7COM1023 Programming Paradigms
|
|
- Marlene Wilkinson
- 5 years ago
- Views:
Transcription
1 7COM Programming Paradigms Practical Answers Expressions We will commence by typing in some expressions to familiarise ourselves with the environment.. Type in the following and evaluate them by pressing return: a) b). c) / d) / e) f). Answers a) > b) >. c) > / d) > / e) > "" "" f) >.. Type in the following expressions and evaluate. Do you get what you expect? a) (+ 4) b) (sqr ) c) (- 9 7) d) (- 7) e) (+ (* ) 4) f) (* (- 4) (+ )) g) (sqr (* 4))
2 Answers a) > (+ 4) 7 b) > (sqr ) c) > (- 9 7) d) > (- 7) -7 e) > (+ (* ) 4) 4 f) > (* (- 4) (+ )) 8 g) > (sqr (* 4)) 44 Write each of the above expressions in standard mathematical notation. a) + 4 b) c) 9 7 d) 7 e) ( * ) + 4 f) ( 4) * ( + ) g) *4
3 . Change each of the following into Lisp expressions and evaluate: a) + b) c) 7-4 d) ( + 4) ( ) e) 4 f) ( * 4) + ((-4)*) g) + *7 Answers a) > (+ ) b) > (sqr ) c) > (- 7 4) d) > (- (+ 4) (- )) e) > (- (sqr ) (sqr 4)) 9 f) > (+ (* 4) (* (- 4) )) g) > (+ (* 7))
4 4. Explore the following lisp functions that each work on numerical arguments: +, -, +, -, gcd, lcm, expt, sqrt, rational, rationalize, numerator, denominator, random. + and functions as above. + and - require further investigation. gcd denotes the greatest common divisor (the largest number to divide into the given numbers) > (gcd 9 ) > (gcd 9 ) > (gcd 9 8 4) lcm denotes the lowest common multiple (the smallest number in each of the sets of multiples generated by te given numbers) > (lcm ) > (lcm 4) > (lcm 4 ) > (lcm 4) 4 > (lcm 9 ) 9 > (lcm ) expt denotes the exponential function a x where a and x are two required input values. > (expt ) > (expt ) > (expt 4) Note that (expt ) gives the same result as (sqr ). sqrt denotes the square root of a value. We have met this function already. rational this function is not defined. Did it denote something in Scheme? Is there an alternative for DrRacket? > (rational (sqrt )) rational: this function is not defined > (rational? (sqrt )) The last result is interesting since the square root of is not a rational number. What could be happening here?
5 rationalize is also not defined. Example: > (rationalize (sqrt )) rationalize: this function is not defined Did it denote something in Scheme? Is there an alternative for DrRacket? Fractions consist of a numerator divided by a denominator. > (numerator /7) > (denominator /7) 7 > (numerator /4) > (denominator /4) 7 The random function generates a random number between and the number that you input. > (random ) > (random ) > (random ) > (random ) > (random ) > (random ) > (random ) > (random ) > (random ) > (random ) > (random ) > (random ) > (random ) > (random ) > (random ) > (random ) > (random ) > (random )
6 . Use ( define <id> <expression> ) to define three constants one, two and three as,, respectively. Evaluate and inspect the results to confirm that they hold the values that you expect. Use these to carry out some simple arithmetic such as (+ one three),. What happens if you now define three to be 4 and then evaluate (+ one three)? Answers. > (define one ) > (define two ) > (define three ) > one > two > three > (+ one three) 4 > (define three 4) three: this name was defined previously and cannot be re-defined > (+ one three) 4. The constant pi is defined already in Lisp. What is it s value? > pi #i
7 7. What do the following achieve? a) (string-append monday tuesday ) b) (substring monday ) c) (string? monday ) d) (string? ) e) (sqrt ) f) (sqrt -) g) (number? 7) h) (number? seven ) i) (equal ) j) (equal one ) Answers. a) > (string-append "monday" "tuesday") "mondaytuesday" b) > (substring "monday" ) "mon" c) > (string? "monday") d) > (string? ) false e) > (sqrt ) f) > (sqrt -) +i g) > (number? 7) h) > (number? "seven") false i) > (equal? ) false j) > (equal? one ) 8. Define a variable called radius and set the variable equal to. Write an expression that will calculate the area of the circle (define radius ) > (* pi (sqr radius)) #i
Section A Arithmetic ( 5) Exercise A
Section A Arithmetic In the non-calculator section of the examination there might be times when you need to work with quite awkward numbers quickly and accurately. In particular you must be very familiar
