New Higher-Proposed Order-Combined Approach. Block 1. Lines 1.1 App. Vectors 1.4 EF. Quadratics 1.1 RC. Polynomials 1.1 RC
|
|
- Geoffrey Ward
- 8 years ago
- Views:
Transcription
1 New Higher-Proposed Order-Combined Approach Block 1 Lines 1.1 App Vectors 1.4 EF Quadratics 1.1 RC Polynomials 1.1 RC Differentiation-but not optimisation 1.3 RC Block 2 Functions and graphs 1.3 EF Logs and Log graphs and exp 1.1 EF Trig graphs 1.3 EF Integration 1.4 RC Recurrence 1.3 App Block 3 Circle 1.2 Ap Trig eqt 1.2 RC TRIG -plus wave function 1.2 EF Application of Differentiation 1.4 App Application of Integration 1.4 App
2 UNIT 1 Higher Maths The Straight Line 10 Periods (a) Finding gradient, using m=tanx Heinemann Ex 1A Maths In Action P4,5 Maths In Action P4,5 (b) Establishing collinearity, finding perpendicular and parallel lines (c) Using Y=mx+c, Re-arrange to General Equation Ax+By+C=0 He Ex 1B, 1C, 1D P6, 7 P6, 7 He Ex 1E, 1F P10 P10 (d) Using y-b=m(x-a) He Ex 1G P11,12,13 P11,12,13 (e) Equation of Perpendicular Bisector, finding midpoint (f) Equation of altitude and median He Ex 1I P12, 13 P12, 13 He Ex1K, 1M P12, 13 P12, 13 (g) Intersecting Lines/Problem Solving He Ex 1N, 1O P14,15,16 P14,15,16, Pegasus Assessment App 1.1 Teaching Notes The vocabulary within this topic e.g. median, altitude and perpendicular bisector should be emphasized and re-emphasized. Re-inforce prior knowledge e.g. parallel lines, equations of horizontal,vertical lines, proving if points lie on a line etc
3 Higher Maths Vectors 11 Periods (d) Find unit vectors and position vectors. Ex 13F, 13G P203, 204, P203, 204 (e) Verify collinearity. Ex 13I P (f) Use Section Formula Ex 13K P205 P205 (g) Find 3D vectors and use properties Ex 13L, 13M, 13N P197, 198 P197, 198 (h) Use scalar product Ex 13O, 13P P209, 210 P209, 210 (i) Calculate angle between vectors (j) Perform calculations for perpendicular vectors (k) Perform calculations w.r.t. properties of scalar product Ex 13Q P212, 213 P212, 213 Ex 13R P214, 215 P214, 215 Ex 13T, 13U P214, 215 P214, 215 Assessment EF 1.4 Teaching Notes Pupils have worked with vectors through N5-a brief review of previous learning should support learning (f) Example: A(3,2), B(7,14). Find the coordinates of P which divides AB in the ratio 1:3.A diagram should be added her!!, is this the best method? m:n = 1:3A(3,2) B(7,14) x P = = 4 y P = 4 4 = 5 So P is point (4,5)
4 Higher Maths Quadratic Functions 7 Periods (a) Sketch a Quadratic Function identifying y intercept, zeros, axis of symmetry and turning point (b) Use the Completing The Square method (c) Solve Quadratic Inequations by sketching the curve) (d) State nature of roots using the Discriminant (e) Determine tangency using the Disciminant or by Factorising Heinemann Ex 8B, 8C Maths In Action P33 Maths In Action P33 Scho lar Ex 8D MIA P30 MIA P30 Ex 8F MIA P118,119 MIA P118,119 Ex 8H, 8I MIA P118,119 MIA P118,119 Ex 8J MIA P120 MIA P120 (f) Problem Solving Ex 8K MIA P123 MIA P123, Pegasys Assessment RC 1.1 Note should be assessed with polynomials Assessment Standard Teaching Notes When stating solutions to problems pupils should use correct language Emphasise tangency and link to circle
5 Higher Maths Polynomials 8 Periods (a) Find degree, roots, coefficients. (b) Use nested form to evaluate. (c) Use synthetic division to find quotient and remainder. (d) Use synthetic division to factorise polynomials. (e) Find values of p and q in a polynomial. (f) Solve polynomial equations. (g) Identify graphs. (h) Sketch graphs of polynomial eqns of order 3 and 4. (i) Find approximate roots. Ex 7A (orally) Ex 7B Exs 7C, 7D Ex 7E Ex 7F Ex 7F Ex 7G Ex 7H Ex 7G Assessment RC 1.1 Should be assessed with Quadratics
6 Higher Maths Differentiation Periods (a) Find/Evaluating the Derivative Heinemann Ex 6D, 6E, 6F Maths In Action P62, 64 Maths In Action P62, 64 of y=x n, y=ax n (b) Find/Evaluating Derivatives of Products and Quotients Ex 6G P63, 65 MMS Bk8 P63, 65 (c) Find equations of tangents Ex 6J P67,68 P67,68 (h) Sketch graph of Derived Function Ex 6P P69,70 P69,70 Link with previous learning of graphs and inverse functions Find derivatives of sinx and cosx Heinemann Ex 14B Maths In Action P221, 222 Maths In Action P221, 222 Find Derivatives of (x+a) n, Ex 14D, 14E, 14F, 14G P225 P225 (ax+b) n Use the Chain Rule Ex 14H P226, 227, 228 P226, 227, 228 Teacher Notes A revision of indices will be needed to begin with. The main focus should be on the gradient of a tangent. Using first principles, work through a couple of examples, then give the general rule: if f(x) = x n, then f (x) =nx n 1 1. Common mistakes made with f(x) = 3 2x type. f(x) = = 3 x not 2 x 3 2x 2 More notes required here e.g. a simple way of understanding the chain rule. Assessment Teachers can assess each assessment standard individually or test as a complete unit
