# WASSCE / WAEC ELECTIVE / FURTHER MATHEMATICS SYLLABUS

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 Visit this link to read the introductory text for this syllabus. 1. Circular Measure Lengths of Arcs of circles and Radians Perimeters of Sectors and Segments measure in radians 2. Trigonometry (i) Sine, Cosine and For O 0 θ Tangent of angles (ii) Trigonometric ratios of the angles 30 0, 45 0, 60 0 Identify without use of tables. (iii) Heights and distances (iv) Angles of elevation and depression (v) Bearings, Positive and negative angles. Simple cases only. (vi) Compound and multiple Their use in simple angles. Identities and solution of trig. ratios. (vii) Graphical solution of simple trig. equation. (viii) Solution of triangles. a cos x + b sin x = c Include the notion of radian and trigonometric ratios of negative angles. 3. Indices, Logarithms and Surds. 1 (a) Indices (i) Elementary theory of Indices. Meaning of a 0, a -n, a n (b) Logarithms (ii) Elementary theory of Calculations involving Logarithm multiplication, division, power and nth log a xy = log a x + log a y, roots: 1 log a x n = nlog a x log a n, log a, log a n (iii) Applications Reduction of a relation

2 such as y = ax b, (a, b are constants) to a linear form. log 10 y = b log 10 x + log 10 a. Consider other examples such as y = ab x.

3 (c) Surds Surds of the form Rationalisation of the Denominator: a, a a and a + b n b where a is rational. b is a positive integer and n is not a perfect square. (d) Sequences: (i) Finite and infinite Linear and sequences Exponential sequences (ii) U n = U 1 + (n 1) d, where d is the common difference. (iii) S n = n (U 1 + U n ) 2 (iv) U n = U 1 r n-1 where r is the common ratio. a + b c - d (e) Use of the Binomial Theorem for a positive integral (v) S n = U 1 (1 - r n ) ; r < 1 1 r or S n = U 1 (r n 1) ; r > 1 r 1 Proof of Binomial Theorem not required. Expansion of (a + b) n index. Use of (1 + x) n 1 + nx for any rational n, where x is sufficiently small e.g. 0(0.998) ⅓ 4. Algebraic Equations (a) Factors and Factorisation. Solution of Quadratic equations using:- (i) completing the square, (ii) formula. (a) Symmetric properties of the equation ax² + bx + c = 0 (b) Solution of two simultaneous equations where one The condition b² - 4ac 0 for the equation to have real roots. Sum and product of roots. Graphical and analytical

4 is linear and the other quadratic. methods permissible. 236

5 5. Polynomials (i) Addition, subtraction and multiplication of polynomials. (ii) Factor and remainder theorems Not exceeding degree 4 (iii) Zeros of a polynomial function. (iv) Graphs of Polynomial functions of degree n 3. (v)division of a polynomial of degree not greater than 4 by a Polynomial of lower degree. 6. Rational Functions e.g. f: x and Partial Fractions ax + b px² + qx + r (i) The four basic operations. (ii) Zeros, domain and range; (iii) Resolution of Sketching not required. rational functions into partial fractions. Rational functions of the form F(x) Q(x) = G(x) G(x) 0 where G(x) and F(x) are polynomials, G(x) must be factorisable into linear and quadratic factors (Degree of Numerator less than that

6 of denominator which is less than or equal to 4)

7 7. Linear Inequalities Graphical and Analytical Solution of simultaneous linear Inequalities in 2 variables and Quadratic inequalities. 8. Logic (i) The truth table, using not Validity of compound P or Q, P and Q. statements involving P implies Q, Q implies P. implications and connectives. (ii) Rule of syntax: true or false statements, rule of logic applied to arguments, implications and deductions Include the use of symbols: ~ P p v q, p ^q, p q Use of Truth tables. 9. Co-ordinate (a) (i) Distance between two Geometry: points; Straight line (ii) Mid-point of a line segment; (iii) Gradient of a line; (iv) Conditions for parallel and perpendicular lines. Gradient of a line as ratio of vertical change and horizontal change. (b) Equation of a line: (i) Intercept form; (ii) Gradient form; (iii) The general form. Conic Sections (c) (i) Equation of a circle; (i) Equation in terms of (iii) Equations of centre and radius e.g. parabola in (ii) Tangents and normals (x-a)² + (y-b)² = r²; rectangular are required for circle. Cartesian (ii) The general form: coordinates. x² + y² + 2gx + 2fy + c = 0; 10. Differentiation (a) (i) The idea of a limit (i) Intuitive treatment of limit. Relate to the