More informationCourse Learning Outcomes for Unit I. Reading Assignment. Unit Lesson. UNIT I STUDY GUIDE Number Theory and the Real Number System
UNIT I STUDY GUIDE Number Theory and the Real Number System Course Learning Outcomes for Unit I Upon completion of this unit, students should be able to: 2. Relate number theory, integer computation, and
More informationRational numbers as decimals and as integer fractions
Rational numbers as decimals and as integer fractions Given a rational number expressed as an integer fraction reduced to the lowest terms, the quotient of that fraction will be: an integer, if the denominator
More informationCOMPETENCY 1.0 UNDERSTAND THE STRUCTURE OF THE BASE TEN NUMERATION SYSTEM AND NUMBER THEORY
SUBAREA I. NUMBERS AND OPERATIONS COMPETENCY.0 UNDERSTAND THE STRUCTURE OF THE BASE TEN NUMERATION SYSTEM AND NUMBER THEORY Skill. Analyze the structure of the base ten number system (e.g., decimal and
More informationMath 083 Final Exam Practice
Math 083 Final Exam Practice Name: 1. Simplify the expression. Remember, negative exponents give reciprocals.. Combine the expressions. 3. Write the expression in simplified form. (Assume the variables
More informationMath 10- Chapter 2 Review
Math 10- Chapter 2 Review [By Christy Chan, Irene Xu, and Henry Luan] Knowledge required for understanding this chapter: 1. Simple calculation skills: addition, subtraction, multiplication, and division
More information17. [Exploring Numbers]
. [Exploring Numbers] Skill. Comparing whole numbers. Compare the size of the digits in the same place, one at a time. Work from left to right across each number. Q. Which number is the A ) 06 B ) 60 C
More informationScheme Quick Reference
Scheme Quick Reference COSC 18 Winter 2003 February 10, 2003 1 Introduction This document is a quick reference guide to common features of the Scheme language. It is by no means intended to be a complete
More informationTABLE OF CONTENTS. About Finish Line PA Core Math 5. UNIT 1: Big Ideas from Grade 7 7 UNIT 1 REVIEW 38. UNIT 2: The Number System 43 UNIT 2 REVIEW 58
TABLE OF CONTENTS About Finish Line PA Core Math 5 UNIT 1: Big Ideas from Grade 7 7 LESSON 1 CC..1.7.D.1 Understanding Proportional Relationships [connects to CC...8.B.] 8 LESSON CC..1.7.E.1 Operations
More informationOdd-Numbered Answers to Exercise Set 1.1: Numbers
Odd-Numbered Answers to Exercise Set.: Numbers. (a) Composite;,,, Prime Neither (d) Neither (e) Composite;,,,,,. (a) 0. 0. 0. (d) 0. (e) 0. (f) 0. (g) 0. (h) 0. (i) 0.9 = (j). (since = ) 9 9 (k). (since
More informationScheme Quick Reference
Scheme Quick Reference COSC 18 Fall 2003 This document is a quick reference guide to common features of the Scheme language. It is not intended to be a complete language reference, but it gives terse summaries
More informationFunctional Programming Languages (FPL)
Functional Programming Languages (FPL) 1. Definitions... 2 2. Applications... 2 3. Examples... 3 4. FPL Characteristics:... 3 5. Lambda calculus (LC)... 4 6. Functions in FPLs... 7 7. Modern functional
More informationHow to Design Programs Languages
How to Design Programs Languages Version 4.1 August 12, 2008 The languages documented in this manual are provided by DrScheme to be used with the How to Design Programs book. 1 Contents 1 Beginning Student
More informationSection 3.1 Factors and Multiples of Whole Numbers:
Chapter Notes Math 0 Chapter : Factors and Products: Skill Builder: Some Divisibility Rules We can use rules to find out if a number is a factor of another. To find out if, 5, or 0 is a factor look at
More informationStandardized Tests: Best Practices for the TI-Nspire CX
The role of TI technology in the classroom is intended to enhance student learning and deepen understanding. However, efficient and effective use of graphing calculator technology on high stakes tests
More informationFractions. Fractions One tenths, two tenths, three tenths
Recognise, Name and Write Chilli Challenge Count up and down in tenths One tenths, two tenths, three tenths 0 0 0 0 0 0 0 0 0 0 0 0 0 Recognise, Name and Write Recognise, Name and Write Recognise that
More informationChoose the correct answer below. 2. Convert the angle to a decimal in degrees.
