# preface It is hoped that this book will help students to gain confidence in the subject and be better equipped to face the examinations.

Size: px
Start display at page:

Download "preface It is hoped that this book will help students to gain confidence in the subject and be better equipped to face the examinations."

Transcription

1 preface Secondary 1 Mathematics Tutorial 1A and 1B are designed to prepare Secondary 1 students in their understanding and application of mathematical concepts, skills and processes. What s covered in this book? Written in accordance with the latest syllabus, each chapter includes Objectives, Key Concepts and Formulae and Worked Examples to supplement and complement the lessons taught in school. Practice questions are structured as core, consolidation and challenging to ensure steady improvement and quick mastery of concepts. Books 1A and 1B cover all the topics for the entire school year. Additional feature that provides important notes, tips, examples and common student errors. Important concepts are highlighted to enhance understanding and retention. Tests and Assessments There are 4 assessment papers: Mid Year Examination Paper 1 and (found in Book 1A) and End of Year Examination Paper 1 and (found in Book 1B). Answer Key Fully worked solutions are provided for students to understand better how each problem is solved. These also serve as a tool for self study and assessment. It is hoped that this book will help students to gain confidence in the subject and be better equipped to face the examinations. The Editorial Team

2 Contents Chapter Objectives Page 1 Prime Numbers, Factors and Multiples Recognise prime numbers Perform prime factorisation on a composite number Find the HCF and LCM of a group of numbers using prime factorisation Find the square root and cube root of a number using prime factorisation Real Numbers and Approximation Identify rational and irrational numbers Perform the four operations on real numbers Approximate using decimal places and significant figures Estimate the results of computations 1 Introduction to Algebra Evaluate algebraic expressions and formulae Express real-world problems in algebraic terms 44 4 Algebraic Manipulation Evaluate and simplify algebraic expressions Factorise algebraic expressions by extracting common factors Express real world problems in algebraic terms 61 Solving Linear Equations and Inequalities Solve linear equations Formulate linear equations to solve word problems Number Patterns Recognise number patterns and find the terms of a sequence Find the general term of a sequence Solve problems involving number patterns and sequences Ratio, Rate and Speed Find ratios involving two or more quantities Calculate average speed Convert speed from one unit to another Solve problems involving ratio, rate and speed Mid Year Examination Paper 1 16 Mid Year Examination Paper 16 Fully worked solutions S1 S8 Complete the course with Secondary 1 Mathematics Tutorial 1B (Chapters 8 14)

3 Chapter 1 Prime Numbers, Factors and Multiples Objectives Recognise prime numbers Perform prime factorisation on a composite number Find the HCF and LCM of a group of numbers using prime factorisation Find the square root and cube root of a number using prime factorisation Key Concepts and Formulae 1 Whole numbers E.g. 0, 1,,, 4,,... Neither Prime nor Composite (0 and 1 only) Prime Numbers has only factors, 1 and itself E.g.,,, 7, 11,... Composite Prime Numbers has more than factors E.g. 4, 6, 8, 9, 10 when expressed in index notation is. Prime Factorisation is the process of expressing a composite number as a product of its prime factors. E.g. 04 = 7 4 Square and Square roots: Square of 6 = 6 = 6 6 = 6 A perfect square is a number whose square root is a whole number. E.g. 1, 4, 9, 16,, 6 are perfect squares. Cube and Cube roots: Cube of = = 1 1 = A perfect cube is a number whose cube root is a whole number. E.g. 1, 8, 7, 64, 1 are perfect cubes. 6 Highest Common Factor (HCF) and Lowest Common Multiple (LCM) can be found using Prime Factorisation.

4 WORKeD example 1 Find the prime factorisation of 10 in index notation. Solution: Method 1: Using the factor tree: 10 7 Hence, the prime factorisation of 10 is. Method : Using successive division: Only use prime numbers when finding the factors Hence, the prime factorisation of 10 is.