7 UNIT 2 Higher Maths Graphs And Functions 5 Periods (a) Understand and use Set notation Heinemann Ex 2A. Exs on board Maths In Action P20 Maths In Action P20 Identify Set Range and Domain (b) Find formula and evaluate Composite Functions and inverse function (c) Identify and draw graphs of Ex 2C P1, 2 P1, 2 Ex 3P, Also MIA P34, 35, 36 P34, 35, 36 y=f(x)+a, y=f(x+a), y=-f(x), y=f(-x), y=kf(x), y=f(kx), 2f(x), f(x+3), f(-x), 2-f(x). Inverse function Assessment EF 1.3 The domain is the set of values x can take. Ask what values x cannot be. E.g. f(x) = For range, ask what f(x) cannot be. And WHY! Pupils should be able to find algebraically and draw Inverse functions 1 x 2. Domain { x : x 2, x R} Pupils should spend time drawing and identifying graphs using small whiteboards or ICT etc rather than jotter work! Inclusion of Trig graphs and unusual graphs (e.g. logs and exp) will support learning and future topics
8 Higher Maths Trigonometric Graphs And Equations 6 Periods (a) Identify/Sketch graphs of Trigonometric Functions. Introduce period and amplitude. Heinemann Ex 4A(orally), 4B Maths In Action P50, 51, 52 Maths In Action P50, 51, 52 (b) Calculate angles in Radians. Ex 4C P45, 46 P45, 46 Convert between Radians and Degrees (c) Use triangles to find exact values (d) Solve Trigonometric equations graphically (e) Solve Trigonometric equations algebraically (f) Solve compound angle equations Ex 4E, P48,49 P48,49 Ex 4G P53 P53 Ex 4H P53,54 P53,54 Ex 4I P55 P55 Assessment RC1.2 Should be assessed after all Trig completed Teaching Notes Pupils should learn exact values from the graphs and from the 30,45,60 triangles ie they should start questions by drawing the triangles Graph sketching should re-inforce the learning from previous topic again use whiteboards to allow pupils to sketch graphs Pupils should be able to solve Trig equations with radians and degrees-some examples here
9 Higher Maths The Wave Function 6 Periods (a) Interpret and draw trigonometric graphs Ex 16A Maths In Action P50, 51 Maths In Action P50, 51 (b) Express acosx+bsinx in the form kcos(x-a) (c) Express asinx+bsinx in other forms including multiple angles Ex 16C, 16D P252, 253 P252, 253 Ex 16E, 16F P253 P253 (d) Find max and min values Ex 16G P254, 255, 256, 257 P254, 255, 256, 257 (e) Solving wave equations Ex 16H P258 P258 Assessment Standards EF1.2- RC1.2 Should be assessed with trig formula etc Teaching notes Should build on from the previous sketching of graphs and solving equations Methodology example of solving an equation Please provide an example-please refer to the SQA marking scheme when providing an example to ensure that pupils gain full credit for their working
10 Higher Maths Trigonometry 8 Periods (a) Expand sin(x+y) and sin(x-y) in order to find exact values (b) Expand cos(x+y), and cos(x-y) in order to find exact values Ex 11B, 11C P P Ex 11D P P (c) Prove Trig. identities Ex 11E P153 P153 (d) Expand sin2x and cos2x in order to find exact values (e) Solve trigonometric equations using double angle formulae Ex 11G P158, 159, 160 P158, 159, 160 Ex 11H P161, 162 P161, 162 Assessment standards RC 1.2 EF 1.2 Should be assessed with wave function Trig identities need now to developed within this topic Previous learning e.g. sin 2 x + cos 2 x = 1 and Tan a = Sin a/cos a should be re-visited Time should be spent at the end of this topic providing pupils with the opportunity to practice all types of trig equations (including previous topics) so that they can identify the appropriate strategy for different equations Assessment Unit 2 can be broken down into Assessment standards or taken as a whole group of topics
11 Higher Maths Logarithms And Exponentials 9 periods (a) Interpret and draw exponential graphs (b) Carry out exponential growth and decay calculations (c) Evaluate/Solve exponential functions to the base e (d) Use properties of logarithms to simplify/evaluate/solve (e) Solve equations using natural logarithms (f) Find a logarithmic formula from experimental data Heinemann Ex 15B Maths In Action P39 Maths In Action P39 Ex 15C P236, 237, 238 P236, 237, 238 Ex 15D P239, 240, 245 P239, 240, 245 Ex 15E, 15F, 15G P242, 243 P242, 243 Ex 15H P244, 245 P244, 245 Ex 15I, 15J P247 P247
12 Higher Maths Basic Integration 8 Periods (a) Find Indefinite Integrals for Ex 9F, 9G, 9H MIA P126 P126 x n and ax n (b) Integrate with Products and Quotients (c) Find area using definite integrals, Fundamental Theorem of Calculus Ex 9I P127, 128 P127, 128 Ex 9K, 9L P128, 129 P128, 129 (d) Find area above and below x axis Ex 9M, 9N P133, 134, 135, 136 P133, 134, 135, 136 (e) Find area between two graphs Ex 9O, 9P P137, 138 P137, 138 (f) Find the solution to Differential Equations Ex 9Q P129, 130 P129, 130 Integrate sinx and cosx Ex 14C P230 P230 Integrate (ax+b) n Ex 14J P229, 230 P229, 230 Integrate sin(ax+b) and cos(ax+b) Ex 14K P231 P231 Teaching notes The integral should be introduced as the anti-derivative, e.g. 3x² dx = x³, so x² dx = 1 x³. Do a few examples, then introduce + C. 3