1. Choose the figure that shows an angle of in standard position. Choose the correct answer below. 2. Convert the angle to a decimal in degrees. (Do not round until the final answer. Then round to two
More informationIntegers are whole numbers; they include negative whole numbers and zero. For example -7, 0, 18 are integers, 1.5 is not.
What is an INTEGER/NONINTEGER? Integers are whole numbers; they include negative whole numbers and zero. For example -7, 0, 18 are integers, 1.5 is not. What is a REAL/IMAGINARY number? A real number is
More informationA) Decimal Notation and Writing Decimals in Words. ecim B) Writing Decimals in Standard Form.
5.1 Introduction to Decimals A) Decimal Notation and Writing Decimals in Words. Decimals The Place Value System for Decimal Numbers Tens/ ones/ decimal point/ tenths/ hundredths/ thousandths/ ten-thousandths
More informationA. Incorrect! To simplify this expression you need to find the product of 7 and 4, not the sum.
Problem Solving Drill 05: Exponents and Radicals Question No. 1 of 10 Question 1. Simplify: 7u v 4u 3 v 6 Question #01 (A) 11u 5 v 7 (B) 8u 6 v 6 (C) 8u 5 v 7 (D) 8u 3 v 9 To simplify this expression you
More informationAnswers Investigation 5
Applications. Heidi s conjecture is correct; any value of x will always equal. 2. B Evan s conjecture is correct; students might argue that it is the largest number in its row and column, so it will be
More informationBuilding Equivalent Fractions, the Least Common Denominator, and Ordering Fractions
Section. PRE-ACTIVITY PREPARATION Building Equivalent Fractions, the Least Common Denominator, and Ordering Fractions You have learned that a fraction might be written in an equivalent form by reducing
More informationLesson 1: THE DECIMAL SYSTEM
Lesson 1: THE DECIMAL SYSTEM The word DECIMAL comes from a Latin word, which means "ten. The Decimal system uses the following ten digits to write a number: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Each time
More informationDigits. Value The numbers a digit. Standard Form. Expanded Form. The symbols used to show numbers: 0,1,2,3,4,5,6,7,8,9
Digits The symbols used to show numbers: 0,1,2,3,4,5,6,7,8,9 Value The numbers a digit represents, which is determined by the position of the digits Standard Form Expanded Form A common way of the writing
More informationHoughton Mifflin MATHSTEPS Level 7 correlated to Chicago Academic Standards and Framework Grade 7
State Goal 6: Demonstrate and apply a knowledge and sense of numbers, including basic arithmetic operations, number patterns, ratios and proportions. CAS A. Describe and apply concepts of real numbers,
More informationFractions and Decimals
Chapter Fractions and Decimals FRACTION: A fraction is a number representing a part of a whole. The whole may be a single object or a group of objects. 5 is a fraction with numerator and denominator 5.