8 gradient of a curve. 238

9 (ii) The derivative of a function. (ii) Its meaning and its determination from first principles in simple cases only. e.g. ax n + b, n 3, (n I) (iii) Differentiation of polynomials e.g. Application of differentiation Quotient rules. 2x 4 4x 3 + 3x² - x + 7 and (a + bx n ) m (iv) Product and Differentiation of implicit functions such as ax² + by² = c (b) (i) Second derivatives and Rates of change; (ii) Concept of maxima and minima. (i) The equation of a tangent to a curve at a point. (ii) Restrict turning points to maxima and minima. (iii) Include curve sketching (up to cubic functions) and linear kinematics. 11. Integration (i) Indefinite Integral (i) Exclude n = -1 in x n dx. (ii) Integration of sum and difference of polynomials e.g. 4 x³ + 3x² - 6x + 5 include linear kinematics. Relate to the area under a curve.

10 (ii) Definite Integral (ii) Simple problems on integration by substitution. 239

11 (iii) Volume of solid of revolution. (iii) Applications of the (iii) Plane areas and definite integral Rate of change. (iv) Approximation restricted to trapezium rule. 12. Sets (i) Idea of a set defined by a {x : x is real},, property. empty set { },,,,C, Set notations and their U (universal set) or meanings. 1 A (Complement of set (ii) Disjoint sets, Universal A). set and Complement of set. (iii) Venn diagrams, use of sets and Venn diagrams to solve problems. (iv) Commutative and Associative laws, Distributive properties over union and intersection 13. Mappings and The notation: e.g. Functions : x 3x + 4 g: x x² where x R. (i) Domain and co-domain of a function. Graphical representation of a function. (ii) One-to-one, onto, identity and constant mapping; Image and the range. (iii) Inverse of a function; (iv) Composition of functions. Notation: fog (x) = f(g(x)) Restrict to simple algebraic functions only.

12 14. Matrices: (i) Matrix representation Restrict to 2 x 2 matrices Some special (a) Algebra of Introduce the notation A, matrices: Matrices. (ii) Equal matrices B, C for a matrix. (i) Reflection in the x-axis; (i) The notation I (iii) Addition of matrices for the unit Reflection in the identity matrix. y-axis. (iv) Multiplication of a Matrix by a scalar. The clockwise and (ii) Zero or null anti-clockwise (v) Multiplication of matrix. matrices. rotation about the origin. (ii) Inverse of a 2 x 2 matrix; (b) Linear Transformation (i) Restrict to the Cartesian plane; (ii) Composition of linear transformation; (iii) Inverse of a linear transformation; (iv) Some special linear transformations: Identity Transformation, Reflection in the x-axis Reflection in the y-axis; Reflection in the line y = x Clockwise and anticlockwise rotation about the origin.

13 (c) Determinants Evaluation of determinants of 2 x 2 and 3 x 3 matrices. Application of determinants to: (i) Areas of triangles and quadrilaterals. (ii) Solution of 3 simultaneous linear equations 15. Operations Binary Operations: Closure, Commutativity, Associativity and Distributivity, Identity elements and inverses.

14 PART II STATISTICS AND PROBABILITY 1. Graphical (i) Frequency tables. representation of data (ii) Cumulative frequency tables. (iii) Histogram (including unequal class intervals) (iv) Frequency curves and ogives for grouped data of equal and unequal class intervals. 2. Measures of Central tendency; Include: location Mean, median, mode, quartiles and percentiles (i) Mode and modal group for grouped data from a histogram; (ii) Median from grouped data and from ogives; (iii) Mean for grouped data, use of an assumed mean required. 3. Measures of (a) Determination of: Dispersion (i) Range, Inter-Quartile range from an ogive. (ii) Variance and standard deviation. Simple applications. For grouped and ungrouped data using an assumed mean or true mean. 4. Correlation (i) Scatter diagrams Meaning of correlation: Rank correlation positive, negative and Spearman s Rank zero correlations from Correlation scatter diagrams. Coefficient. Use data without ties

15 (ii) Line of fit Use of line of best fit to predict one variable from another. 243 Meaning and applications.