5 WORKeD example Find the HCF and LCM of the numbers 40, 60 and 100. Solution: Method 1: Using prime factorisation: 40 = 60 = In Method 1, you will need to find the prime factorisation of each number first. 100 = HCF = Extract common factors with lowest index. LCM = Extract common factors with highest index and all remaining factors. HCF = = 0 LCM = = 600 Method : Using successive division: Common prime factors 40, 60, 100 0, 0, 0 10, 1,,, Stop dividing when there are no common factors between any two numbers Use only prime numbers when performing prime factorisation. HCF = = 0 LCM = = 600

6 WORKeD example Buses on different routes start their journey from the interchange at regular intervals. Buses for route A leave the interchange every 18 minutes, buses for route B leave every 0 minutes and buses for route C leave every 4 minutes. Given that all the first buses for all routes leave at 7 a.m., what time will they next leave together? Solution: Successive division is a more efficient way to find LCM/HCF. Find the LCM of 18, 0 and 4. 18, 0, 4 9, 10, 1 9,, 6 9,,,, 1 1,, 1 1, 1, 1 LCM = = minutes = hours The buses will next leave together at 10 a.m. WORKeD example 4 Using prime factorisation, find the (a) square root of 784, (b) cube root of 16. Solution: a a = a b b b = b (a) Using prime factorisation, 784 = = ( 7) ( 7) = 7 = 8 (b) Using prime factorisation, 16 = 16 = ( ) ( ) ( ) = = 6 4

7 Prime Factorisation core Practice 1 Express the following numbers in index notation. index = Base To find the prime factorisation of a number: Method 1: Factor tree Method : Successive division (a) 7 (b) (c) (d) 7 (e) (f) (g) (h) (i) (j) 19 19

8 Find the prime factorisation of the following numbers. A number is divisible by if the sum of its digits is divisible by. A number is divisible by if its last digit is 0 or. (a) 00 (b) 94 (c) 7 (d) 1000 (e) 10 (f) 17 6

### grasp of the subject while attaining their examination objectives.

PREFACE SUCCESS IN MATHEMATICS is designed with the purpose of assisting students in their preparation for important school and state examinations. Students requiring revision of the concepts covered in

### Preface.

hapter 1 Prime Numbers, Factors and Multiples Preface Secondary 1 (N) Mathematics Tutorial 1 and 1 are designed to prepare Secondary 1 students in their understanding and application of mathematical concepts,

### Maths Scheme of Work. Class: Year 10. Term: autumn 1: 32 lessons (24 hours) Number of lessons

Maths Scheme of Work Class: Year 10 Term: autumn 1: 32 lessons (24 hours) Number of lessons Topic and Learning objectives Work to be covered Method of differentiation and SMSC 11 OCR 1 Number Operations

### Basic Algebra. CAPS Mathematics

Basic Algebra CAPS Mathematics 1 Outcomes for this TOPIC In this TOPIC you will: Revise factorization. LESSON 1. Revise simplification of algebraic fractions. LESSON. Discuss when trinomials can be factorized.

### CHAPTER 1 REAL NUMBERS KEY POINTS

CHAPTER 1 REAL NUMBERS 1. Euclid s division lemma : KEY POINTS For given positive integers a and b there exist unique whole numbers q and r satisfying the relation a = bq + r, 0 r < b. 2. Euclid s division

### MATHEMATICS X l Let x = p q be a rational number, such l If p, q, r are any three positive integers, then, l that the prime factorisation of q is of t

CHAPTER 1 Real Numbers [N.C.E.R.T. Chapter 1] POINTS FOR QUICK REVISION l Euclid s Division Lemma: Given two positive integers a and b, there exist unique integers q and r satisfying a = bq + r, 0 r

### Masters Tuition Center

1 REAL NUMBERS Exercise 1.1 Q.1. Use Euclid s division algorithm to find the HCF of: (i) 135 and 225 (ii) 196 and 38220 (iii) 867 and 255 Solution. (i) In 135 and 225, 225 is larger integer. Using Euclid

### not to be republished NCERT REAL NUMBERS CHAPTER 1 (A) Main Concepts and Results

REAL NUMBERS CHAPTER 1 (A) Main Concepts and Results Euclid s Division Lemma : Given two positive integers a and b, there exist unique integers q and r satisfying a = bq + r, 0 r < b. Euclid s Division