More information6-8 Math Adding and Subtracting Polynomials Lesson Objective: Subobjective 1: Subobjective 2:
6-8 Math Adding and Subtracting Polynomials Lesson Objective: The student will add and subtract polynomials. Subobjective 1: The student will add polynomials. Subobjective 2: The student will subtract
More informationMath 085 Final Exam Review
Math 08 Final Exam Review Objective : Use the rules of signed number arithmetic to perform operations on integers. These operations include, but are not limited to, addition, subtraction, multiplication,
More informationPrentice Hall Mathematics Course Correlated to: Archdiocese of Chicago (Illinois) Mathematics Curriculum Frameworks (2004) Grades 6-12
Archdiocese of Chicago (Illinois) Mathematics Curriculum Frameworks (2004) Grades 6-12 Goal Outcome Outcome Statement Priority Code Chapter Topic 6 6.01 6.06.01 - Represent place values from millionths
More information- 0.8.00-0.8. 7 ANSWERS: ) : ) : ) : ) : 8 RATIO WORD PROBLEM EXAMPLES: Ratio Compares two amounts or values; they can be written in ways. As a fraction With a colon : With words to A classroom has girls
More informationAccuplacer Arithmetic Study Guide
Accuplacer Arithmetic Study Guide I. Terms Numerator: which tells how many parts you have (the number on top) Denominator: which tells how many parts in the whole (the number on the bottom) Example: parts
More informationFor Module 2 SKILLS CHECKLIST. Fraction Notation. George Hartas, MS. Educational Assistant for Mathematics Remediation MAT 025 Instructor
Last Updated: // SKILLS CHECKLIST For Module Fraction Notation By George Hartas, MS Educational Assistant for Mathematics Remediation MAT 0 Instructor Assignment, Section. Divisibility SKILL: Determine
More informationSCHOOL OF ENGINEERING & BUILT ENVIRONMENT. Mathematics. Numbers & Number Systems
SCHOOL OF ENGINEERING & BUILT ENVIRONMENT Mathematics Numbers & Number Systems Introduction Numbers and Their Properties Multiples and Factors The Division Algorithm Prime and Composite Numbers Prime Factors
More information2.1 Basics of Functions and Their Graphs
.1 Basics of Functions and Their Graphs Section.1 Notes Page 1 Domain: (input) all the x-values that make the equation defined Defined: There is no division by zero or square roots of negative numbers
More information1 Elementary number theory
Math 215 - Introduction to Advanced Mathematics Spring 2019 1 Elementary number theory We assume the existence of the natural numbers and the integers N = {1, 2, 3,...} Z = {..., 3, 2, 1, 0, 1, 2, 3,...},
More informationr the COR d e s 3 A lg e b r a Alabama Pathways
BUI LT fo COM r the MON COR E Gra 2013 2014 d e s 3 A lg e b r a Alabama Pathways I Grade 3 Operations and Algebraic Thinking Operations and Algebraic Thinking Operations and Algebraic Thinking Number
More informationr the COR d e s 3 A lg e b r a New York Common Core Pathways
BUI LT fo COM r the MON COR E Gra 2013 2014 d e s 3 A lg e b r a New York Common Core Pathways I Grade 3 Number and Operations - Fractions Measurement and Data Geometry Place Value with Whole Numbers Place
More informationWhat is a Fraction? Fractions. One Way To Remember Numerator = North / 16. Example. What Fraction is Shaded? 9/16/16. Fraction = Part of a Whole
// Fractions Pages What is a Fraction? Fraction Part of a Whole Top Number? Bottom Number? Page Numerator tells how many parts you have Denominator tells how many parts are in the whole Note: the fraction
More informationChapter 4. Number Theory. 4.1 Factors and multiples
Chapter 4 Number Theory We ve now covered most of the basic techniques for writing proofs. So we re going to start applying them to specific topics in mathematics, starting with number theory. Number theory
More informationMontana City School GRADE 5
Montana City School GRADE 5 Montana Standard 1: Students engage in the mathematical processes of problem solving and reasoning, estimation, communication, connections and applications, and using appropriate
More informationReview Guide for Term Paper (Teza)
Review Guide for Term Paper (Teza) We will soon have a term paper over the material covered in Chapters 1, 2, 8, 9, 15, 22, 23, 16 and 3. In Chapter 1 we covered: Place value, multiplying and dividing
More informationLoops / Repetition Statements
Loops / Repetition Statements Repetition statements allow us to execute a statement multiple times Often they are referred to as loops C has three kinds of repetition statements: the while loop the for
More informationDEPARTMENT OF ACADEMIC UPGRADING
DEPARTMENT OF ACADEMIC UPGRADING COURSE OUTLINE WINTER 2014 INTRODUCTION TO MATH 0081 INSTRUCTOR: Joelle Reynolds PHONE: (780) 539-2810 or 2204 OFFICE: Math Lab A210 E-MAIL: jreynolds@gprc.ab.ca OFFICE