16 5. Probability Meaning of probability E.g. tossing 2 dice once, Relative frequency drawing balls from a box Calculation of Probability. without replacement. Use of simple sample spaces. Equally likely events and Addition and multiplication of mutually exclusive events Probability Distribuprobabilities. only to be used. tion. Binomial Probability P(x = r) = n C r p r q n-r where Probability of success = P Probability of failure = q, p + q = 1 and n is the number of trials. Simple problems only. 6. Permutations and Simple cases of number of e.g. (i) arrangement of Combinations. arrangements on a line. students in a row. (ii) drawing balls from a box. Simple problems only. n n! P r = (n r)! Simple cases of combination of objects. n! n Cr = r!(n r)!

17 PART III VECTORS AND MECHANICS 1. Vectors (i) Definitions of scalar and vector quantities. (ii) Representation of Vectors. (iii) Algebra of vectors. (iii) Addition and subtraction of vectors, Multiplication of vector by vectors and by scalars. Equation of vectors. (iv) Commutative, (iv) Illustrate through Associative and diagram, Distributive properties. diagrammatic representation. Illustrate by solving problems in elementary plane geometry e.g. concurrency of medians and diagonals. (v) The parallelogram Law. (vi) Unit Vectors. The notation i for the unit vector 1 0and j for the unit vector 0

18 1 along the x and y axis respectively. (vii) Position and free Vectors. 245

19 (viii) Resolution and (viii) Not more than Composition of three vectors need Vectors. be composed. (ix) Scalar (dot) product and its application. Using the dot product to establish such trigonometric formulae as (i) Cos (a ± b) = cos a cos b ± sin a sin b (ii) sin (a ± b) = sin a cos b ± sin b cos a (iii) c² = a² + b² -2abCos c Finding angle between two vectors. 2. Statics (i) Definition of a force. (ii) Representation of Forces. (iii) Composition and resolution of coplanar forces acting at a point. (iv) Equilibrium of particles. (iv) Apply to simple problems e.g. suspension of particles by strings. (v) Lami s theorem (v) Apply to simple problems on equivalent system of forces. (vi) Determination of Resultant. (vi) Composition and resolution of general coplanar forces on rigid bodies. (viii) Moments of forces.

20 Friction: Distinction between smooth and rough planes. Determination of the coefficient of friction required. 3. Dynamics (a) (i) The concepts of Motion, Time and Space. (ii) The definitions of displacement, velocity, acceleration and speed. (iii) Composition of velocities and accelerations. (b) Equations of motion (i) Rectilinear motion; (ii) Newton s Law of motion. Application of the equations of motions: V = u + at; S =ut + ½ at²; (iii) Consequences of Newton s Laws: V² = u² + 2as. The impulse and momentum equations: Conservation of Linear Momentum. (iv) Motion under gravity. Motion along inclined planes.

21 Visit for WASSCE / WAEC Syllabus on different subjects. Larnedu also provides other resources and information to help you ace the WASSCE.

### MATHEMATICS (CLASSES XI XII)

MATHEMATICS (CLASSES XI XII) General Guidelines (i) All concepts/identities must be illustrated by situational examples. (ii) The language of word problems must be clear, simple and unambiguous. (iii)

### PURE MATHEMATICS AM 27

AM Syllabus (015): Pure Mathematics AM SYLLABUS (015) PURE MATHEMATICS AM 7 SYLLABUS 1 AM Syllabus (015): Pure Mathematics Pure Mathematics AM 7 Syllabus (Available in September) Paper I(3hrs)+Paper II(3hrs)

### PURE MATHEMATICS AM 27

AM SYLLABUS (013) PURE MATHEMATICS AM 7 SYLLABUS 1 Pure Mathematics AM 7 Syllabus (Available in September) Paper I(3hrs)+Paper II(3hrs) 1. AIMS To prepare students for further studies in Mathematics and

### IB Mathematics SL :: Checklist. Topic 1 Algebra The aim of this topic is to introduce students to some basic algebraic concepts and applications.