13 Higher Maths Recurrence Relations 6 Periods (a) Construct/Evaluate formula for nth term in a sequence Heinemann Ex 5A Maths In Action P88, 89 Maths In Action P88, 89 (b) Find/Use a Recurrence Relation Ex 5B, 5C P91 P91 (c) Construct/Evaluate a Linear Recurrence Relation (d) Establishing if Limit exists Calculating limit Ex 5D P92 MIA Prep. For Ass. P15 P92 MIA Prep. For Ass. P15 Ex 5H (2 periods) P91 MIA Prep. For Ass. P16 P91 MIA Prep. For Ass. P16 (e) Solving Recurrence Relations to find a and b Ex 5I P92 P92 Assessment Standard App 1.3 Teaching Note Time should be spent solving problems and becoming familiar with the language used within the questions Example of finding the limit methodology should be given here e.g. L = 0.5 L + 0.4
14 UNIT 3 Higher Maths The Circle 8 Periods (a) Use the Distance Formula Heinemann Ex 12A,12B Maths In Action P2, 3 Maths In Action P2, 3 (b) Find the equation of a circle with centre at the origin and radius r (c) Find the equation of a circle with centre (a,b) and radius r (d) Use the general equation of circle to find g, f, c and then r (e) Find point(s) of intersection for a line and circle (f) Find the point of intersection and equation of tangent to a circle Ex 12D P168, 169 P168, 169 Ex 12F P170, 171 P170, 171 Ex 12G, 12H P172, 173 P172, 173 Ex 12I, Ex 12J P174, 175 P174, 175 Ex 12K, 12L P176, 177, 178 P176, 177, 178 Assessment App 1.2 Teaching notes Review previous knowledge of circles including angles /diameter and tangents/properties of a Kite/Rhombus etc Pupils should be encouraged to solve problems by drawing diagrams, looking for isosceles triangles, right angled triangles and if required looking for additional information to improve diagrams to allow problems to be attempted Previous learning within quadratics and polynomials support solving problems and should be emphasized
15 Higher Maths Applications of Differentiation 13 Periods (d) Determine whether functions are increasing or decreasing Ex 6L P73 P73 Rate of change problem (e) Find Stationary Points Ex 6L P72 P72 Determine Nature (f) Sketch curve by identifying x- intercept, y intercept, stationary points, large values of + and - x (g) Determine max and min values of function for closed interval (h) Sketch graph of Derived Function Ex 6N P74, 75 MMS Bk8 P74, 75 Ex 6O P76, 77 P76, 77 Ex 6P P69,70 P69,70 Link to inverse functions and previous graph work Perform optimisation calculations Ex 6Q, 6R P76, 77, 78 P76, 77, 78 Teaching notes Exam technique in difficult optimisation problems-could include- attempting the proof at the end of the question after completing finding the x value etc!!
16 Higher Maths Application of Integration 8 Periods Find area using definite integrals, Fundamental Theorem of Calculus Ex 9K, 9L P128, 129 P128, 129 Find area above and below x axis Ex 9M, 9N P133, 134, 135, 136 P133, 134, 135, 136 Find area between two graphs Ex 9O, 9P P137, 138 P137, 138 Find the solution to Differential Equations Ex 9Q P129, 130 P129, 130 Assessment App 1.2 Assessed with differentiation application Further Notes HW-could we produce a standard set of HWs? revising current and previous topics as we go through the course-including 1 or 2 reasoning questions/ past paper type questions METHODOLOGY We should provide further guidance on effective methodology-bringing together the experience of all our teachers-providing a a more consistent approach and support to less experienced teachers Activities-link to good teaching activities-hyperlinks?-video clips?-smart board resources Assessment Support Assessments and re-assessments to be provided plus a recording tracking grid Could we also produce student assessment review sheets-ie what I have learned what I have still to learn and a link to resources to assist learning?
Algebra and Geometry Review (61 topics, no due date)
Course Name: Math 112 Credit Exam LA Tech University Course Code: ALEKS Course: Trigonometry Instructor: Course Dates: Course Content: 159 topics Algebra and Geometry Review (61 topics, no due date) Properties
More informationBiggar High School Mathematics Department. National 5 Learning Intentions & Success Criteria: Assessing My Progress
Biggar High School Mathematics Department National 5 Learning Intentions & Success Criteria: Assessing My Progress Expressions & Formulae Topic Learning Intention Success Criteria I understand this Approximation
More informationPRE-CALCULUS GRADE 12
PRE-CALCULUS GRADE 12 [C] Communication Trigonometry General Outcome: Develop trigonometric reasoning. A1. Demonstrate an understanding of angles in standard position, expressed in degrees and radians.
More informationThnkwell s Homeschool Precalculus Course Lesson Plan: 36 weeks
Thnkwell s Homeschool Precalculus Course Lesson Plan: 36 weeks Welcome to Thinkwell s Homeschool Precalculus! We re thrilled that you ve decided to make us part of your homeschool curriculum. This lesson
More informationSouth Carolina College- and Career-Ready (SCCCR) Pre-Calculus
South Carolina College- and Career-Ready (SCCCR) Pre-Calculus Key Concepts Arithmetic with Polynomials and Rational Expressions PC.AAPR.2 PC.AAPR.3 PC.AAPR.4 PC.AAPR.5 PC.AAPR.6 PC.AAPR.7 Standards Know
More informationCore Maths C2. Revision Notes
Core Maths C Revision Notes November 0 Core Maths C Algebra... Polnomials: +,,,.... Factorising... Long division... Remainder theorem... Factor theorem... 4 Choosing a suitable factor... 5 Cubic equations...