More informationHow to Design Programs Languages
How to Design Programs Languages Version 6.6 July 22, 2016 The languages documented in this manual are provided by DrRacket to be used with the How to Design Programs book. When programs in these languages
More informationYEAR 7 SCHEME OF WORK - EXTENSION
YEAR 7 SCHEME OF WORK - EXTENSION Autumn Term 1 Number Skills Spring Term 1 Angles and Shape Summer Term 1 Multiplicative Reasoning Analysing and displaying data Decimals Perimeter, Area and Volume Half
More informationWhat is a Fraction? A fraction is a part or piece of something. The way we write fractions tells us the size of the piece we are referring to
October 0, 0 What is a Fraction? A fraction is a part or piece of something. The way we write fractions tells us the size of the piece we are referring to ⅝ is the numerator is the denominator is the whole
More informationLesson 1: Arithmetic Review
In this lesson we step back and review several key arithmetic topics that are extremely relevant to this course. Before we work with algebraic expressions and equations, it is important to have a good
More informationor 5.00 or 5.000, and so on You can expand the decimal places of a number that already has digits to the right of the decimal point.
1 LESSON Understanding Rational and Irrational Numbers UNDERSTAND All numbers can be written with a For example, you can rewrite 22 and 5 with decimal points without changing their values. 22 5 22.0 or
More informationEXPLORE MATHEMATICS TEST
EXPLORE MATHEMATICS TEST Table 4: The College Readiness The describe what students who score in the specified score ranges are likely to know and to be able to do. The help teachers identify ways of enhancing
More informationIntro to Computational Programming in C Engineering For Kids!
CONTROL STRUCTURES CONDITIONAL EXPRESSIONS Take the construction like this: Simple example: if (conditional expression) statement(s) we do if the condition is true statement(s) we do if the condition is
More informationExcerpt from "Art of Problem Solving Volume 1: the Basics" 2014 AoPS Inc.
Chapter 5 Using the Integers In spite of their being a rather restricted class of numbers, the integers have a lot of interesting properties and uses. Math which involves the properties of integers is
More information15-110: Principles of Computing, Spring Problem Set 3 (PS3) Due: Friday, February 9 by 2:30PM on Gradescope
15-110: Principles of Computing, Spring 2018 Problem Set 3 (PS3) Due: Friday, February 9 by 2:30PM on Gradescope HANDIN INSTRUCTIONS Download a copy of this PDF file. You have two ways to fill in your
More informationIntro to Rational Expressions
Intro to Rational Expressions Fractions and Exponents Review Fractions Review Adding and Subtracting Fractions Always find a common denominator when adding or subtracting fractions! a) b) Multiplying and
More informationMath Glossary Numbers and Arithmetic
Math Glossary Numbers and Arithmetic Version 0.1.1 September 1, 200 Next release: On or before September 0, 200. E-mail edu@ezlink.com for the latest version. Copyright 200 by Brad Jolly All Rights Reserved
More informationExample: Which of the following expressions must be an even integer if x is an integer? a. x + 5
8th Grade Honors Basic Operations Part 1 1 NUMBER DEFINITIONS UNDEFINED On the ACT, when something is divided by zero, it is considered undefined. For example, the expression a bc is undefined if either
More informationMAC 1105 Fall Term 2018
MAC 1105 Fall Term 2018 Each objective covered in MAC 1105 is listed below. Along with each objective is the homework list used with MyMathLab (MML) and a list to use with the text (if you want to use
More informationChapter 1 & 2 Calculator Test Study Guide
Chapter 1 & 2 Calculator Test Study Guide Powers and Exponents 1) To put a number to the second power, simply hit the x 2 key, then enter. 2) To put a number to the third or a higher power, key in base,
More informationHOW TO DIVIDE: MCC6.NS.2 Fluently divide multi-digit numbers using the standard algorithm. WORD DEFINITION IN YOUR WORDS EXAMPLE
MCC6.NS. Fluently divide multi-digit numbers using the standard algorithm. WORD DEFINITION IN YOUR WORDS EXAMPLE Dividend A number that is divided by another number. Divisor A number by which another number
More informationMini-Lectures by Section
Mini-Lectures by Section BEGINNING AND INTERMEDIATE ALGEBRA, Mini-Lecture 1.1 1. Learn the definition of factor.. Write fractions in lowest terms.. Multiply and divide fractions.. Add and subtract fractions..