### NCERT Solutions. 95% Top Results. 12,00,000+ Hours of LIVE Learning. 1,00,000+ Happy Students. About Vedantu. Awesome Master Teachers

Downloaded from Vedantu NCERT Solutions About Vedantu Vedantu is India s biggest LIVE online teaching platform with over 450+ best teachers from across the country. Every week we are coming up with awesome

### Instructors Manual Algebra and Trigonometry, 2e Cynthia Y. Young

Dear Instructor, Instructors Manual Algebra and Trigonometry, 2e Cynthia Y. Young I hope that when you read my Algebra and Trigonometry book it will be seamless with how you teach. My goal when writing

### Quantitative Aptitude

WWW.UPSCMANTRA.COM Quantitative Aptitude Concept 1 1. Number System 2. HCF and LCM 2011 Prelims Paper II NUMBER SYSTEM 2 NUMBER SYSTEM In Hindu Arabic System, we use ten symbols 0, 1, 2, 3, 4, 5, 6, 7,

### SAMPLE. stinction. Secondary. Ivan Lau Kim Soon. ~ Marshall Cavendish ~Education

stinction Ivan Lau Kim Soon Secondary ~ Marshall Cavendish ~Education 0 Marshall Cavendish International (Singapore) Private Limited Published by Marshall Cavendish Education An imprint of Marshall Cavendish

### Section 4. Quantitative Aptitude

Section 4 Quantitative Aptitude You will get 35 questions from Quantitative Aptitude in the SBI Clerical 2016 Prelims examination and 50 questions in the Mains examination. One new feature of the 2016

Topic : Real Numbers Class : X Concepts 1. Euclid's Division Lemma 2. Euclid's Division Algorithm 3. Prime Factorization 4. Fundamental Theorem of Arithmetic 5. Decimal expansion of rational numbers A

### TECHNIQUES IN FACTORISATION

TECHNIQUES IN FACTORISATION The process where brackets are inserted into an equation is referred to as factorisation. Factorisation is the opposite process to epansion. METHOD: Epansion ( + )( 5) 15 Factorisation

### Basic properties of real numbers. Solving equations and inequalities. Homework. Solve and write linear equations.

August Equations and inequalities S. 1.1a,1.2a,1.3a, 2.1a, 2.3 a-c, 6.2a. Simplifying expressions. Algebra II Honors Textbook Glencoe McGraw Hill Algebra II and supplements McDougal Littell Houghton Miffin

### Maths Book Part 1. By Abhishek Jain

Maths Book Part 1 By Abhishek Jain Topics: 1. Number System 2. HCF and LCM 3. Ratio & proportion 4. Average 5. Percentage 6. Profit & loss 7. Time, Speed & Distance 8. Time & Work Number System Understanding

### ANNUAL NATIONAL ASSESSMENT 2014 ASSESSMENT GUIDELINES MATHEMATICS GRADE 9

INTRODUCTION The 2014 cycle of Annual National Assessment (ANA 2014) will be administered in all public and designated 1 independent schools from 16 to 19 September 2014. During this period all learners

### Mathematics. Differentiation. Applying the Differentiation of Trigonometric Functions

Mathematics Stills from our new series Differentiation Differentiation is one of the most fundamental tools in calculus. This series can be used to introduce or review this important topic through 13 targeted

### BLOOM PUBLIC SCHOOL Vasant Kunj, New Delhi Lesson Plan Subject: MATHEMATICS Class: X. Month: April No of Periods: 12 TTT: 4 Periods WT: 8 Periods

BLOOM PUBLIC SCHOOL Vasant Kunj, New Delhi Lesson Plan Subject: MATHEMATICS Class: X Month: April No of Periods: 12 TTT: 4 Periods WT: 8 Periods Chapter-: 1 Learning Objectives Chapter s Name :REAL NUMBERS

### Department Curriculum Map

Department Curriculum Map 2018-19 Department Mathematics Subject Specific Skills Wider key skills To be able to involving: Number Algebra Ratio, Proportion & Rates of Change Logic skills Problem solving

