use fooplot to graph each quadratic and then transfer the graphs onto the handout, where we can make some conclusions.
 * what does the parabola look like if a is positive or negative?**
 * what if a > 1 or between 0 and 1?**
 * which way does the parabola shift if we change the value of h?**
 * which way does the parabola shift if we change the value of k?** || [[file:quadFunctionsAssign.pdf|here is the assignment]] which is due on Thursday this week ||
 * Mar 6 || Return unit tests - you will have an opportunity to redo part of this test - same as last semester (100/80/60 % rule) ||  ||
 * Mar 8 - 17 || Spring Break - Relax! ||  ||
 * Mar 19 || A few students still need to share their parabolas assignment

If the standard form is y = ax² + bx + c, the x-intercepts are given by the formula to the right. And we can show that the answers are x = 1.24 and x = -3.24 || Use the Quadratic formula to solve each of the following and then use fooplot to check your answers. y = x ² + 3x - 1 y = x² + 4x - 6 y = (x+2)² - 5 y = (x -1)² - 7 || Y ou will review the work from last class with the Quadratic Formula Key points: 1. Always convert your quadratic to standard form before solving for x-intercepts 2. If you CAN factor the quadratic, factoring is almost always simpler than using the Quadratic Formula 3. If you can't factor the quadratic, use the Quadratic Formula 4. Many times the Quadratic Formula will give 2 answers, but sometimes it will give 1 or 0 answers; we will discuss this next week 5. When a problem asks for EXACT solutions, you must keep the square root in your answer; so if b ² - 4ac = 20, the answer contains √ 20 instead of 4.47 6. The easiest ways to check your work with the quadratic formula are to ask a friend or to use fooplot to sketch the quadratic || For next class, use the quadratic formula to solve for the x-intercepts and then use fooplot to check your answers
 * Mar 21 || Mr Guetter is gone to a robotics competition today.

Remember to write the quadratic in standard form first! || We did a review of simplifying root expressions - ex: √ 20 = 2√ 5 here are two places for you to review this concept: [|Purplemath] [|Khan Academy] || Finish work from p 300 # 2,9 make sure that your exact answers match those in the book. Simplify radicals. Then work on p 300 # 3 - only find the x-intercepts || Are there quadratics that have less than two x-intercepts? Yes, a quadratic might have zero, one, or two x-intercepts. How can we tell? 1. the quadratic cannot be factored or solved with the quadratic formula 2. we can use the vertex form of the parabola to locate the vertex and the direction of opening NOTE: if √ b² - 4ac < 0 then there are zero x-intercepts. Think about the square root of a negative number if √ b² - 4ac = 0 there is only ONE x-intercept if √ b² - 4ac > 0 there are TWO x-intercepts || Homework - for each of the following, find the vertex, the y-intercept, the x-intercepts (if they exist), and then sketch all on one graph: 1. y = x² - 4x + 2 2. y = 2(x+1)² - 4 *3. y = 2x² + 5x - 4 4. y = -(x-3)² + 5 *5. y = 3x² + 5x - 2 *= don't find vertex (yet) || graphing, transformations, factoring, vertex form, quadratic formula, number of x-intercepts ||  || problems on -transformations y = a(x-h)² + k -quadratic formula (exact vs approximate answers) -vertex, standard, and factored forms of quadratics -sketching parabolas after finding intercepts and vertex ||  || n the problem OR you need to use a diagram to generate the quadratic. Here are three examples we did in class: 1. A suspension bridge cable has a parabolic shape, with three known coordinates: (0,70), (40,10), and (80,70) all in metres from the left edge and above the road level. Find the vertex form of the parabola. Answer y = (3/80) (x-40) ² + 10 2. The height of a ball (in metres, after t seconds) is given by h = -5t ² + 30t + 2. Find the maximum height of the ball. Answer: after 3 sec, the height is 47 m. 3. The St Louis Arch is 630 ft high and 630 ft wide. Taking the bottom of the arch as (0,0), in the equation of the parabolic arch in vertex form. || p 270 # 7,8,10 || y = 3x² + 18x + 5 and for y = -2x² + 8x + 5 Review of applications of quadratic functions - either we are given a function and have to answer questions OR we are given points and we have to find the quadratic. Here are two more examples: 1. Ball thrown upwards from ground, reaches max height of 18 m after 3 sec, and then hits ground 3 sec later. Find the quadratic function for this motion - vertex form, standard form, and factored form 2. Path of firework is given by h = -5(x-5)²+ 127 where x is in seconds and h is in metres. Find the vertex AND the intercepts. Explain what the vertex and intercepts represent in this problem. then sketch the parabola || Finish two problems from class then do p 187 # 13 a,b || If anyone else wants to do the last quiz in class, ask me for new numbers. Then hand in your checked quiz. Applications - we continue for a few more classes with applications. Then we have a final unit test and move on to Trigonometry. ||  || Hand back quiz from Wednesday, [|another one today] || P 192 # 8, 193 # 10,11 290 # 9 || We have a TEST next Friday - everything on applications and vertex form with A not equal to 1. Review of quiz problems and the homework from last class - problems 192 # 8 and 193 # 10 - good test questions! || New problems: P 272 # 18, 21 P 290 # 8, 10 Challenge problems - only if the other problems are easy for you: P 270 # 13, P 290 # 11,19 || Today's work will focus on test preparation for Friday. Our preparation will involve reviewing many of the problems that have been assigned since March break: - finding x intercepts by factoring and by using the quadratic formula - finding the vertex by completing the square - focus on problems with A not equal to 1 - solving word problems that deal with projectiles (thrown objects) and structures that are parabolic in shape. - in the word problems you are either given the quadratic or you need to use the given information to find the quadratic. ||
 * Mar 25 || Review of the quadratic formula - review of exact vs approximate answers.
 * Mar 27 || Quiz on using the quadratic formula for exact and approximate solutions.
 * April 2 || Review of quadratics for Thursday's test
 * April 4 || Test on quadratics - everything since the beginning of the unit
 * April 8 || What if you are given a parabola (A not equal to 1) in standard form, and you
 * April 10 || Quiz on vertex form with a not equal to 1. Find the vertex for
 * April 12 || Quiz on vertex form and applications next class - Tuesday
 * April 16 || Review of quadratic applications
 * April 18 || Quiz - we did the same quiz again, and you could use your books after 10 minutes of working from memory.
 * April 22 || Mr Guetter is gone for soccer today - he may be back before the end of the period.