More informationLISP. Everything in a computer is a string of binary digits, ones and zeros, which everyone calls bits.
LISP Everything in a computer is a string of binary digits, ones and zeros, which everyone calls bits. From one perspective, sequences of bits can be interpreted as a code for ordinary decimal digits,
More informationSection 1.2 Fractions
Objectives Section 1.2 Fractions Factor and prime factor natural numbers Recognize special fraction forms Multiply and divide fractions Build equivalent fractions Simplify fractions Add and subtract fractions
More informationMacro Programming Reference Guide. Copyright 2005 Scott Martinez
Macro Programming Reference Guide Copyright 2005 Scott Martinez Section 1. Section 2. Section 3. Section 4. Section 5. Section 6. Section 7. What is macro programming What are Variables What are Expressions
More informationCreating a new data type
Appendix B Creating a new data type Object-oriented programming languages allow programmers to create new data types that behave much like built-in data types. We will explore this capability by building
More informationA Framework for Achieving the Essential Academic Learning. Requirements in Mathematics Grades 8-10 Glossary
A Framework for Achieving the Essential Academic Learning Requirements in Mathematics Grades 8-10 Glossary absolute value the numerical value of a number without regard to its sign; the distance of the
More informationRadical Expressions LESSON. 36 Unit 1: Relationships between Quantities and Expressions
LESSON 6 Radical Expressions UNDERSTAND You can use the following to simplify radical expressions. Product property of radicals: The square root of a product is equal to the square root of the factors.
More informationIntroduction to Modular Arithmetic
Randolph High School Math League 2014-2015 Page 1 1 Introduction Introduction to Modular Arithmetic Modular arithmetic is a topic residing under Number Theory, which roughly speaking is the study of integers
More informationReview Test 2. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Review Test MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Determine if the number is divisible by, 3, 4,, 6, 8, 9, 10, and/or 1. 1) 36 A) 3, 4 B),
More informationDEPARTMENT OF ACADEMIC UPGRADING
DEPARTMENT OF ACADEMIC UPGRADING COURSE OUTLINE WINTER 2013 INTRODUCTION TO MATH 0081 INSTRUCTOR: Sukhvir Sandhu PHONE: (780) 539-2810 or 2234 OFFICE: Math Lab A210 or C310 E-MAIL: ssandhu@gprc.ab.ca OFFICE
More informationHigher-Order Procedures
Higher-Order Procedures Today s topics Procedural abstractions Capturing patterns across procedures Higher Order Procedures Procedural abstraction Process of procedural abstraction Define formal parameters,
More informationSummer 2013 Modules 9-13
Summer 201 Modules 9-1 Mastering the Fundamentals Chris Millett Copyright 201 All rights reserved. Written permission must be secured from the author to use or reproduce any part of this book. Academic
More information5.1 to 5.3 P4.ink. Carnegie Unit 3 Examples & Class Notes
Carnegie Unit 3 Examples & Class Notes 1 2 3 This number is called the index. 1 Only multiply the numbers inside radical symbols, if and only if, they have the same index. 4 5 1 Use the times tables &
More informationIntroduction to Computer Programming in Python Dr. William C. Bulko. Data Types
Introduction to Computer Programming in Python Dr William C Bulko Data Types 2017 What is a data type? A data type is the kind of value represented by a constant or stored by a variable So far, you have
More informationTOURNAMENT OF THE TOWNS, Glossary