More informationHigher Education Math Placement
Higher Education Math Placement Placement Assessment Problem Types 1. Whole Numbers, Fractions, and Decimals 1.1 Operations with Whole Numbers Addition with carry Subtraction with borrowing Multiplication
More informationNational 5 Mathematics Course Assessment Specification (C747 75)
National 5 Mathematics Course Assessment Specification (C747 75) Valid from August 013 First edition: April 01 Revised: June 013, version 1.1 This specification may be reproduced in whole or in part for
More informationLyman Memorial High School. Pre-Calculus Prerequisite Packet. Name:
Lyman Memorial High School Pre-Calculus Prerequisite Packet Name: Dear Pre-Calculus Students, Within this packet you will find mathematical concepts and skills covered in Algebra I, II and Geometry. These
More informationEstimated Pre Calculus Pacing Timeline
Estimated Pre Calculus Pacing Timeline 2010-2011 School Year The timeframes listed on this calendar are estimates based on a fifty-minute class period. You may need to adjust some of them from time to
More informationCurriculum Map by Block Geometry Mapping for Math Block Testing 2007-2008. August 20 to August 24 Review concepts from previous grades.
Curriculum Map by Geometry Mapping for Math Testing 2007-2008 Pre- s 1 August 20 to August 24 Review concepts from previous grades. August 27 to September 28 (Assessment to be completed by September 28)
More informationChapter 7 Outline Math 236 Spring 2001
Chapter 7 Outline Math 236 Spring 2001 Note 1: Be sure to read the Disclaimer on Chapter Outlines! I cannot be responsible for misfortunes that may happen to you if you do not. Note 2: Section 7.9 will
More informationExtra Credit Assignment Lesson plan. The following assignment is optional and can be completed to receive up to 5 points on a previously taken exam.
Extra Credit Assignment Lesson plan The following assignment is optional and can be completed to receive up to 5 points on a previously taken exam. The extra credit assignment is to create a typed up lesson
More informationUnderstanding Basic Calculus
Understanding Basic Calculus S.K. Chung Dedicated to all the people who have helped me in my life. i Preface This book is a revised and expanded version of the lecture notes for Basic Calculus and other
More informationPrentice Hall Mathematics: Algebra 2 2007 Correlated to: Utah Core Curriculum for Math, Intermediate Algebra (Secondary)
Core Standards of the Course Standard 1 Students will acquire number sense and perform operations with real and complex numbers. Objective 1.1 Compute fluently and make reasonable estimates. 1. Simplify
More informationContents. 2 Lines and Circles 3 2.1 Cartesian Coordinates... 3 2.2 Distance and Midpoint Formulas... 3 2.3 Lines... 3 2.4 Circles...
Contents Lines and Circles 3.1 Cartesian Coordinates.......................... 3. Distance and Midpoint Formulas.................... 3.3 Lines.................................. 3.4 Circles..................................
More informationPrecalculus REVERSE CORRELATION. Content Expectations for. Precalculus. Michigan CONTENT EXPECTATIONS FOR PRECALCULUS CHAPTER/LESSON TITLES
Content Expectations for Precalculus Michigan Precalculus 2011 REVERSE CORRELATION CHAPTER/LESSON TITLES Chapter 0 Preparing for Precalculus 0-1 Sets There are no state-mandated Precalculus 0-2 Operations
More informationMATH 095, College Prep Mathematics: Unit Coverage Pre-algebra topics (arithmetic skills) offered through BSE (Basic Skills Education)
MATH 095, College Prep Mathematics: Unit Coverage Pre-algebra topics (arithmetic skills) offered through BSE (Basic Skills Education) Accurately add, subtract, multiply, and divide whole numbers, integers,
More information2312 test 2 Fall 2010 Form B
2312 test 2 Fall 2010 Form B 1. Write the slope-intercept form of the equation of the line through the given point perpendicular to the given lin point: ( 7, 8) line: 9x 45y = 9 2. Evaluate the function
More informationGeorgia Department of Education Kathy Cox, State Superintendent of Schools 7/19/2005 All Rights Reserved 1
Accelerated Mathematics 3 This is a course in precalculus and statistics, designed to prepare students to take AB or BC Advanced Placement Calculus. It includes rational, circular trigonometric, and inverse
More informationThe Mathematics Diagnostic Test
The Mathematics iagnostic Test Mock Test and Further Information 010 In welcome week, students will be asked to sit a short test in order to determine the appropriate lecture course, tutorial group, whether
More informationAlgebra 1 Course Title
Algebra 1 Course Title Course- wide 1. What patterns and methods are being used? Course- wide 1. Students will be adept at solving and graphing linear and quadratic equations 2. Students will be adept
More informationwww.mathsbox.org.uk ab = c a If the coefficients a,b and c are real then either α and β are real or α and β are complex conjugates
Further Pure Summary Notes. Roots of Quadratic Equations For a quadratic equation ax + bx + c = 0 with roots α and β Sum of the roots Product of roots a + b = b a ab = c a If the coefficients a,b and c
More informationBirmingham City Schools
Activity 1 Classroom Rules & Regulations Policies & Procedures Course Curriculum / Syllabus LTF Activity: Interval Notation (Precal) 2 Pre-Assessment 3 & 4 1.2 Functions and Their Properties 5 LTF Activity:
More informationMathematics for Engineering Technicians
Unit 4: Mathematics for Engineering Technicians Unit code: A/600/0253 QCF Level 3: BTEC National Credit value: 10 Guided learning hours: 60 Aim and purpose This unit aims to give learners a strong foundation
More informationx(x + 5) x 2 25 (x + 5)(x 5) = x 6(x 4) x ( x 4) + 3
CORE 4 Summary Notes Rational Expressions Factorise all expressions where possible Cancel any factors common to the numerator and denominator x + 5x x(x + 5) x 5 (x + 5)(x 5) x x 5 To add or subtract -
More informationAppendix 3 IB Diploma Programme Course Outlines
Appendix 3 IB Diploma Programme Course Outlines The following points should be addressed when preparing course outlines for each IB Diploma Programme subject to be taught. Please be sure to use IBO nomenclature
More informationMATH. ALGEBRA I HONORS 9 th Grade 12003200 ALGEBRA I HONORS
* Students who scored a Level 3 or above on the Florida Assessment Test Math Florida Standards (FSA-MAFS) are strongly encouraged to make Advanced Placement and/or dual enrollment courses their first choices
More informationMATH BOOK OF PROBLEMS SERIES. New from Pearson Custom Publishing!