- we will take these up on Wednesday || the second answer to #3 c is 5.22 sec ||
 * April 24 || I am gone for the first half of class, but will be available in room 205 at lunch tomorrow and at homework club tomorrow. One correction to the answers from yesterday's review:

|| You will have to switch between standard and vertex form, locate the vertex and intercepts on a graph, and solve two problems - one with projectiles and one with arches. When you finish, you should start an introductory set of problems on similar triangles - the beginning of our unit on trigonometry. || p 333 # 5,7,8 || Two triangles are similar if: - the ratios of corresponding sides are equal - two sets of corresponding angles are equal Notation: ΔABC ~ ΔXYZ if vertices A, B, and C on one triangle correspond to vertices X, Y, and Z on the second triangle
 * April 26 || Test - final test on quadratics.
 * April 30 || Introduction to similar triangles

You need to recall ways to show that angles in a corresponding triangles are equal: F, C, and Z-patterns in parallel lines, opposite angles || p 333 # 5,7,8 p 348 # 6,7 || Review of similar triangles and ratios of sides in similar triangles. We need to know this stuff well because the next topic is new - trigonometry. Retest for those who did not do well on the quadratic applications test. The date is next Monday, during class **. Your entry ticket for the retest is to fix up the questions that you had errors on. Why? because the retest will have similar questions and you need to practice the skills of completing the square, solving for x-intercepts, and determining the A-value for a parabola. || p 386 # 3,4,5 p 349 # 9, 10, 11, 14 if you need a challenge - # 30 || Sin A = opposite/hypotenuse Cos A = adjacent/hypotenuse Tan A = opposite/adjacent And we use a neat rule to remember the order: SohCahToa - try saying it. || Finish worksheet then p 362 # 1 p 372 # 1 Next time we will learn how to find the angle if we are given the sides. || If you know the angle, you can use the Sin, Cos, or Tan function to find the ratio, and use that ratio to solve for missing parts of the triangle If you DON'T know the angle, you need to use the INVERSE Sin, Cos, or Tan function to find the angle, and use that angle to solve for missing parts of the triangle. Check your calculator: 1. it must be in DEGREES, not radians or gradians (if you're not sure, ask) 2. if you know the angle, use the Sin, Cos, or Tan button; if you need the angle, use the INV or 2nd button and then the Sin, Cos, or Tan button || p 362 # 5,6 p 373 # 10 you need to solve for ALL the missing parts of the triangle. Use Sin, Cos, and Tan once for each problem. || We are reviewing the right angle trig ratios and how to solve for missing angles and sides in triangles using those ratios. remember to write out an expression with sin, cos or tan first, and then solve for the missing parts. Don't just give an answer - that doesn't help us very much. || Finish p 362 and 373 New: p 362 # 7, p 374 # 12-14 In each problem solve for ALL of the missing angles and sides. Use each trig ratio ONLY ONCE. || solving triangles with trig ratios hand-in assignment for test on May 30 ||
 * May 2 || Homework not done well - so we need to challenge ourselves to do better.
 * May 6 || Worksheet on similar triangles and trig ratios. For a right angled triangle with one angle (not the right angle) labeled "A", we define three ratios:
 * May 8 || Solving right angled triangles using trig ratios.
 * May 10 || Mr Guetter is gone today - assignment given in class
 * May 16 || review of trig ratios in right angle triangles

here are the || Law of sines a/Sin A = b/Sin B Law of cosines c² = a² + b² - 2ab Cos C The hardest part, initially, is deciding whether to use the law of sines or the law of cosines. This list may help: -if you know three sides of a triangle and need an angle, use Cosines (SSS) -if you know two sides and the angle between them, use Cosines (SAS) -if you know two angles and one side, use Sines (ASA or AAS) -if you know an angle and its opposite side, use Sines || Homework assigned from textbook You will need to do at least an hour of homework between now and next week Tuesday if you want to learn these trig laws well. p 402 # 1,2,4,5,6 p 409 # 1,2,4 Here are For your project day on Friday, you can work on p 402, 409 AND p 418 # 1,2,5 || Homework for next class - Applications of right triangles and oblique triangles ||  || - equations and graphs of lines - systems of linear equations (algebra, graphs and applications) - analytic geometry - calculations of midpoint, slope, and length for geometric figures || The exam covers the entire course, with an emphasis on the second semester. We will work through much of the work from pages 438-447 p 438-441 # 2c,3bc,4bc,5,8,9, 10,(11), 12,15,25,27ab,30 || - quadratic expressions, equations, graphs, and applications || p 441-444 # 34-39,43-49,51, 53-55, 56,59,60,62,63 || - trigonometry (shortest section of the exam) || p 445 # 64,65,69-74,75-83,85,86 ||
 * May 22 || Solving for sides and angles in oblique triangles (no right angle) - here are the [[file:sinesCosinesHandout.pdf|in-class notes and examples]]
 * May 28 || Review of trigonometry - right triangles and oblique triangles ||  ||
 * May 30 || Test on trigonometry
 * June 3 || Exam Review - Day 1 (30% of exam)
 * June 5 || Exam Review - Day 2 (50% of exam)
 * June 7 || Exam Review - Day 3 (20% of exam)
 * June 11 || Last class of the year

There is a list of basic review skills on pages 458 - 475. If you need practice with the basic skills in this course, you should do thes problems || There are challenge review problems on pages 448-457. If you expect to get an A or A+, you should be familiar with some of these ||

