Warrnambool College Maths Methods Unit & 0 Unit Topics: Linear functions Quadratic functions Cubic functions Eponential & logarithmic functions Functions & relations Unit Topics: Circular functions Differentiation Matrices Probabilit Combinatorics Assessment tasks There will be a test for each of these topics. Students are allowed to bring their workbooks into the test (with notes & questions). CAS calculators can be used in most tests, although some will have a calculator free component. Tests will contribute 80% of the mark for each topic area. 0% of the mark for each topic will come from having completed the set Khan Academ tasks. Each semester there will be one problem solving / project task and eam. Semester reports will include a grade for each topic test, as well as the semester eam and problem solving task.. At Warrnambool College students will have met the outcomes for a unit if the: achieve 0% or better on all topics. complete the set class work and completed the relevant revision work. complete the problem solving / project task. attend at least 80% of classes.
Maths Methods Blog Page To give students the opportunit to learn the concepts and work through at their own pace, podcast videos and printed notes for all topic areas have been prepared. These are all available on the school network and the podcast videos can be accessed freel through the itunes store (Maths Methods Podcast: itpc://mathsmethods.podomatic.com/rss.ml) or the blog site. The blog site http://methods.global.vic.edu.au/ is also available for students to download these materials, as well as eam revision, worksheets, Khan Academ links etc. All students will be given a username & password to contribute to the site. Students can also post questions and answer other students questions. It is epected that all students will have obtained these before resources in advance of the topic and are watching / reading as part of a regular homework routine. This preparation will allow students to better use the class time to work on problems and clarif an difficulties. Khan Academ The Khan Academ website provides video tutorials and eercises in all areas of mathematics. All students will be able to sign into the Khan Academ using their Warrnambool College GMail account. (Please make our username our full name for identification.) Class teachers (vincent.justin.t@edumail.vic.gov.au or twitt.greg.c@edumail.vic.gov.au ) need to be added as coaches. CAS calculators It is presumed that all students will have a CAS calculator for class and assessment tasks. Some of the assessment tasks will require the use of the calculator, for other tasks it will be of assistance. The essential skills that students will need for the start of the ear include: Ke operations Saving documents Navigating through multiple tabs Drawing graphs Finding values from equations Solving equations Tet book It is epected that all students will have a current (third edition) or the previous edition of the tet book: MathsQuest Mathematical Methods CAS and separate CAS calculator guide. (These have blue covers). Older (brown covered) editions are not advised.
CAS introductor task For the linear function = 0 + : a) Plot the graph over the domain (-0,0). b) Find the value of when =. c) Find the and intercepts. d) Find the value of for which =. e) Find the point where the function intersections the line =. Show how questions can be completed using the CAS calculator. You must show at least two was that questions b - e can be answered using the calculator. Save this document on our calculator for all of our linear functions work. Headstart work tasks A - Solving linear equations: Q (ESQ) B - Rearrangement and substitution: Q, C - Gradient of a straight line: Q (ESQ), 7,8 D - Equations of the form = m+c: Q (CAS activit), - 8 (ESQ)
EXERCISE A ebookplus Digital doc Spreadsheet 00 Equation solvers Solving linear equations and inequations WE Solve the following linear equations. a 9 b 7 c 9 9 d e g 7 8 9 WE Solve the following linear equations. f 7 h 0 i 7 8 77 a 9 ( ) b 7 7( ) c ( ) d 7 ( ) e f ( ) 9 EXERCISE B g h 0 7 ( ) i 7 9 j 9 k 7 9 7 9 8 l 8 9 WE Solve the following linear inequations. a b c 9 7 d 7( ) e 7 ( ) f ( ) Rearrangement and substitution Rearrangement and substitution WE Calculate the value of the subject (the first mentioned pronumeral), given the values of the other pronumerals. k a I k 0, d d b E K mgh K 0, m, g 0, h c D( n ) n,.8 d E hf 0 W h., f 0 000, W 0 000 e v r, r., WE The perimeter, P, of a rectangle of length l and width w ma be found using the equation P (l w). a Find the perimeter of a rectangle of length cm and width cm. b Rearrange the equation to make w the subject. c Find the width of a rectangle that has perimeter 0 mm and length 0 mm.