TOURNAMENT OF THE TOWNS, 2003 2004 Glossary Absolute value The size of a number with its + or sign removed. The absolute value of 3.2 is 3.2, the absolute value of +4.6 is 4.6. We write this: 3.2 = 3.2
More informationCS3110 Spring 2017 Lecture 10 a Module for Rational Numbers
CS3110 Spring 2017 Lecture 10 a Module for Rational Numbers Robert Constable Abstract The notes and lecture start with a brief summary of the relationship between OCaml types, Coq types and logic that
More informationCSc 520 Principles of Programming Languages
CSc 520 Principles of Programming Languages 3: Scheme Introduction Christian Collberg collberg@cs.arizona.edu Department of Computer Science University of Arizona Copyright c 2005 Christian Collberg [1]
More information6.3 ADDING and SUBTRACTING Rational Expressions REVIEW. When you ADD rational numbers (fractions): 1) Write each number with common denominator
6.3 ADDING and SUBTRACTING Rational REVIEW When you ADD rational numbers (fractions): 1) Write each number with common denominator 4 5 + 10 12 = 6.3 ADDING and SUBTRACTING Rational 4 5 + 10 12 = REVIEW
More informationWelcome to CS 135 (Winter 2018)
Welcome to CS 135 (Winter 2018) Instructors: Sandy Graham, Paul Nijjar Other course personnel: see website for details ISAs (Instructional Support Assistants) IAs (Instructional Apprentices) ISC (Instructional
More informationX Std. Topic Content Expected Learning Outcomes Mode of Transaction
X Std COMMON SYLLABUS 2009 - MATHEMATICS I. Theory of Sets ii. Properties of operations on sets iii. De Morgan s lawsverification using example Venn diagram iv. Formula for n( AÈBÈ C) v. Functions To revise
More informationMath 6 Notes Unit One: Whole Numbers and Patterns
Math 6 Notes Unit One: Whole Numbers and Patterns Whole Numbers The following is the set of numbers on the number line called whole numbers: {0, 1,, 3, 4, } All numbers in base 10 are made up of 10 digits:
More informationScheme Tutorial. Introduction. The Structure of Scheme Programs. Syntax
Scheme Tutorial Introduction Scheme is an imperative language with a functional core. The functional core is based on the lambda calculus. In this chapter only the functional core and some simple I/O is
More informationSWALLOW SCHOOL DISTRICT CURRICULUM GUIDE. Stage 1: Desired Results
SWALLOW SCHOOL DISTRICT CURRICULUM GUIDE Curriculum Area: Math Course Length: Full Year Grade: 5th Date Last Approved: June 2015 Stage 1: Desired Results Course Description and Purpose: 5th grade offers
More informationMini-Lesson 1. Section 1.1: Order of Operations PEMDAS
Name: Date: 1 Section 1.1: Order of Operations PEMDAS If we are working with a mathematical expression that contains more than one operation, then we need to understand how to simplify. The acronym PEMDAS
More information2. The Wheel of Theodorus in Problem 4.1 includes only the first 11 triangles in the wheel. The wheel can go on forever.
A C E Applications Connections Extensions Applications 1. The hypotenuse of a right triangle is 15 centimeters long. One leg is 9 centimeters long. How long is the other leg? 2. The Wheel of Theodorus
More informationName Course Days/Start Time
Name Course Days/Start Time Mini-Project : The Library of Functions In your previous math class, you learned to graph equations containing two variables by finding and plotting points. In this class, we
More informationUCT Algorithm Circle: Number Theory
UCT Algorithm Circle: 7 April 2011 Outline Primes and Prime Factorisation 1 Primes and Prime Factorisation 2 3 4 Some revision (hopefully) What is a prime number? An integer greater than 1 whose only factors
More information6.034 Artificial Intelligence February 9, 2007 Recitation # 1. (b) Draw the tree structure corresponding to the following list.