Homework policies, quizzes, chapter assignments || Find the equation of the line through the points (-1,1) and (3,3) and sketch the graph (label points and axes, use ruler, arrowheads) Finish name tag - minimum of two colours, something to associate with your name - make it level 4 work. ||  || will laminate them for next class. Check one homework problem and work in class to review other ways of graphing and determining equations of lines || p 4-5 # 2,4,5,6,7 - do at least half of the questions; more if they seem hard. Show a step if expanding or substituting; Underline final answer; check back of book ||  || Solving for the intersection of two lines: a. if both are given in slope-intercept form, set the equations equal to each other, solve for x, then substitute and solve for y. You can use either equation to solve for y, right? Example: y = 2x+4 and y = x-3 (-7,-10) b. if only one equation is given in slope-intercept form, substitute one equation into the other, solve for x, substitute into either equation and solve for y. Example: x + 2y - 3 + 0 and y = x + 9 (-5,4) || p. 17 # 8 a-d, 9 a-d [|Chapter 1 pdf] ||  || Handout to review lines, graphs, forms, and intersection
 * **First**
 * Semester** || **Class Topics and Summary** || **Handouts and Homework** ||  ||
 * Sept 4 || How to succeed in this course - course syllabus and timeline (see main page), Grading policies (most consistent, most recent, lates/zeros)
 * Sept 6 || Hand in your level 4 name cards and Mr Guetter
 * Sept 10 || Quiz from problems on p 4-5
 * Sept 12 || Hand back quiz # 1 - there is room for improvement

Review of solving two equations with two unknowns -if there are fractions in the equations you can multiply by the common denominator to clear the fractions. This should make it easier to solve. Using graph paper to solve for the point of intersection Using online utilities to solve: [|fooplot], [|google], [|wolfram alpha] || you must use a computer to make graphs that show the intersection for FOUR problems from You must use at least two of these three websites Copy and paste each graph - not the entire window - into a one-page document that you print and hand in NEXT CLASS. When we get to class, you will use algebra to solve these problems and hand in as well. ||  || Hand in sheet with four graphs AND a single handwritten sheet with your best algebra work for the same four problems. || You have already solved many of the problems from # 8,9 and 10. This is a chance for you to show what you already know. I expect two pages handed in - one with graphs and one with your work ||  || A sample problem looks like this: Find the intersection of 2x + 3y - 4 = 0 and 3x + 5y = 7 answer (-1,2) As you can see, we can't easily write y=mx+b for even one line We could graph the lines, but that is a lot more work than using algebra. || Handout - graph and solve using one of the three methods outlined in class: A. y = x - 5, y = -2x + 7 (4,-1) B. y = 2x + 1, x + 3y = 10 (1,3) C. 3x + 4y + 1 = 0, 2x - 3y = -12 (-3,2)
 * Sept 14 || By the end of class today:
 * Sept 18 || We will identify the third strategy for solving intersection problems - one in which we can't very easily make a substitution for x or y. We call this the method of "elimination".