MATH BOOK OF PROBLEMS SERIES New from Pearson Custom Publishing! The Math Book of Problems Series is a database of math problems for the following courses: Pre-algebra Algebra Pre-calculus Calculus Statistics
More informationZero: If P is a polynomial and if c is a number such that P (c) = 0 then c is a zero of P.
MATH 11011 FINDING REAL ZEROS KSU OF A POLYNOMIAL Definitions: Polynomial: is a function of the form P (x) = a n x n + a n 1 x n 1 + + a x + a 1 x + a 0. The numbers a n, a n 1,..., a 1, a 0 are called
More informationTaylor and Maclaurin Series
Taylor and Maclaurin Series In the preceding section we were able to find power series representations for a certain restricted class of functions. Here we investigate more general problems: Which functions
More information*X100/12/02* X100/12/02. MATHEMATICS HIGHER Paper 1 (Non-calculator) MONDAY, 21 MAY 1.00 PM 2.30 PM NATIONAL QUALIFICATIONS 2012
X00//0 NTIONL QULIFITIONS 0 MONY, MY.00 PM.0 PM MTHEMTIS HIGHER Paper (Non-calculator) Read carefully alculators may NOT be used in this paper. Section Questions 0 (40 marks) Instructions for completion
More information1 TRIGONOMETRY. 1.0 Introduction. 1.1 Sum and product formulae. Objectives
TRIGONOMETRY Chapter Trigonometry Objectives After studying this chapter you should be able to handle with confidence a wide range of trigonometric identities; be able to express linear combinations of
More informationSimplify the rational expression. Find all numbers that must be excluded from the domain of the simplified rational expression.
MAC 1105 Final Review Simplify the rational expression. Find all numbers that must be excluded from the domain of the simplified rational expression. 1) 8x 2-49x + 6 x - 6 A) 1, x 6 B) 8x - 1, x 6 x -
More informationHIGH SCHOOL: GEOMETRY (Page 1 of 4)
HIGH SCHOOL: GEOMETRY (Page 1 of 4) Geometry is a complete college preparatory course of plane and solid geometry. It is recommended that there be a strand of algebra review woven throughout the course
More informationGeometry Course Summary Department: Math. Semester 1
Geometry Course Summary Department: Math Semester 1 Learning Objective #1 Geometry Basics Targets to Meet Learning Objective #1 Use inductive reasoning to make conclusions about mathematical patterns Give
More informationDear Accelerated Pre-Calculus Student:
Dear Accelerated Pre-Calculus Student: I am very excited that you have decided to take this course in the upcoming school year! This is a fastpaced, college-preparatory mathematics course that will also
More informationSequence of Mathematics Courses
Sequence of ematics Courses Where do I begin? Associates Degree and Non-transferable Courses (For math course below pre-algebra, see the Learning Skills section of the catalog) MATH M09 PRE-ALGEBRA 3 UNITS
More informationMATH 2 Course Syllabus Spring Semester 2007 Instructor: Brian Rodas
MATH 2 Course Syllabus Spring Semester 2007 Instructor: Brian Rodas Class Room and Time: MC83 MTWTh 2:15pm-3:20pm Office Room: MC38 Office Phone: (310)434-8673 E-mail: rodas brian@smc.edu Office Hours:
More informationSemester 2, Unit 4: Activity 21
Resources: SpringBoard- PreCalculus Online Resources: PreCalculus Springboard Text Unit 4 Vocabulary: Identity Pythagorean Identity Trigonometric Identity Cofunction Identity Sum and Difference Identities
More informationThe Australian Curriculum Mathematics
The Australian Curriculum Mathematics Mathematics ACARA The Australian Curriculum Number Algebra Number place value Fractions decimals Real numbers Foundation Year Year 1 Year 2 Year 3 Year 4 Year 5 Year
More informationJUST THE MATHS UNIT NUMBER 1.8. ALGEBRA 8 (Polynomials) A.J.Hobson
JUST THE MATHS UNIT NUMBER 1.8 ALGEBRA 8 (Polynomials) by A.J.Hobson 1.8.1 The factor theorem 1.8.2 Application to quadratic and cubic expressions 1.8.3 Cubic equations 1.8.4 Long division of polynomials
More informationGeoGebra. 10 lessons. Gerrit Stols
GeoGebra in 10 lessons Gerrit Stols Acknowledgements GeoGebra is dynamic mathematics open source (free) software for learning and teaching mathematics in schools. It was developed by Markus Hohenwarter
More informationX On record with the USOE.