Topic 1 Algebra The aim of this topic is to introduce students to some basic algebraic concepts and applications. Check Topic 1 Book Arithmetic sequences and series; Sum of finite arithmetic series; Geometric

### Introduction. The Aims & Objectives of the Mathematical Portion of the IBA Entry Test

Introduction The career world is competitive. The competition and the opportunities in the career world become a serious problem for students if they do not do well in Mathematics, because then they are

### INTERNATIONAL BACCALAUREATE (IB) MATH STANDARD LEVEL, YEARS 1 AND 2 Grades 11, 12

INTERNATIONAL BACCALAUREATE (IB) MATH STANDARD LEVEL, YEARS 1 AND 2 Grades 11, 12 Unit of Credit: 1 Year for Year 1 and 1 Year for Year 2 Pre-requisite: Algebra 2 for Year 1 IB Math Standard Level Year

### Higher 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

### Biggar 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

### Advanced Algebra 2. I. Equations and Inequalities

Advanced Algebra 2 I. Equations and Inequalities A. Real Numbers and Number Operations 6.A.5, 6.B.5, 7.C.5 1) Graph numbers on a number line 2) Order real numbers 3) Identify properties of real numbers

### Thnkwell 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

### MATH 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

### AQA Level 2 Certificate FURTHER MATHEMATICS

AQA Qualifications AQA Level 2 Certificate FURTHER MATHEMATICS Level 2 (8360) Our specification is published on our website (www.aqa.org.uk). We will let centres know in writing about any changes to the

### 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

### 1.6 Powers of 10 and standard form Write a number in standard form. Calculate with numbers in standard form.

Unit/section title 1 Number Unit objectives (Edexcel Scheme of Work Unit 1: Powers, decimals, HCF and LCM, positive and negative, roots, rounding, reciprocals, standard form, indices and surds) 1.1 Number

APPLIED MATHEMATICS ADVANCED LEVEL INTRODUCTION This syllabus serves to examine candidates knowledge and skills in introductory mathematical and statistical methods, and their applications. For applications

### Able Enrichment Centre - Prep Level Curriculum

Able Enrichment Centre - Prep Level Curriculum Unit 1: Number Systems Number Line Converting expanded form into standard form or vice versa. Define: Prime Number, Natural Number, Integer, Rational Number,

### Prep for Calculus. Curriculum

Prep for Calculus This course covers the topics shown below. Students navigate learning paths based on their level of readiness. Institutional users may customize the scope and sequence to meet curricular

### Algebra 2/ Trigonometry Extended Scope and Sequence (revised )

Algebra 2/ Trigonometry Extended Scope and Sequence (revised 2012 2013) Unit 1: Operations with Radicals and Complex Numbers 9 days 1. Operations with radicals (p.88, 94, 98, 101) a. Simplifying radicals

### Algebra II. Larson, Boswell, Kanold, & Stiff (2001) Algebra II, Houghton Mifflin Company: Evanston, Illinois. TI 83 or 84 Graphing Calculator

Algebra II Text: Supplemental Materials: Larson, Boswell, Kanold, & Stiff (2001) Algebra II, Houghton Mifflin Company: Evanston, Illinois. TI 83 or 84 Graphing Calculator Course Description: The purpose

### pp. 4 8: Examples 1 6 Quick Check 1 6 Exercises 1, 2, 20, 42, 43, 64

Semester 1 Text: Chapter 1: Tools of Algebra Lesson 1-1: Properties of Real Numbers Day 1 Part 1: Graphing and Ordering Real Numbers Part 1: Graphing and Ordering Real Numbers Lesson 1-2: Algebraic Expressions

### REVISED GCSE Scheme of Work Mathematics Higher Unit T3. For First Teaching September 2010 For First Examination Summer 2011

REVISED GCSE Scheme of Work Mathematics Higher Unit T3 For First Teaching September 2010 For First Examination Summer 2011 Version 1: 28 April 10 Version 1: 28 April 10 Unit T3 Unit T3 This is a working

### Montana Common Core Standard

Algebra 2 Grade Level: 10(with Recommendation), 11, 12 Length: 1 Year Period(s) Per Day: 1 Credit: 1 Credit Requirement Fulfilled: Mathematics Course Description This course covers the main theories in

### Construction of the Real Line 2 Is Every Real Number Rational? 3 Problems Algebra of the Real Numbers 7

About the Author v Preface to the Instructor xiii WileyPLUS xviii Acknowledgments xix Preface to the Student xxi 1 The Real Numbers 1 1.1 The Real Line 2 Construction of the Real Line 2 Is Every Real Number