Here's one more for practice 2x - 5y + 1 = 0 5x - 3y = 7 (2,1) ||  || Solving for intersection of two lines - we could graph, but... So we use one of the methods outlined in chapter one of the textbook - substitution and elimination BOTH of these methods are really substitution || p 26 # 4,5 p. 40 # 3,4,5 You must come to Friday's class with TEN of these problems solved ||  || Quiz - intersection of lines - one problem from homework - need to graph both lines AND use algebra to find the point of intersection. Review of solving systems of equations - two lines that are related to eachother. I have prepared a handout so that my work is easier to follow - BUT it should not keep you from following my work on the board. || [|Solving Linear Systems] you must finish solving the problems on this handout - there are only TWO, but they must be solved using different methods. PLUS - everyone must finish the problems from Sept 26 homework. - pick one - if you were absent, hand this in on Monday; if your score was less than 80% try it again. You can check your answers at WolframAlpha.com ||  || 1. find points on a line, find intercepts 2. graph one or two lines on an x-y axes 3. solve intersection problems using algebra || finish the quiz - answers are (3,1) (3,2) and (6,8) Review problems: p 48 # 4, 9, 10, 12 ||  || Homework - based on our work with linear systems: for each word problem, please do the following: - write a let statement: x=the number of dimes, or x=the speed of the river, etc. - write TWO equations for each word problem - DON'T SOLVE THE EQUATIONS - we do that on Friday || Sample: Julie sold sandwiches and drinks for a job. One day she sold a total of 20 sandwiches and drinks and made $40.00. How many of each did she sell if drinks are $1.50 and sandwiches are $2.75 Let x = # sandwiches, Let y = # drinks x+ y = 20, 2.75(x) + 1.50(y) = 40 # 8,9,15,17 p. 46-47 # 7,8,11,12 ||  || sandwiches = x and # drinks = 20 - x and then solved: 2.75x + 1.5(20 - x) = 40 This year, we use TWO variables, not one. || solve dist-rate-time problems 7 and 8 (p. 46) on board Handout - # 6,7,9,13 - find two equations and then solve. ||  || New - solutions and percentages: We need to make 10 litres of a 34% solution but all we have is a container of 20% solution and a container of 50% solution. How much of each do we use? x=the number of litres of 20% solution y=the number of litres of 50% solution so... x+y = 10 (litres) and 0.2(x) + 0.5(y) = 0.34(10) we can use algebra to solve these equations || Everyone needs to finish # 6,7,9,13 for next class. New:handout: 10, 11, then 8 p 47 # 9, 10, 14 find this on [|Chapter1.pdf] Test Recovery - tomorrow at lunch for all those who need another chance to pass the test or to improve their current mark. At lunch in 205 - no exceptions. ||  || P 49 # 14,15,16 P 51 # 17,18,19
 * || Quebec Trip and Walk-Bike-Work-a-thon ||  ||   ||
 * Sept 26 || Welcome back to math class - let's start again...
 * Sept 28 || Check homework - how many of you have TEN problems finished?? Only 10/26 in the class finished - meh....
 * Oct 2 || Walk-bike-work ||  ||   ||
 * Oct 4 || Review for next week's test - if you are leaving early for sports, you must write at lunch - no exceptions.
 * Oct 10 || Test # 1 - lines, intercepts, graphing, intersection -you must write at lunch if you are gone last period today
 * Oct 12 || One change from last year (gr 9) is that you did substitution without even calling it that. Last year you would have taken the sample problem and said:
 * Oct 16 || take up homework from dist-rate-time problems.
 * Oct 18 || Read through sample problems in textbook - look for hints about how to solve word problems in two variables.
 * Test on Word problems next Wednesday** - yes, the last day before your October break. This is a good chance for many of you to improve your first term mark. || P 47 # 17,18