EXERCISE C Gradient of a straight line WE7 Calculate the gradient of each of the following linear graphs using the intercepts shown. a b ebookplus Digital doc Spreadsheet 0 Gradient of a straight line WE8 Without drawing a graph, calculate the gradient of the line passing through: a (, ) and (0, 0) b (, ) and (, ) c (0, ) and (, ) d (, ) and ( 7, ) WE9a Calculate the gradient (accurate to decimal places) of a line making the angle given with the positive -ais. a 0 b 7 c 0 d 0 e 0 f 0 g h 89 WE9b Calculate the gradient of each line below. Give answers to decimal places. a b 9 c d 8
Which of these lines has: a a non-zero positive gradient? b a negative gradient? c a zero gradient? d an undefined gradient? A B D 0 C MC a Which of the following lines has a gradient of? B A C D E 0 b Which of the following lines has a gradient of? D A C 0 E B 7 Burghar plots the coordinates of a proposed drivewa on a plan which is shown at the top of the facing page. What is the gradient of the proposed drivewa? Garage Drivewa m 7 m 8 An assembl line is pictured below. What is the gradient of the sloping section? (Give our answer as a fraction.) BOFFO Made in Australia BOFFO Made in Australia 0.8 m BOFFO Made in Australia m 9
EXERCISE D ebookplus Digital doc Spreadsheet 07 Linear graphs Sketching linear functions Use a CAS calculator or other method to sketch graphs of the following equations on the same set of aes. a b c d e What is the effect on the graph of the number in front of the (the -coefficient or gradient )? Use a CAS calculator or other method to sketch graphs of the following equations on the same set of aes. a b c d Use a CAS calculator or other method to sketch graphs of the following equations on the same set of aes. a b 7 c d What is the effect on the graph of the number at the end of the equation (the -intercept )? Write the equation of a line having the following properties (where m gradient and c -intercept). a m, c 7 b m, c c m, c d m, c e m, c f -intercept, gradient 7 Rearrange the following equations and state the gradient and -intercept for each. a 8 0 b c d 8 e 7 f 0 g h 8 0 i 0 j 7 0 8 State the equation for each of the following graphs. a 0 b 0 c 0 d 0
CHAPTER Linear functions Eercise A Solving linear equations and inequations a b 8 c d 7 e f g h i a b c d e f g 9 h i j k 9 l 7 a b e f 7 9 7 9 c d Eercise B Rearrangement and substitution A a P A L b l w d C c t d r v E e f r Fd mu g v m i w S lh ( l h) h v rt kqq F j H S r r a 0.7 b 0 c 7 d 00 e.98 a l A, 7. 7 b r c e V 0,. v u a,. 7 d l g T l ( ) K c,,. 97 a cm b w P l w P or l c 0 mm a 0 m A A bh b a b or a c 8 cm h h a $.0 A A D b r D 00 00 c.% D uv 7 a f u v b u fv v f 8 b 9 h cm c 0 cm Eercise C Gradient of a straight line a b a b c d a.9 b.078 c 0.7 d 0.77 e 0.77 f 0 g h 7.90 a 0.9 b. c 0. d.7 a D b C c A d B a B b E 7 7 8 7 00 9 a b c d 0 a No b Yes c cm Eercise D Sketching linear functions a e The higher the number, the steeper the graph. Positive values make the graph slope up when moving (or tracing) to the right; negative values make the graph slope down when moving to the right. a d a d 7 0 + 7 The number is where the graph cuts the -ais (hence the name -intercept ). a 7 b c d e f 7 a, b, 8 c, d, e 7, 9 f, g, h i, j, 7 8, 8 a b c d e f 9 a b