### Senior Secondary Australian Curriculum

Senior Secondary Australian Curriculum Mathematical Methods Glossary Unit 1 Functions and graphs Asymptote A line is an asymptote to a curve if the distance between the line and the curve approaches zero

### Section 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

### Higher Education Math Placement

Higher Education Math Placement 1. Whole Numbers, Fractions, and Decimals 1.1 Operations with Whole Numbers Addition with carry (arith050) Subtraction with borrowing (arith006) Multiplication with carry

### Precalculus 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

### Mathematics. 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

Table of Contents I. Introduction II. Chapter of Signed Numbers B. Introduction and Zero Sum Game C. Adding Signed Numbers D. Subtracting Signed Numbers 1. Subtracting Signed Numbers 2. Rewriting as Addition

### ALGEBRA I / ALGEBRA I SUPPORT

Suggested Sequence: CONCEPT MAP ALGEBRA I / ALGEBRA I SUPPORT August 2011 1. Foundations for Algebra 2. Solving Equations 3. Solving Inequalities 4. An Introduction to Functions 5. Linear Functions 6.

### Analytical Methods for Engineers

Unit 1: Analytical Methods for Engineers Unit code: A/601/1401 QCF level: 4 Credit value: 15 Aim This unit will provide the analytical knowledge and techniques needed to carry out a range of engineering

### NEW 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

### Diploma Plus in Certificate in Advanced Engineering

Diploma Plus in Certificate in Advanced Engineering Mathematics New Syllabus from April 2011 Ngee Ann Polytechnic / School of Interdisciplinary Studies 1 I. SYNOPSIS APPENDIX A This course of advanced

### GCSE Maths Linear Higher Tier Grade Descriptors

GSE Maths Linear Higher Tier escriptors Fractions /* Find one quantity as a fraction of another Solve problems involving fractions dd and subtract fractions dd and subtract mixed numbers Multiply and divide

### (Mathematics Syllabus Form 3 Track 3 for Secondary Schools June 2013) Page 1 of 9

(Mathematics Syllabus Form 3 Track 3 for Secondary Schools June 2013) Page 1 of 9 Contents Pages Number and Applications 3-4 Algebra 5-6 Shape Space and Measurement 7-8 Data Handling 9 (Mathematics Syllabus

### Algebra 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.

### South 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

### Appendix 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

### Rockhurst High School Algebra 1 Topics

Rockhurst High School Algebra 1 Topics Chapter 1- Pre-Algebra Skills Simplify a numerical expression using PEMDAS. Substitute whole numbers into an algebraic expression and evaluate that expression. Substitute

### Maths curriculum information

Maths curriculum information Year 7 Learning outcomes Place value, add and subtract Multiply and divide Geometry Fractions Algebra Percentages & pie charts Topics taught Place value (inc decimals) Add

### KS4 Curriculum Plan Maths FOUNDATION TIER Year 9 Autumn Term 1 Unit 1: Number

KS4 Curriculum Plan Maths FOUNDATION TIER Year 9 Autumn Term 1 Unit 1: Number 1.1 Calculations 1.2 Decimal Numbers 1.3 Place Value Use priority of operations with positive and negative numbers. Simplify

### Specification. GCE Mathematics

Specification GCE Mathematics Pearson Edexcel Level 3 Advanced Subsidiary GCE in Mathematics (8371) Pearson Edexcel Level 3 Advanced Subsidiary GCE in Further Mathematics (8372) Pearson Edexcel Level 3

### Mathematics 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

### Moore Catholic High School Math Department COLLEGE PREP AND MATH CONCEPTS

Moore Catholic High School Math Department COLLEGE PREP AND MATH CONCEPTS The following is a list of terms and properties which are necessary for success in Math Concepts and College Prep math. You will

### MATH 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,

### Mathematics Scope and Sequence: Foundation to Year 6

Number Algebra Number place value Fractions decimals Real numbers Foundation Year Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Establish understing of the language processes of counting by naming numbers

### 4. Factor polynomials over complex numbers, describe geometrically, and apply to real-world situations. 5. Determine and apply relationships among syn

I The Real and Complex Number Systems 1. Identify subsets of complex numbers, and compare their structural characteristics. 2. Compare and contrast the properties of real numbers with the properties of

### Utah Core Curriculum for Mathematics

Core Curriculum for Mathematics correlated to correlated to 2005 Chapter 1 (pp. 2 57) Variables, Expressions, and Integers Lesson 1.1 (pp. 5 9) Expressions and Variables 2.2.1 Evaluate algebraic expressions

### MATHS 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

### Precalculus Workshop - Functions

Introduction to Functions A function f : D C is a rule that assigns to each element x in a set D exactly one element, called f(x), in a set C. D is called the domain of f. C is called the codomain of f.