6.034 Artificial Intelligence February 9, 2007 Recitation # 1 1 Lists and Trees (a) You are given two lists: (define x (list 1 2 3)) (define y (list 4 5 6)) What would the following evaluate to: (append
More informationMath 1314 Lesson 13 Analyzing Other Types of Functions
Math 1314 Lesson 13 Analyzing Other Types of Functions Asymptotes We will need to identify any vertical or horizontal asymptotes of the graph of a function. A vertical asymptote is a vertical line x a
More informationExponents. Although exponents can be negative as well as positive numbers, this chapter will only address the use of positive exponents.
Section 6.2 PRE-ACTIVITY PREPARATION Exponents Exponents enable you to simplify the presentation of a numerical expression containing repeated multiplication into a concise form that is easier to read
More information4.3 Rational Thinking
RATIONAL EXPRESSIONS & FUNCTIONS -4.3 4.3 Rational Thinking A Solidify Understanding Task The broad category of functions that contains the function!(#) = & ' is called rational functions. A rational number
More informationNorth Thurston Public Schools Sixth Grade Math Power Standard 1 Unit Assessment #1 and #3
Math Power Standard 1 Unit Assessment #1 and #3 PS 1 - Estimate products and quotients of fractions and decimals (6.1.C) Big Idea: Estimating helps us decide if our answers make sense. Essential Questions:
More informationBasic memory model Using functions Writing functions. Basics Prototypes Parameters Return types Functions and memory Names and namespaces
Basic memory model Using functions Writing functions Basics Prototypes Parameters Return types Functions and memory Names and namespaces When a program runs it requires main memory (RAM) space for Program
More informationBig Apple Academy 2017 Mathematics Department
Big Apple Academy 201 Mathematics Department Grade Homework Math Package It is important that you keep practicing your mathematical Knowledge over the summer to be ready for 5 th grade. In this Package
More informationabsolute value- the absolute value of a number is the distance between that number and 0 on a number line. Absolute value is shown 7 = 7-16 = 16
Grade Six MATH GLOSSARY absolute value- the absolute value of a number is the distance between that number and 0 on a number line. Absolute value is shown 7 = 7-16 = 16 abundant number: A number whose
More informationMath Introduction to Advanced Mathematics
Math 215 - Introduction to Advanced Mathematics Number Theory Fall 2017 The following introductory guide to number theory is borrowed from Drew Shulman and is used in a couple of other Math 215 classes.
More informationMath: Grade 6 Unit: Data About Us: Statistics Suggested Length: 5-6 weeks
Reporting Category: Data and Analysis Math: Grade 6 Unit: Data About Us: Statistics Suggested Length: 5-6 weeks Enduring Understanding and Essential Questions Concepts & Eligible Content (6 th grade PA
More informationWelcome to CS 135 (Fall 2018) Themes of the course. Lectures. cs135/
Welcome to CS 135 (Fall 2018) Instructors: Byron Weber Becker, Charles Clarke, Gord Cormack, Robert Hackman, Kevin Lanctot, Paul Nijjar, Adrian Reetz Other course personnel: see website for details ISAs
More informationUnit 7 Evaluation. Multiple-Choice. Evaluation 07 Second Year Algebra 1 (MTHH ) Name I.D. Number
Name I.D. Number Unit 7 Evaluation Evaluation 07 Second Year Algebra (MTHH 09 09) This evaluation will cover the lessons in this unit. It is open book, meaning you can use your tetbook, syllabus, and other
More informationAdd the fractions by first finding. f + D U C
Add the fractions by first finding the LCD. U + C U C (Circle the LCD) Rewrite the fractions using the LCD and then add. Remember to reduce the answer if you can. Add the fractions by first finding M the
More informationAlgebra Domains of Rational Functions
Domains of Rational Functions Rational Expressions are fractions with polynomials in both the numerator and denominator. If the rational expression is a function, it is a Rational Function. Finding the
More informationUNIT 1 PLACE VALUE AND WHOLE NUMBERS
UNIT 1 PLACE VALUE AND WHOLE NUMBERS INTRODUCTION We will begin our study of Arithmetic by learning about the number system we use today. The Base-10 Number System or Hindu-Arabic Numeral System began
More information