Determine equations for each problem and then solve TWO of each type. ||  || You must do AT LEAST THREE of each type (=6 total) ||   || Begin new unit on Analytic Geometry - that is, working with lines and shapes on an x-y grid. We will learn (or relearn) how to: a. find the slope of a line segment b. find the length of a line segment c. find the midpoint of a line segment d. know when two lines are parallel or perpendicular || Homework: Midpoint: think of this as the average or the balance point of a line segment. If we have a line segement that is 8 units long, the balance point is in the middle - at 4. If we have two marks of 72 and 88, the average (or middle) is 80. Length: think of this as how far you need to walk in a straight line to get from A to B. We sometimes call this: "as the crow flies". We use the Pythagorean Theorem to solve problems of length since it is easiest to determine how far across and how far up/down one point is in relation to another. For the points (-2,5) and (6,1), we can calculate both midpoint and length: M = x-average of -2 and 6 and y-average of 5 and 1: (2,2) L = pythagorean length from (-2,5) to (6,1) change in x is 8, change in y is 4, so the length is L² = 8² + 4² and the length is 8.9 ||
 * Oct 22 || Quiz on word problems - one dist-rate-time problem and one mixture problem. || [[file:review6.6-6.8.pdf|Review exercises]] - most of your work should be finding TWO equations for each word problem, since we already know how to solve two equations with substitution or elimination.
 * Oct 24 || Test - half class - on word problems - you will have to find equations and solve for the variables. Again, if you are gone last period, you will have to write at noon in room 205.
 * 3,4 slope of a line
 * 5,6 equation of a line in y = mx+b form ||  ||
 * Oct 30 || Today we learned how to calculate the midpoint of a line segment and the length of a line segment.

Homework: Finish side 2 of the Plus p.66 # 1 b,d 2 c,d 3 b,c p 77 # 1 c 2 c,d 3 b,c ||  || New: use geogebraweb.appspot.com to visually solve problems involving midpoint and length of a line segment. || [|Geogebraweb.appspot.com] 1. solve side 2 from yesterday's handout using geogebraweb 2. solve for midpoint and length on p 66 # 4a,b Ignore the textbook instructions for #4; just find the midpoint and length for each side of the triangle. ||  || New: using slopes to find right angles. If two line segments are perpendicular, they form a right angle = 90 degrees. using slopes we can show that line segments are perpendicular one of two ways: - if m1 * m2 = -1 the line segments are perpendicular - if the slopes are negative reciprocals of each other, the line segments are perpendicular. || Homework: p 89
 * Nov 1 || Take up homework from p 66 and 77
 * Nov 5 || Review of last class work - find the length and midpoint for #4b
 * 1) 5 - show that the triangle is a right triangle by using BOTH slopes and lengths (Pythag)