### REVISED GCSE Scheme of Work Mathematics Higher Unit 6. For First Teaching September 2010 For First Examination Summer 2011 This Unit Summer 2012

REVISED GCSE Scheme of Work Mathematics Higher Unit 6 For First Teaching September 2010 For First Examination Summer 2011 This Unit Summer 2012 Version 1: 28 April 10 Version 1: 28 April 10 Unit T6 Unit

### MATHEMATICS 31 A. COURSE OVERVIEW RATIONALE

MATHEMATICS 31 A. COURSE OVERVIEW RATIONALE To set goals and make informed choices, students need an array of thinking and problem-solving skills. Fundamental to this is an understanding of mathematical

### STAGE - 1 SYLLABUS : CLASS XI PHYSICS STAGE - 2 SYLLABUS : CLASS XI PHYSICS STAGE - 1 SYLLABUS : CLASS XII PHYSICS STAGE - 2. SYLLABUS : Class XII

1. Physical world and measurement 2. Kinematics 3. Laws of Motion 4. Work Energy Power 5. Motion of System of Particles & Rigid body 1. Physical world and measurement 2. Kinematics 3. Laws of Motion 4.

### Chapter R - Basic Algebra Operations (69 topics, due on 05/01/12)

Course Name: College Algebra 001 Course Code: R3RK6-CTKHJ ALEKS Course: College Algebra with Trigonometry Instructor: Prof. Bozyk Course Dates: Begin: 01/17/2012 End: 05/04/2012 Course Content: 288 topics

### MATH Activities ver3

MATH Activities ver3 This content summary list is for the 2011-12 school year. Detailed Content Alignment Documents to State & Common Core Standards are posted on www.pendalearning.com NOTE: Penda continues

### Biggar High School Mathematics Department. National 4 Learning Intentions & Success Criteria: Assessing My Progress

Biggar High School Mathematics Department National 4 Learning Intentions & Success Criteria: Assessing My Progress Expressions and Formulae Topic Learning Intention Success Criteria I understand this Algebra

### Functions and Equations

Centre for Education in Mathematics and Computing Euclid eworkshop # Functions and Equations c 014 UNIVERSITY OF WATERLOO Euclid eworkshop # TOOLKIT Parabolas The quadratic f(x) = ax + bx + c (with a,b,c

### Precalculus with Limits Larson Hostetler. `knill/mathmovies/ Assessment Unit 1 Test

Unit 1 Real Numbers and Their Properties 14 days: 45 minutes per day (1 st Nine Weeks) functions using graphs, tables, and symbols Representing & Classifying Real Numbers Ordering Real Numbers Absolute

### Algebra I Vocabulary Cards

Algebra I Vocabulary Cards Table of Contents Expressions and Operations Natural Numbers Whole Numbers Integers Rational Numbers Irrational Numbers Real Numbers Absolute Value Order of Operations Expression

### KEANSBURG SCHOOL DISTRICT KEANSBURG HIGH SCHOOL Mathematics Department. HSPA 10 Curriculum. September 2007

KEANSBURG HIGH SCHOOL Mathematics Department HSPA 10 Curriculum September 2007 Written by: Karen Egan Mathematics Supervisor: Ann Gagliardi 7 days Sample and Display Data (Chapter 1 pp. 4-47) Surveys and

### Math 4 Review Problems

Topics for Review #1 Functions function concept [section 1. of textbook] function representations: graph, table, f(x) formula domain and range Vertical Line Test (for whether a graph is a function) evaluating

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.