### Numbers of Different Size: Notation and Presentation

Numbers of Different Size: Notation and Presentation Content Powers and roots, index notation Multiples and factors Prime factorisation H.C.F./L.C.M. Standard form What is it for why do we do this? These

### Learning Objectives These show clearly the purpose and extent of coverage for each topic.

Preface This book is prepared for students embarking on the study of Additional Mathematics. Topical Approach Examinable topics for Upper Secondary Mathematics are discussed in detail so students can focus

### N= {1,2,3,4,5,6,7,8,9,10,11,...}

1.1: Integers and Order of Operations 1. Define the integers 2. Graph integers on a number line. 3. Using inequality symbols < and > 4. Find the absolute value of an integer 5. Perform operations with

### P2 GCSE Maths best-guess paper 2018

P2 GCSE Maths best-guess paper 2018 Name: Class: Date: Time: 90 minutes Marks: 80 marks This is a predicted paper based on topics that have already come up in P1 Comments: This is a best guess paper and

### REAL NUMBERS. Any positive integer a can be divided by another positive integer b in such a way that it leaves a remainder r that is smaller than b.

REAL NUMBERS Introduction Euclid s Division Algorithm Any positive integer a can be divided by another positive integer b in such a way that it leaves a remainder r that is smaller than b. Fundamental

### and LCM (a, b, c) LCM ( a, b) LCM ( b, c) LCM ( a, c)

CHAPTER 1 Points to Remember : REAL NUMBERS 1. Euclid s division lemma : Given positive integers a and b, there exists whole numbers q and r satisfying a = bq + r, 0 r < b.. Euclid s division algorithm

### Preface. Enhanced Learning

Preface This book is just what you are looking for Secondary 2 Mathematics made easy and comprehensible so you need not struggle to make sense of all the new and unfamiliar concepts. Specially written

### A group of figures, representing a number, is called a numeral. Numbers are divided into the following types.

1. Number System Quantitative Aptitude deals mainly with the different topics in Arithmetic, which is the science which deals with the relations of numbers to one another. It includes all the methods that

### Daily Skill Builders:

Daily Skill Builders: Pre-Algebra By WENDI SILVANO COPYRIGHT 2008 Mark Twain Media, Inc. ISBN 978-1-58037-445-3 Printing No. CD-404086 Mark Twain Media, Inc., Publishers Distributed by Carson-Dellosa Publishing

### Latest Syllabus - NMO

Latest Syllabus - NMO CLASS 1 Numerals and Number Name (2 digit numbers) Addition, Subtraction Knowledge of currency notes. Knowledge of clock. Knowledge of basic units of Length,. Knowledge of basic figures

### NAME DATE PERIOD. A negative exponent is the result of repeated division. Extending the pattern below shows that 4 1 = 1 4 or 1. Example: 6 4 = 1 6 4

Lesson 4.1 Reteach Powers and Exponents A number that is expressed using an exponent is called a power. The base is the number that is multiplied. The exponent tells how many times the base is used as

### Year 9 Mastery Statements for Assessment 1. Topic Mastery Statements - I can Essential Knowledge - I know

Year 9 Mastery Statements for Assessment 1 Topic Mastery Statements - I can Essential Knowledge - I know Whole Numbers and Decimals Measures, perimeter area and volume Expressions and formulae Indices

### Glades Middle School Summer Math Program

Summer Math Program Attention Cougars, It s time for SUMMER MATH!! Research studies have shown that during an extended summer vacation, children can lose an average of 2.6 months of knowledge. This is

### Elementary Algebra

Elementary Algebra 978-1-63545-008-8 To learn more about all our offerings Visit Knewton.com/highered Source Author(s) (Text or Video) Title(s) Link (where applicable) Flatworld Text John Redden Elementary

### Mesaieed International School

Mesaieed International School SUBJECT: Mathematics Year: 10H Overview of the year: The contents below reflect the first half of the two-year IGCSE Higher course which provides students with the opportunity

### Divisibility, Factors, and Multiples

Divisibility, Factors, and Multiples An Integer is said to have divisibility with another non-zero Integer if it can divide into the number and have a remainder of zero. Remember: Zero divided by any number