 * 1) 9 - Isosceles triangles have two equal length sides. Is this triangle isosceles? ||  ||
 * Nov 7

and

Nov 9 || Some of you are here for take-our-kids-to-work day. We will look closely at the homework from last class - both using algebra and using computer. This is your project day assignment as well. You will have an assignment that uses geogebraweb very soon, so this is a good opportunity to practice. || P 89 # 5,9 P 89 # 7,10 - do these graphically and using geogebraweb; next week we will look at algebraic solutions to these problems. Here is the and here is ||   || Application problems with slope, midpoint, and length. You need to complete the geogebraweb assignment at home, since we will use those skills to do an assignment next week. || p 67 # 10,16,17,19 p 77 # 5, 6, 13 Draw a diagram on graph paper for each and then solve using formulas. Here is the ||   || Check and take up two problems from homework - well done Review of the calculations needed to solve analytic geometry problems: slope, midpoint, length Quiz - hand in by end of class. You must write on top whether you used your notes/textbook or if you did the work from memory. You may ALWAYS use your review sheet - even on the test. || A few of you need to finish your work from p 67 and 77 New questions from p 89 (textbook pages are given on Oct 30) P 89 # 7a, 9, 17, 18 for the students who were gone - hand in at the beginning of next class ||  || Quizzes returned - please keep your review sheet updated with definitions, formulas and examples to use on quizzes and tests. New Work: How to find the shortest distance from a point to a line We did two examples in class and followed these steps: -find the slope and equation of the original line -find the slope of the perpendicular -use the perpendicular slope and the point to find the equation of the second line -solve for the point of intersection between the two lines -use length formula or Pythagorean Theorem to find the distance || Homework - not optional! 1.finish = shortest distance from D to AC 2.finish problem 18 from last class 3. p 90 # 21 a,b and # 27 a,b
 * Nov 13 || Review sheet of terms that we know already and terms that we will need to learn. You may add any information to this sheet AND use it when we have a test.
 * Nov 15 || Fill in formulas and definitions on the Review Sheet
 * Nov 19 || Check homework - most had 7, 9, and 17 done. Problem # 18 is your entry ticket to class on Wednesday - no exceptions.

We will have a test next week Thursday on our analytic geometry unit - Nov 29. You will be able to write formulas, definitions, and examples on your review sheet. ||  || Can you: - determine the equation of a MEDIAN? - calculate the point of intersection of two MEDIANS? - calculate the equation of a PERPENDICULAR BISECTOR? - calculate the point of intersection of two PERPENDICULAR BISECTORS? || ||   || Finish problems from p 104 || Homework - p 104# 8a,b,c 9a,b 11a,b,c 12a (do this two different ways) ||  || work on p 104-105 assignment plus the last quiz Make sure your review sheet has definitions, formulas, examples written out so that you can do an excellent job on the test. || ||   || we will use computer software to investigate properties of triangles, quadrilaterals, and circles. We start with last week's test problems. You will save each problem to a word or google document, as shown in the sample and in class. It will be very important to add text boxes to identify points, equations, lengths, slopes, and other specific features that are important in the question or answer of a problem. || - from the test problems In number 3, the equation of the line does not match the points that are given... so ... don't use that equation. Instead, use the line tool to draw and find the equation of the line between the given points. Then finish the problem ||  || - lengths of sides and classification of triangle - right or not-right triangle - centroid of triangle; where do the medians meet? - midpoints of the sides of a triangle; slope and length || triangles in Geogebraweb to find the area of a triangle you can enter this command: Area[vertex1, vertex2, vertex3] ||  || - midpoints of a quadrilateral - when is a quadrilateral a parallelogram? - midpoints of the diagonals in a parallelogram || quadrilaterals in Geogebraweb p 143 # 5,9 (you can do 11 and 15 if you need practice) ||  || - right bisector of a chord - three points on a circle - orthocentre and circumcentre of a circle - angles in a semi-circle || circles in Geogebraweb p 150 # 9, 12, 14 ||  || Today's work: You must finish your geogebra assignment and either hand in, email or share a document that has the following: - 2 problems from first assignment - Dec 3 - 2 problems from p 125 - Dec 5 - both problems from quadrilaterals - Dec 7 - two problems from p 150 - Dec 11 For each problem you must: - write a one to two sentence summary of the question - include your geogebraweb picture (with all the work and textboxes) - write a one to two sentence explanation of your answer || As an example (p 125 # 9) summary: connect the midpoints of two sides of a triangle and show that this new line segment is parallel to the third side and half the length.
 * Nov 21 || Review of Analytic Geometry for the test next week THURSDAY
 * Nov 23 || last quiz on analytic geometry
 * Nov 27 || Review for analytic geometry test
 * Nov 29 || Test on Analytic Geometry - whole class ||  ||   ||
 * Dec 3 || Using Geogebraweb to investigate properties of plane figures
 * Dec 5 || Look at specific triangle properties in geogebraweb:
 * Dec 7 || Look at specific quadrilateral properties in geogebraweb:
 * Dec 11 || Look at specific circle properties in geogebraweb:
 * Dec 13 || At lunch - test recovery - you can redo two parts of last test and earn up to 80%