### MTH304: Honors Algebra II

MTH304: Honors Algebra II This course builds upon algebraic concepts covered in Algebra. Students extend their knowledge and understanding by solving open-ended problems and thinking critically. Topics

### Algebra 1 Chapter 3 Vocabulary. equivalent - Equations with the same solutions as the original equation are called.

Chapter 3 Vocabulary equivalent - Equations with the same solutions as the original equation are called. formula - An algebraic equation that relates two or more real-life quantities. unit rate - A rate

Math SYLLABUS (1 st ~ 8 th Grade, Advance, SAT/ACT) Math -- 1 st Grade 1. Kindergarteners or 1 st graders in regular school 2. At least 5 years old Syllabus 1. Numeration (0 through 99) 2. Addition (2

### Prep for College Algebra

Prep for College Algebra This course covers the topics shown below. Students navigate learning paths based on their level of readiness. Institutional users may customize the scope and sequence to meet

### In 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

### Understanding 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

### Prentice 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

Fortismere: Maths GCSE Grade Descriptors Grade Description Clip 1 Interpreting Real-Life Tables 6 1 Names of Angles 13 1 Ordering Decimals 3 1 Ordering Integers 2 1 Pictograms 16 1 Place Value 1 1 Polygons

### Montana Common Core Standard

Algebra I Grade Level: 9, 10, 11, 12 Length: 1 Year Period(s) Per Day: 1 Credit: 1 Credit Requirement Fulfilled: A must pass course Course Description This course covers the real number system, solving

### The 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

### www.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

### The standards in this course continue the work of modeling situations and solving equations.

Algebra II Overview View unit yearlong overview here Building on the understanding of linear, quadratic and exponential functions from Algebra I, this course will extend function concepts to include polynomial,

### The Not-Formula Book for C1

Not The Not-Formula Book for C1 Everything you need to know for Core 1 that won t be in the formula book Examination Board: AQA Brief This document is intended as an aid for revision. Although it includes

### Math Department Student Learning Objectives Updated April, 2014

Math Department Student Learning Objectives Updated April, 2014 Institutional Level Outcomes: Victor Valley College has adopted the following institutional outcomes to define the learning that all students

### Alabama Course of Study Mathematics Algebra 2 with Trigonometry

A Correlation of Prentice Hall Algebra 2 to the Alabama Course of Study Mathematics THE COMPLEX NUMBER SYSTEM NUMBER AND QUANTITY Perform arithmetic operations with complex numbers. 1. Know there is a

### Chapter 1 Quadratic Equations in One Unknown (I)

Tin Ka Ping Secondary School 015-016 F. Mathematics Compulsory Part Teaching Syllabus Chapter 1 Quadratic in One Unknown (I) 1 1.1 Real Number System A Integers B nal Numbers C Irrational Numbers D Real

### Infinite Algebra 1 supports the teaching of the Common Core State Standards listed below.

Infinite Algebra 1 Kuta Software LLC Common Core Alignment Software version 2.05 Last revised July 2015 Infinite Algebra 1 supports the teaching of the Common Core State Standards listed below. High School

### Final Exam Practice--Problems

Name: Class: Date: ID: A Final Exam Practice--Problems Problem 1. Consider the function f(x) = 2( x 1) 2 3. a) Determine the equation of each function. i) f(x) ii) f( x) iii) f( x) b) Graph all four functions

### Essential Mathematics for Computer Graphics fast

John Vince Essential Mathematics for Computer Graphics fast Springer Contents 1. MATHEMATICS 1 Is mathematics difficult? 3 Who should read this book? 4 Aims and objectives of this book 4 Assumptions made

### Pre-Algebra - MA1100. Topic Lesson Objectives. Variables and Expressions

Variables and Expressions Problem Solving: Using a Problem-Solving Plan Use a four-step plan to solve problems. Choose an appropriate method of computation. Numbers and Expressions Use the order of operations

### Edexcel Maths Linear Topic list HIGHER Edexcel GCSE Maths Linear Exam Topic List - HIGHER

Edexcel GCSE Maths Linear Exam Topic List - HIGHER NUMBER Add, subtract, multiply, divide Order numbers Factors, multiples and primes Write numbers in words Write numbers from words Add, subtract, multiply,

### INTERNATIONAL ADVANCED LEVEL. Mathematics, Further Mathematics and Pure Mathematics

INTERNATIONAL ADVANCED LEVEL Mathematics, Further Mathematics and Pure Mathematics SPECIFICATION Pearson Edexcel International Advanced Subsidiary in Mathematics (XMA01) Pearson Edexcel International Advanced