### Step-by-step and detailed demonstrations of how a specific concept or technique is applied in solving problems.

PREFACE Synergy for Success in Mathematics 7 contains all the required learning competencies and is supplemented with some additional topics for enrichment. Lessons are presented using effective Singapore

### Real Number. Euclid s division algorithm is based on the above lemma.

1 CHAPTER We are Starting from a Point but want to Make it a Circle of Infinite Radius Basic Concepts 1. Euclid s division lemma Given two positive integers a and b, there exist unique integers q and r

### New York City Scope and Sequence for CMP3

New York City Scope and Sequence for CMP3 The following pages contain a high-level scope and sequence for Connected Mathematics 3 and incorporate the State s pre- and poststandards guidance (see http://www.p12.nysed.gov/assessment/math/

### Tin Ka Ping Secondary School F.2 Mathematics Teaching Syllabus

Tin Ka Ping Secondary School 05-06 F. Mathematics Syllabus Chapter Rate and Time Guide. Rates. s A. Basic Concept of s B. s of Three Quantities Learn the concept of a rate. Learn the concepts of a ratio

### PP

Algebra I Reviewers Nancy Akhavan Lee Richmond School Hanford, CA Kristi Knevelbaard Caruthers Elementary School Caruthers, CA Sharon Malang Mickey Cox Elementary School Clovis, CA Jessica Mele Valley

### CLASS - X Mathematics (Real Number)

CLASS - X Mathematics (Real Number) 1. 7 11 13 15 + 15is a (a) Composite number (c) Prime number (b) Whole number (d) None of these. For what least value of n a natural number, ( 4) n is divisible by 8?

### SEVENTH EDITION and EXPANDED SEVENTH EDITION

SEVENTH EDITION and EXPANDED SEVENTH EDITION Slide 5-1 Chapter 5 Number Theory and the Real Number System 5.1 Number Theory Number Theory The study of numbers and their properties. The numbers we use to

### Tenth Bit Bank Mathematics Real Numbers

Tenth Bit Bank Mathematics Real Numbers 1. The rational number among the following is... i) 4.28 ii) 4.282828... iii) 4.288888... A) i) & ii) B) ii) & iii) C) i) & iii) D) All the above 2. A rational number

### NUMBERS( A group of digits, denoting a number, is called a numeral. Every digit in a numeral has two values:

NUMBERS( A number is a mathematical object used to count and measure. A notational symbol that represents a number is called a numeral but in common use, the word number can mean the abstract object, the

### Course Readiness and Skills Review Handbook (83 topics) Course Readiness (21 topics) Course Name: Algebra Course Code: UY6JA-RATXM

Course Name: Algebra 1 2014-15 Course Code: UY6JA-RATXM ALEKS Course: Algebra 1A Instructor: Ms. Dalton Course Dates: Begin: 11/18/2014 End: 06/18/2015 Course Content: 335 Topics (334 goal + 1 prerequisite)

### Units: 10 high school credits UC requirement category: c General Course Description:

Summer 2015 Units: 10 high school credits UC requirement category: c General Course Description: ALGEBRA I Grades 7-12 This first year course is designed in a comprehensive and cohesive manner ensuring

### Number Theory and Divisibility

Number Theory and Divisibility Recall the Natural Numbers: N = {1, 2, 3, 4, 5, 6, } Any Natural Number can be expressed as the product of two or more Natural Numbers: 2 x 12 = 24 3 x 8 = 24 6 x 4 = 24

### MATHEMATICS SYLLABUS SECONDARY 4th YEAR

European Schools Office of the Secretary-General Pedagogical Development Unit Ref.:010-D-591-en- Orig.: EN MATHEMATICS SYLLABUS SECONDARY 4th YEAR 6 period/week course APPROVED BY THE JOINT TEACHING COMMITTEE

### MATH Spring 2010 Topics per Section

MATH 101 - Spring 2010 Topics per Section Chapter 1 : These are the topics in ALEKS covered by each Section of the book. Section 1.1 : Section 1.2 : Ordering integers Plotting integers on a number line

### Livingston American School Quarter 3 Plan

Livingston American School Quarter 3 Plan Concept - Topic To Teach: Variables, Expressions, and Integers: Presenting data in tables Presenting data graphically Statistical measures of data *New pre-algebra