Textbook Alignment to the Utah Core Algebra 2 Name of Company and Individual Conducting Alignment: Chris McHugh, McHugh Inc. A Credential Sheet has been completed on the above company/evaluator and is
More informationMathematics I, II and III (9465, 9470, and 9475)
Mathematics I, II and III (9465, 9470, and 9475) General Introduction There are two syllabuses, one for Mathematics I and Mathematics II, the other for Mathematics III. The syllabus for Mathematics I and
More informationAdvanced Math Study Guide
Advanced Math Study Guide Topic Finding Triangle Area (Ls. 96) using A=½ bc sin A (uses Law of Sines, Law of Cosines) Law of Cosines, Law of Cosines (Ls. 81, Ls. 72) Finding Area & Perimeters of Regular
More information2009 Chicago Area All-Star Math Team Tryouts Solutions
1. 2009 Chicago Area All-Star Math Team Tryouts Solutions If a car sells for q 1000 and the salesman earns q% = q/100, he earns 10q 2. He earns an additional 100 per car, and he sells p cars, so his total
More informationBookTOC.txt. 1. Functions, Graphs, and Models. Algebra Toolbox. Sets. The Real Numbers. Inequalities and Intervals on the Real Number Line
College Algebra in Context with Applications for the Managerial, Life, and Social Sciences, 3rd Edition Ronald J. Harshbarger, University of South Carolina - Beaufort Lisa S. Yocco, Georgia Southern University
More informationFurther Mathematics for Engineering Technicians
Unit 28: Further Mathematics for Engineering Technicians Unit code: QCF Level 3: Credit value: 10 Guided learning hours: 60 Aim and purpose H/600/0280 BTEC Nationals This unit aims to enhance learners
More informationMath 241, Exam 1 Information.
Math 241, Exam 1 Information. 9/24/12, LC 310, 11:15-12:05. Exam 1 will be based on: Sections 12.1-12.5, 14.1-14.3. The corresponding assigned homework problems (see http://www.math.sc.edu/ boylan/sccourses/241fa12/241.html)
More informationNorth Carolina Math 2
Standards for Mathematical Practice 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively 3. Construct viable arguments and critique the reasoning of others 4.
More informationNEW YORK STATE TEACHER CERTIFICATION EXAMINATIONS
NEW YORK STATE TEACHER CERTIFICATION EXAMINATIONS TEST DESIGN AND FRAMEWORK September 2014 Authorized for Distribution by the New York State Education Department This test design and framework document
More informationCourse outline, MA 113, Spring 2014 Part A, Functions and limits. 1.1 1.2 Functions, domain and ranges, A1.1-1.2-Review (9 problems)
Course outline, MA 113, Spring 2014 Part A, Functions and limits 1.1 1.2 Functions, domain and ranges, A1.1-1.2-Review (9 problems) Functions, domain and range Domain and range of rational and algebraic
More informationAdministrative - Master Syllabus COVER SHEET
Administrative - Master Syllabus COVER SHEET Purpose: It is the intention of this to provide a general description of the course, outline the required elements of the course and to lay the foundation for
More informationMath 131 College Algebra Fall 2015
Math 131 College Algebra Fall 2015 Instructor's Name: Office Location: Office Hours: Office Phone: E-mail: Course Description This course has a minimal review of algebraic skills followed by a study of
More informationFINAL EXAM SECTIONS AND OBJECTIVES FOR COLLEGE ALGEBRA
FINAL EXAM SECTIONS AND OBJECTIVES FOR COLLEGE ALGEBRA 1.1 Solve linear equations and equations that lead to linear equations. a) Solve the equation: 1 (x + 5) 4 = 1 (2x 1) 2 3 b) Solve the equation: 3x
More informationDEFINITION 5.1.1 A complex number is a matrix of the form. x y. , y x
Chapter 5 COMPLEX NUMBERS 5.1 Constructing the complex numbers One way of introducing the field C of complex numbers is via the arithmetic of matrices. DEFINITION 5.1.1 A complex number is a matrix of
More informationMath Placement Test Practice Problems
Math Placement Test Practice Problems The following problems cover material that is used on the math placement test to place students into Math 1111 College Algebra, Math 1113 Precalculus, and Math 2211
More informationMathematics Georgia Performance Standards
Mathematics Georgia Performance Standards K-12 Mathematics Introduction The Georgia Mathematics Curriculum focuses on actively engaging the students in the development of mathematical understanding by
More informationClovis Community College Core Competencies Assessment 2014 2015 Area II: Mathematics Algebra
Core Assessment 2014 2015 Area II: Mathematics Algebra Class: Math 110 College Algebra Faculty: Erin Akhtar (Learning Outcomes Being Measured) 1. Students will construct and analyze graphs and/or data
More informationAlgebra 1 2008. Academic Content Standards Grade Eight and Grade Nine Ohio. Grade Eight. Number, Number Sense and Operations Standard
Academic Content Standards Grade Eight and Grade Nine Ohio Algebra 1 2008 Grade Eight STANDARDS Number, Number Sense and Operations Standard Number and Number Systems 1. Use scientific notation to express
More informationAlgebra 2: Themes for the Big Final Exam
Algebra : Themes for the Big Final Exam Final will cover the whole year, focusing on the big main ideas. Graphing: Overall: x and y intercepts, fct vs relation, fct vs inverse, x, y and origin symmetries,
More informationPCHS ALGEBRA PLACEMENT TEST
MATHEMATICS Students must pass all math courses with a C or better to advance to the next math level. Only classes passed with a C or better will count towards meeting college entrance requirements. If
More informationHow To Understand And Solve Algebraic Equations
College Algebra Course Text Barnett, Raymond A., Michael R. Ziegler, and Karl E. Byleen. College Algebra, 8th edition, McGraw-Hill, 2008, ISBN: 978-0-07-286738-1 Course Description This course provides
More informationKey Topics What will ALL students learn? What will the most able students learn?