### Roots and Coefficients of a Quadratic Equation Summary

Roots and Coefficients of a Quadratic Equation Summary For a quadratic equation with roots α and β: Sum of roots = α + β = and Product of roots = αβ = Symmetrical functions of α and β include: x = and

### Mercer County Public Schools PRIORITIZED CURRICULUM. Mathematics Content Maps Algebra II Revised August 07

Mercer County Public Schools PRIORITIZED CURRICULUM Mathematics Content Maps Algebra II Revised August 07 Suggested Sequence: C O N C E P T M A P ALGEBRA I I 1. Solving Equations/Inequalities 2. Functions

Algebra I 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, with an emphasis

### PRECALCULUS Semester I Exam Review Sheet

PRECALCULUS Semester I Exam Review Sheet Chapter Topic P.1 Real Numbers {1, 2, 3, 4, } Natural (aka Counting) Numbers {0, 1, 2, 3, 4, } Whole Numbers {, -3, -2, -2, 0, 1, 2, 3, } Integers Can be expressed

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

### Lecture 1 (Review of High School Math: Functions and Models) Introduction: Numbers and their properties

Lecture 1 (Review of High School Math: Functions and Models) Introduction: Numbers and their properties Addition: (1) (Associative law) If a, b, and c are any numbers, then ( ) ( ) (2) (Existence of an

### Mathematics 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

### Calculus C/Multivariate Calculus Advanced Placement G/T Essential Curriculum

Calculus C/Multivariate Calculus Advanced Placement G/T Essential Curriculum UNIT I: The Hyperbolic Functions basic calculus concepts, including techniques for curve sketching, exponential and logarithmic

### REVIEW SHEETS COLLEGE ALGEBRA MATH 111

REVIEW SHEETS COLLEGE ALGEBRA MATH 111 A Summary of Concepts Needed to be Successful in Mathematics The following sheets list the key concepts that are taught in the specified math course. The sheets present

### ALGEBRA I A PLUS COURSE OUTLINE

ALGEBRA I A PLUS COURSE OUTLINE OVERVIEW: 1. Operations with Real Numbers 2. Equation Solving 3. Word Problems 4. Inequalities 5. Graphs of Functions 6. Linear Functions 7. Scatterplots and Lines of Best

### CAMI Education linked to CAPS: Mathematics

- 1 - TOPIC 1.1 Whole numbers _CAPS Curriculum TERM 1 CONTENT Properties of numbers Describe the real number system by recognizing, defining and distinguishing properties of: Natural numbers Whole numbers

### Advanced Higher Mathematics Course Assessment Specification (C747 77)

Advanced Higher Mathematics Course Assessment Specification (C747 77) Valid from August 2015 This edition: April 2016, version 2.4 This specification may be reproduced in whole or in part for educational

Question: What is the quadratic fmula? Question: What is the discriminant? Question: How do you determine if a quadratic equation has no real roots? The discriminant is negative ie Question: How do you

### Class Notes for MATH 2 Precalculus. Fall Prepared by. Stephanie Sorenson

Class Notes for MATH 2 Precalculus Fall 2012 Prepared by Stephanie Sorenson Table of Contents 1.2 Graphs of Equations... 1 1.4 Functions... 9 1.5 Analyzing Graphs of Functions... 14 1.6 A Library of Parent

### C A R I B B E A N E X A M I N A T I O N S C O U N C I L REPORT ON CANDIDATES WORK IN THE SECONDARY EDUCATION CERTIFICATE EXAMINATION MAY/JUNE 2011

C A R I B B E A N E X A M I N A T I O N S C O U N C I L REPORT ON CANDIDATES WORK IN THE SECONDARY EDUCATION CERTIFICATE EXAMINATION MAY/JUNE 2011 MATHEMATICS GENERAL PROFICIENCY EXAMINATION Copyright

### Curriculum Mapping - Key Stage 3 Subject : Mathematics Topics addressed Skills acquired Cross-curricular links Progression links to future years

Year 7 (CORE) Sequences and rules Order, add and subtract decimals Order, add and subtract negative s Rounding and estimates Paper and pencil methods to add, subtract, divide and multiply Perimeter and