### Module 1: Whole Numbers Module 2: Fractions Module 3: Decimals and Percent Module 4: Real Numbers and Introduction to Algebra

Course Title: College Preparatory Mathematics I Prerequisite: Placement with a score below 20 on ACT, below 450 on SAT, or assessing into Basic Applied Mathematics or Basic Algebra using Accuplacer, ASSET

### Mathematics Class (IX-X)

Mathematics Class (IX-X) Objectives 1. Students of Secondary stage will be able to apply knowledge acquired at upper primary stage to learn real number system and other topics. They will be able to distinguish

### Course Text. Course Description. Course Objectives. Course Prerequisites. Important Terms. StraighterLine Introductory Algebra

Introductory Algebra Course Text Dugopolski, Mark. Elementary Algebra, 6th edition. McGraw-Hill, 2009. ISBN 9780077224790 [This text is available as an etextbook at purchase or students may find used,

### DAWOOD PUBLIC SCHOOL COURSE OUTLINE FOR CLASS VI MATHEMATICS

DAWOOD PUBLIC SCHOOL COURSE OUTLINE FOR CLASS VI MATHEMATICS 2014-15 Books: Sang, T.et al, 2008, New Syllabus Mathematics 1(6 th Edition), Singapore; Oxford University Press. Introduction: This syllabus

### PREFACE. Synergy for Success in Mathematics 7 is designed for Grade 7 students. The textbook

Synergy for Success in Mathematics 7 is designed for Grade 7 students. The textbook contains all the required learning competencies and is supplemented with some additional topics for enrichment. Lessons

### AUSTRALIAN ISLAMIC COLLEGE Western Australian Curriculum Mathematics 2018 Year 8 Holiday Homework

AUSTRALIAN ISLAMIC COLLEGE Western Australian Curriculum Mathematics 2018 Year 8 Holiday Homework Name: Student ID: Teacher: Instructions: Show your working. Demonstrate clear understanding. Include the

### Foundation tier unit 1a check in test. Non-calculator

Foundation tier unit 1a check in test Non-calculator Q1. The table shows the heights of four mountains. Mountain Height (metres) Diran 7266 Lhotse 8516 Cho Oyu 8188 Makalu 8485 What is the name of the

### FACTORS AND MULTIPLES

FACTORS AND MULTIPLES.(A) Find the prime factors of : (i) (ii) (iii) Ans. (i) (ii) (B.) If P n means prime - factors of n, find : (i) P (ii) P (iii) P (iv) P Ans. (i) F =,,, P (Prime factor of ) = and.

### Give (one word answer) and Take (one mark in future):

Star Sums: Give (one word answer) and Take (one mark in future): 1. If is a rational number, what is the condition on q so that the decimal representation of is terminating. 2. Find the (H.C.F X L.C.M)

### Arithmetic, Algebra, Number Theory

Arithmetic, Algebra, Number Theory Peter Simon 21 April 2004 Types of Numbers Natural Numbers The counting numbers: 1, 2, 3,... Prime Number A natural number with exactly two factors: itself and 1. Examples:

### OPTIONAL: Watch the Flash version of the video for Section 6.1: Rational Expressions (19:09).

UNIT V STUDY GUIDE Rational Expressions and Equations Course Learning Outcomes for Unit V Upon completion of this unit, students should be able to: 3. Perform mathematical operations on polynomials and

### Math 7 Notes Unit Two: Integers

Math 7 Notes Unit Two: Integers Syllabus Objective: 2.1 The student will solve problems using operations on positive and negative numbers, including rationals. Integers the set of whole numbers and their

### AS Mathematics AS Further Mathematics Transition Booklet. Name: Bridging the gap to A Level!

AS Mathematics AS Further Mathematics Transition Booklet Name: Bridging the gap to A Level! Introduction You will be starting an A-Level Maths course in September, and it is important that you are ready

### Massachusetts Tests for Educator Licensure (MTEL )

Massachusetts Tests for Educator Licensure (MTEL ) BOOKLET 2 Mathematics Subtest Copyright 2010 Pearson Education, Inc. or its affiliate(s). All rights reserved. Evaluation Systems, Pearson, P.O. Box 226,

### October 28, S4.4 Theorems about Zeros of Polynomial Functions

MAT 171 Precalculus Algebra Dr. Claude Moore Cape Fear Community College CHAPTER 4: Polynomial and Rational Functions 4.1 Polynomial Functions and Models 4.2 Graphing Polynomial Functions 4.3 Polynomial

### Algebra 1 Course Syllabus. Algebra 1, Part 1

Course Description: Algebra 1 Course Syllabus In Algebra 1, students will study the foundations of algebra, including the understanding of variables, expressions, and working with real numbers to simplify

### GCSE Maths. Paul Metcalf Series Editor: Jayne de Courcy

GCSE Maths Paul Metcalf Series Editor: Jayne de Courcy PerfectBound An e-book from HarperCollins Publishers 77 85 Fulham Palace Road Hammersmith, London W6 8JB First published 00 HarperCollinsPublishers

### CONTENTS CHECK LIST ACCURACY FRACTIONS INDICES SURDS RATIONALISING THE DENOMINATOR SUBSTITUTION

CONTENTS CHECK LIST - - ACCURACY - 4 - FRACTIONS - 6 - INDICES - 9 - SURDS - - RATIONALISING THE DENOMINATOR - 4 - SUBSTITUTION - 5 - REMOVING BRACKETS - 7 - FACTORISING - 8 - COMMON FACTORS - 8 - DIFFERENCE

1st Nine Weeks Equations 8.EE.7 Solve linear equations in one variable including rational coefficients. a. Give examples of linear equations in one variable with one solution, infinitely many solutions,

### The Grade Descriptors below are used to assess work and student progress in Mathematics from Year 7 to

Jersey College for Girls Assessment criteria for KS3 and KS4 Mathematics In Mathematics, students are required to become familiar, confident and competent with a range of content and procedures described

### Key competencies (student abilities)

Year 9 Mathematics Cambridge IGCSE Mathematics is accepted by universities and employers as proof of mathematical knowledge and understanding. Successful Cambridge IGCSE Mathematics candidates gain lifelong

### Expressions and Equations Grade 8 Math Grade 8 Math Start Date: September 09, 2013 End Date : November 08, 2013

Unit Overview Students will be able to: Apply properties of integer exponents. Use square and cube roots to represent solutions of equations. Create, use, and manipulate scientific notation to represent

### Essentials of Mathematics Lesson Objectives

Essentials of Mathematics Lesson Unit 1: NUMBER SENSE Reviewing Rational Numbers Practice adding, subtracting, multiplying, and dividing whole numbers, fractions, and decimals. Practice evaluating exponents.

### Algebra 1 Duxbury Middle School > > Grade 8 > Mathematics > Algebra 1 > Iacadoro, Stephanie Tuesday, February 28, 2017, 11:58AM

Algebra 1 Duxbury Middle School > 2016-2017 > Grade 8 > Mathematics > Algebra 1 > Iacadoro, Stephanie Tuesday, February 28, 2017, 11:58AM Unit Unit 0: Preparing for Algebra * for 282 only (Week 1, 9 Skills

### PREFACE. Synergy for Success in Mathematics 8 is designed for Grade 8 students. The textbook contains

Synergy for Success in Mathematics 8 is designed for Grade 8 students. The textbook contains all the required learning competencies and is supplemented with some additional topics for enrichment. Lessons

### COMMON CORE STATE STANDARDS TO BOOK CORRELATION

COMMON CORE STATE STANDARDS TO BOOK CORRELATION Conceptual Category: Number and Quantity Domain: The Real Number System After a standard is introduced, it is revisited many times in subsequent activities,

### Pre-Algebra Unit 2. Rational & Irrational Numbers. Name

Pre-Algebra Unit 2 Rational & Irrational Numbers Name Core Table 2 Pre-Algebra Name: Unit 2 Rational & Irrational Numbers Core: Table: 2.1.1 Define Rational Numbers Vocabulary: Real Numbers the set of

### Yes zero is a rational number as it can be represented in the

1 REAL NUMBERS EXERCISE 1.1 Q: 1 Is zero a rational number? Can you write it in the form 0?, where p and q are integers and q Yes zero is a rational number as it can be represented in the form, where p

### In Exercises 1 12, list the all of the elements of the given set. 2. The set of all positive integers whose square roots are less than or equal to 3

APPENDIX A EXERCISES In Exercises 1 12, list the all of the elements of the given set. 1. The set of all prime numbers less than 20 2. The set of all positive integers whose square roots are less than

### ASSIGNMENT NO -1 (SIMILAR TRIANGLES)

ASSIGNMENT NO -1 (SIMILAR TRIANGLES) 1. In an equilateral Δ ABC, the side BC is trisected at D. Prove that 9AD2 = 7AB2 2. P and Q are points on sides AB and AC respectively, of ΔABC. If AP = 3 cm,pb =

### Sequence of Grade 7 Modules Aligned with the Standards

Sequence of Grade 7 Modules Aligned with the Standards Module 1: Ratios and Proportional Relationships Module 2: Rational Numbers Module 3: Expressions and Equations Module 4: Percent and Proportional

### Section 3-4: Least Common Multiple and Greatest Common Factor

Section -: Fraction Terminology Identify the following as proper fractions, improper fractions, or mixed numbers:, proper fraction;,, improper fractions;, mixed number. Write the following in decimal notation:,,.

### ALGEBRA I FORM I. Textbook: Algebra, Second Edition;Prentice Hall,2002

ALGEBRA I FORM I Textbook: Algebra, Second Edition;Prentice Hall,00 Prerequisites: Students are expected to have a knowledge of Pre Algebra and proficiency of basic math skills including: positive and

### Contents. To the Teacher... v

Katherine & Scott Robillard Contents To the Teacher........................................... v Linear Equations................................................ 1 Linear Inequalities..............................................

FLORIDA STANDARDS TO BOOK CORRELATION FOR GRADE 7 ADVANCED After a standard is introduced, it is revisited many times in subsequent activities, lessons, and exercises. Domain: The Number System 8.NS.1.1

### San Jose Unified School District. Algebra 2 Pacing Calendar

San Jose Unified School District Algebra 2 Pacing Calendar 2009-2010 SJUSD ALGEBRA 2 TIMELINE 2009-2010 Page 1 of 10 SJUSD ALGEBRA 2 PACING GUIDE FOR 2009-2010 The Algebra 2 curriculum has been broken

### Algebra 2 Secondary Mathematics Instructional Guide

Algebra 2 Secondary Mathematics Instructional Guide 2009-2010 ALGEBRA 2AB (Grade 9, 10 or 11) Prerequisite: Algebra 1AB or Geometry AB 310303 Algebra 2A 310304 Algebra 2B COURSE DESCRIPTION Los Angeles

### Section 1.2 Factors and Factor Operators

Section 1. Factors and Factor Operators The most basic component of mathematics is the factor. Factors are parts of multiplication, therefore, in the product or or the factors are and. And, since 1, we

### Chapter 3: Section 3.1: Factors & Multiples of Whole Numbers

Chapter 3: Section 3.1: Factors & Multiples of Whole Numbers Prime Factor: a prime number that is a factor of a number. The first 15 prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43,

### Year 8 Autumn Term Topics Covered Calculations Ratio, Proportion and Compound Measures Manipulating Algebraic Expressions Fractions

Year 8 Autumn Term Topics Covered Note: grades given are our own internal 'Sprowston' grades used as a guide for the purpose of tracking students' progress Calculations Grade 2 Multiply and divide integers

### Natural Numbers: Also called the counting numbers The set of natural numbers is represented by the symbol,.

Name Period Date: Topic: Real Numbers and Their Graphs Standard: 9-12.A.1.3 Objective: Essential Question: What is the significance of a point on a number line? Determine the relative position on the number

### Mathematics Grade 7. Updated 3/1/11 36

Mathematics Grade 7 In Grade 7, instructional time should focus on four critical areas: (1) developing understanding of and applying proportional relationships; (2) developing understanding of operations