2013 2014 Scheme of Work Subject MATHS Year 9 Course/ Year Term 1 Key Topics What will ALL students learn? What will the most able students learn? Number Written methods of calculations Decimals Rounding
More informationAlgebra 2 Chapter 1 Vocabulary. identity - A statement that equates two equivalent expressions.
Chapter 1 Vocabulary identity - A statement that equates two equivalent expressions. verbal model- A word equation that represents a real-life problem. algebraic expression - An expression with variables.
More informationSolutions to Exercises, Section 5.1
Instructor s Solutions Manual, Section 5.1 Exercise 1 Solutions to Exercises, Section 5.1 1. Find all numbers t such that ( 1 3,t) is a point on the unit circle. For ( 1 3,t)to be a point on the unit circle
More informationSQA Higher Mathematics Unit 3
SCHOLAR Study Guide SQA Higher Mathematics Unit 3 Jane Paterson Heriot-Watt University Dorothy Watson Balerno High School Heriot-Watt University Edinburgh EH14 4AS, United Kingdom. First published 2001
More informationy intercept Gradient Facts Lines that have the same gradient are PARALLEL
CORE Summar Notes Linear Graphs and Equations = m + c gradient = increase in increase in intercept Gradient Facts Lines that have the same gradient are PARALLEL If lines are PERPENDICULAR then m m = or
More informationMath Placement Test Study Guide. 2. The test consists entirely of multiple choice questions, each with five choices.
Math Placement Test Study Guide General Characteristics of the Test 1. All items are to be completed by all students. The items are roughly ordered from elementary to advanced. The expectation is that
More informationMathematics programmes of study: key stage 4. National curriculum in England
Mathematics programmes of study: key stage 4 National curriculum in England July 2014 Contents Purpose of study 3 Aims 3 Information and communication technology (ICT) 4 Spoken language 4 Working mathematically
More informationMath Course Descriptions & Student Learning Outcomes
Math Course Descriptions & Student Learning Outcomes Table of Contents MAC 100: Business Math... 1 MAC 101: Technical Math... 3 MA 090: Basic Math... 4 MA 095: Introductory Algebra... 5 MA 098: Intermediate
More informationCENTRAL COLLEGE Department of Mathematics COURSE SYLLABUS
CENTRAL COLLEGE Department of Mathematics COURSE SYLLABUS MATH 1314: College Algebra Fall 2010 / Tues-Thurs 7:30-9:00 pm / Gay Hall Rm 151 / CRN: 47664 INSTRUCTOR: CONFERENCE TIMES: CONTACT INFORMATION:
More informationMath 1280/1300, Pre-Calculus
Math 1280/1300, Pre-Calculus Instructor: Office: Office Hours: Phone: E-mail: MyMathLab Course Code: Text and Materials: ISBN: 1269594060 Author: Blitzer Title: Precalculus, Books a la Carte Edition Package
More informationGRE Prep: Precalculus
GRE Prep: Precalculus Franklin H.J. Kenter 1 Introduction These are the notes for the Precalculus section for the GRE Prep session held at UCSD in August 2011. These notes are in no way intended to teach
More informationa. all of the above b. none of the above c. B, C, D, and F d. C, D, F e. C only f. C and F
FINAL REVIEW WORKSHEET COLLEGE ALGEBRA Chapter 1. 1. Given the following equations, which are functions? (A) y 2 = 1 x 2 (B) y = 9 (C) y = x 3 5x (D) 5x + 2y = 10 (E) y = ± 1 2x (F) y = 3 x + 5 a. all
More informationMathematics. GCSE subject content and assessment objectives
Mathematics GCSE subject content and assessment objectives June 2013 Contents Introduction 3 Subject content 4 Assessment objectives 11 Appendix: Mathematical formulae 12 2 Introduction GCSE subject criteria
More informationSection 1: How will you be tested? This section will give you information about the different types of examination papers that are available.
REVISION CHECKLIST for IGCSE Mathematics 0580 A guide for students How to use this guide This guide describes what topics and skills you need to know for your IGCSE Mathematics examination. It will help
More informationhttp://school-maths.com Gerrit Stols
For more info and downloads go to: http://school-maths.com Gerrit Stols Acknowledgements GeoGebra is dynamic mathematics open source (free) software for learning and teaching mathematics in schools. It
More informationFriday, January 29, 2016 9:15 a.m. to 12:15 p.m., only
ALGEBRA /TRIGONOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION ALGEBRA /TRIGONOMETRY Friday, January 9, 016 9:15 a.m. to 1:15 p.m., only Student Name: School Name: The possession
More informationExam 1 Sample Question SOLUTIONS. y = 2x
Exam Sample Question SOLUTIONS. Eliminate the parameter to find a Cartesian equation for the curve: x e t, y e t. SOLUTION: You might look at the coordinates and notice that If you don t see it, we can
More informationNational 5 Mathematics Course Support Notes
National 5 Mathematics Course Support Notes This specification may be reproduced in whole or in part for educational purposes provided that no profit is derived from reproduction and that, if reproduced
More informationhttp://www.aleks.com Access Code: RVAE4-EGKVN Financial Aid Code: 6A9DB-DEE3B-74F51-57304
MATH 1340.04 College Algebra Location: MAGC 2.202 Meeting day(s): TR 7:45a 9:00a, Instructor Information Name: Virgil Pierce Email: piercevu@utpa.edu Phone: 665.3535 Teaching Assistant Name: Indalecio
More informationSPECIFICATION. Mathematics 6360 2014. General Certificate of Education
Version 1.0: 0913 General Certificate of Education Mathematics 6360 014 Material accompanying this Specification Specimen and Past Papers and Mark Schemes Reports on the Examination Teachers Guide SPECIFICATION
More informationMATHS LEVEL DESCRIPTORS
MATHS LEVEL DESCRIPTORS Number Level 3 Understand the place value of numbers up to thousands. Order numbers up to 9999. Round numbers to the nearest 10 or 100. Understand the number line below zero, and
More information04 Mathematics CO-SG-FLD004-03. Program for Licensing Assessments for Colorado Educators
04 Mathematics CO-SG-FLD004-03 Program for Licensing Assessments for Colorado Educators Readers should be advised that this study guide, including many of the excerpts used herein, is protected by federal
More informationUsing GeoGebra to create applets for visualization and exploration.
Handouts for ICTCM workshop on GeoGebra, March 2007 By Mike May, S.J. mikemaysj@gmail.com Using GeoGebra to create applets for visualization and exploration. Overview: I) We will start with a fast tour
More informationPre-Calculus Semester 1 Course Syllabus
Pre-Calculus Semester 1 Course Syllabus The Plano ISD eschool Mission is to create a borderless classroom based on a positive student-teacher relationship that fosters independent, innovative critical
More informationAlgebra Unpacked Content For the new Common Core standards that will be effective in all North Carolina schools in the 2012-13 school year.
This document is designed to help North Carolina educators teach the Common Core (Standard Course of Study). NCDPI staff are continually updating and improving these tools to better serve teachers. Algebra
More informationSOLUTIONS. f x = 6x 2 6xy 24x, f y = 3x 2 6y. To find the critical points, we solve
SOLUTIONS Problem. Find the critical points of the function f(x, y = 2x 3 3x 2 y 2x 2 3y 2 and determine their type i.e. local min/local max/saddle point. Are there any global min/max? Partial derivatives
More informationIn mathematics, there are four attainment targets: using and applying mathematics; number and algebra; shape, space and measures, and handling data.
MATHEMATICS: THE LEVEL DESCRIPTIONS In mathematics, there are four attainment targets: using and applying mathematics; number and algebra; shape, space and measures, and handling data. Attainment target
More informationZeros of Polynomial Functions
Review: Synthetic Division Find (x 2-5x - 5x 3 + x 4 ) (5 + x). Factor Theorem Solve 2x 3-5x 2 + x + 2 =0 given that 2 is a zero of f(x) = 2x 3-5x 2 + x + 2. Zeros of Polynomial Functions Introduction
More informationPHILOSOPHY OF THE MATHEMATICS DEPARTMENT
PHILOSOPHY OF THE MATHEMATICS DEPARTMENT The Lemont High School Mathematics Department believes that students should develop the following characteristics: Understanding of concepts and procedures Building
More informationMath 113 HW #7 Solutions
Math 3 HW #7 Solutions 35 0 Given find /dx by implicit differentiation y 5 + x 2 y 3 = + ye x2 Answer: Differentiating both sides with respect to x yields 5y 4 dx + 2xy3 + x 2 3y 2 ) dx = dx ex2 + y2x)e
More informationExamples of Tasks from CCSS Edition Course 3, Unit 5
Examples of Tasks from CCSS Edition Course 3, Unit 5 Getting Started The tasks below are selected with the intent of presenting key ideas and skills. Not every answer is complete, so that teachers can
More informationGymnázium, Brno, Slovanské nám. 7, SCHEME OF WORK Mathematics SCHEME OF WORK. http://agb.gymnaslo. cz
SCHEME OF WORK Subject: Mathematics Year: Third grade, 3.X School year:../ List of topics Topics Time period 1. Revision (functions, plane geometry) September 2. Constructive geometry in the plane October
More informationPROVINCE OF THE EASTERN CAPE EDUCATION
PROVINCE OF THE EASTERN CAPE EDUCATION DIRECTORATE: CURRICULUM FET PROGRAMMES LESSON PLANS TERM 3 MATHEMATICS GRADE 10 FOREWORD The following Grade 10, 11 and 12 Lesson Plans were developed by Subject
More informationCourse Outlines. 1. Name of the Course: Algebra I (Standard, College Prep, Honors) Course Description: ALGEBRA I STANDARD (1 Credit)
Course Outlines 1. Name of the Course: Algebra I (Standard, College Prep, Honors) Course Description: ALGEBRA I STANDARD (1 Credit) This course will cover Algebra I concepts such as algebra as a language,
More informationSecondary Mathematics Syllabuses
Secondary Mathematics Syllabuses Copyright 006 Curriculum Planning and Development Division. This publication is not for sale. All rights reserved. No part of this publication may be reproduced without
More informationAlgebra I Credit Recovery
Algebra I Credit Recovery COURSE DESCRIPTION: The purpose of this course is to allow the student to gain mastery in working with and evaluating mathematical expressions, equations, graphs, and other topics,
More information