Answer: both slopes are equal, as shown in the diagram, and the shorter side is one-half the length of the third side, also shown in the diagram. ||  || Introduce students to expanding and factoring - first part of our new unit on quadratic expressions and functions. Lots of examples on the presentation Learn the special cases: (a+b)², (a-b)², (a+b)(a-b) Factoring quadratic expressions like x² + bx + c - we need to look for two numbers that add to "b" and multiply to "c" || finish p 217 and 225 for homework - every single problem ||  || Review of FOIL - introduction to applications and to harder problems || P 218 # 7,8 - these are harder, multi-step problems then do # 9a, 10b,c, 13, 15, 16a,b ||  || Examples like: expand: (2x+1)(x-3) factor: 2x² + x - 6 If "a" is not equal to 1, we use a method called decomposition, we will review this on the first day back. [|Here is a link] - you should be able to find many more examples on the web ||  ||   || And factoring, both where the x² term is 1 and where it is NOT 1. We reviewed the method of decomposition (2 numbers that add to the middle term and that multiply to the PRODUCT of the first and last tems) In 2x² + x - 6, we need two numbers that add to 1 and multiply to -12 Introduction to factoring special quadratics - especially ones in which the middle term is ZERO. || factor each one, then FOIL to check # 3 a-g ||  || New - finish unit on expanding binomials and factoring trinomials - more practice problems and word problems || word problems - p 226 # 11,12 p 241 # 6,14 p 247 # 12 algebra practice - p 246 # 4 handout - finish # 3 ||  || 1. Lines, equations, applications: find the equation of a line, sketch one or more lines on a graph, solve for the point of intersection between two lines, applications involving speed,distance,time and percentages 2. Geometry, terms, calculations, longer problems like - equation of median, altitude, perpendicular bisector; distance from point to line, classify triangles as equilateral, isosceles, scalene, classify quadrilaterals as parallelograms 3. Multiplying and factoring algebraic expressions, special cases, word problems involving multiplying and factoring algebraic expressions. || Note for review assignment - you do NOT have to do the review problems that involve circles. We did some of this in geogebra, but it will NOT be on the exam. ||  || 1. fully factor: 9x² - 36y² 2. factor: 3x² + 7x - 6 3. find the shortest distance from (4,2) to the line x-y+4=0 d= √ 18 ||  ||   ||
 * Dec 17 || check form problems with the geogebraweb assignment due on Wed.
 * Dec 19 || Geogebra assignment due today. School policy allows me to deduct up to 10% if your assignment is submitted on time. I will exercise this option for anything not received by the end of class on Friday.
 * Dec 21 || Continue with Foil and Factor - this time in cases where the x² term is not 1.
 * Jan 8 || Review of FOIL with binomials (2 term expressions)
 * Jan 10 || take up five problems from yesterday's homework - give starting points.
 * Jan 14 || Review - day 1 - summary of key topics in each unit:
 * Jan 16 || Three review problems: