IB Mathematical Studies Logic Practice Name
|
|
|
- Violet Riley
- 7 years ago
- Views:
Transcription
1 IB Mathematical Studies Logic Practice Name Note the markscheme is at the end!!!! 1. Police in a town are investigating the theft of mobile phones one evening from three cafés, Alan s Diner, Sarah s Snackbar and Pete s Eats. They interviewed two suspects, Matthew and Anna about that evening. Matthew said: I visited Pete s Eats and visited Alan s Diner and I did not visit Sarah s Snackbar Let p, q and r be the statements: p : I visited Alan s Diner q : I visited Sarah s Snackbar r : I visited Pete s Eats (a) Write down Matthew s statement in symbolic logic form. What Anna said was lost by the police, but in symbolic form it was (q r ) p Write down, in words, what Anna said. 2. In a particular school, students must choose at least one of three optional subjects: art, psychology or history. Consider the following propositions a: I choose art, p: I choose psychology, h: I choose history. (a) Write, in words, the compound proposition h ( p a). IB Questionbank Mathematical Studies 3rd edition 1
2 Complete the truth table for a p. a p a a p T T F T F F F T T F F T (1) State whether a p is a tautology, a contradiction or neither. Justify your answer. 3. Consider two propositions p and q. (a) Complete the truth table below. p q q p q p p q T T T F F T F F (4) Decide whether the compound proposition (p q) ( p q) is a tautology. State the reason for your decision. 4. (a) Complete the truth table shown below. p q p q T T T F F T F F p (p q) (p ( p q)) p IB Questionbank Mathematical Studies 3rd edition 2
3 State whether the compound proposition(p ( p q)) p is a contradiction, a tautology or neither. (1) Consider the following propositions. p: Feng finishes his homework q: Feng goes to the football match Write in symbolic form the following proposition. If Feng does not go to the football match then Feng finishes his homework. 5. (a) Complete the following truth table. p q... p q T T F T F T F T F F F T Consider the propositions p: Cristina understands logic q: Cristina will do well on the logic test. Write down the following compound proposition in symbolic form. If Cristina understands logic then she will do well on the logic test Write down in words the contrapositive of the proposition given in part. 6. Consider the two propositions p and q. IB Questionbank Mathematical Studies 3rd edition 3
4 p: The sun is shining q: I will go swimming Write in words the compound propositions (a) p q; p q. The truth table for these compound propositions is given below. p q p q p p q T T T T T F F F F T T T F F T T Complete the column for p. (1) (d) State the relationship between the compound propositions p q and p q. (1) 7. Consider the following propositions p: The number is a multiple of five. q: The number is even. r: The number ends in zero. (a) Write in words (q r) p Consider the statement If the number is a multiple of five, and is not even then it will not end in zero. (i) (ii) Write this statement in symbolic form. Write the contrapositive of this statement in symbolic form. (6) (Total 9 marks) 8. Consider the statement p: IB Questionbank Mathematical Studies 3rd edition 4
5 If a quadrilateral is a square then the four sides of the quadrilateral are equal. (a) Write down the inverse of statement p in words. Write down the converse of statement p in words. Determine whether the converse of statement p is always true. Give an example to justify your answer. Consider the statement If the number is a multiple of five, and is not even then it will not end in zero. (i) (ii) Write this statement in symbolic form. Write the contrapositive of this statement in symbolic form. (6) (Total 9 marks) IB Questionbank Mathematical Studies 3rd edition 5
6 Worked Out Solutions 1. (a) r p q 1)(A1) Note: Award (A1) for two conjunctions, (A1) for negation seen on q, (A1) for correct compound statement. (C3) If I visited (either) Sarah s Snackbar or Pete s Eats (then) I did not visit Alan s Diner 1)(A1) Note: Award (A1) for If (then), (A1) for Sarah s Snackbar or Pete s Eats, (A1) for did not visit Alan s Diner. (C3) 2. (a) If I do not choose history then I choose either psychology or I choose art 1)(A1) Notes: Award (A1) for if (then) Award (A1) for not choose history. Award (A1) for choose (either) psychology or art (or both). If the order of the statements is wrong award at most 1)(A0) (C3) a p a a p T T F T T F F T F T T T F F T F (A1) (C1) Neither, because not all the entries in the last column are the same )(R1) Notes: Do not award (R0)(A1). Follow through from their answer to part. Reasoning must be consistent with their answer to part. (A1)(ft (C2) IB Questionbank Mathematical Studies 3rd edition 6
7 3. (a) p q q p q p p q T T F F F T T F T T F T F T F T T T F F T T T F 1)(ft) 1)(ft) Note: Award (A1) for each correct column (second column (ft) from first, fourth (ft) from third). Follow through from second column to fourth column for a consistent mistake in implication. (C4) Since second and fourth columns are not identical (R1)(ft) Not a tautology (A1)(ft ) (C2) Note: (R0)(A1) may not be awarded. 4. (a) p q p q p (p q) (p ( p q)) p T T T T T T F F T T F T F F T F F F F T 1)(ft)(A1)(ft) Note: Award (A1) for each correct column. (C3) tautology (A1)(ft ) (C1) Note: Follow through from their last column. q p IB Questionbank Mathematical Studies 3rd edition 7
8 Note: Award (A1) for q and p in correct order, (A1) for sign. 5. (a) p q q p q T T F F T F T T F T F T F F T T Note: Award (A1) for q, (A1) for last column. p q Note: Award (A1) for, (A1) for p and q in the correct order. If Cristina does not do well on the logic test then she does not understand logic. Note: Award (A1) for If (then), must be an implication, (A1) for the correct propositions in the correct order. 6. (a) If the sun is shining then I will go swimming. Note: Award (A1) for if then and (A1) for correct order. Either the sun is not shining or I will go swimming. Note: Award (A1) for both correct statements and (A1) for either or. p q p q p p q T T T F T T F F F F F T T T T F F T T T IB Questionbank Mathematical Studies 3rd edition 8
9 (A1) (C1) (d) They are (logically) equivalent. (A1) (C1) Note: Do not accept any other answers. 7. (a) If the number is even and the number does not end in zero, (then) the number is not a multiple of five. 1)(A1) Note: Award (A1) for if (then), (A1) for the number is even and the number does not end in zero, (A1) for the number is not a multiple of 5. (i) (p q) r 1)1) (A1) for, (A1) for, (A1) for p and q, (A1) for r Note: If parentheses not present award at most 1)0). (ii) r ( p q) OR r (p q) )(A1)(ft) Note: Award (A1)(ft) for reversing the order, (A1) for negating the statements on both sides. If parentheses not present award at most (A1)(ft)(A0). Do not penalise twice for missing parentheses in (i) and (ii). (A1)(ft [9] 8. (a) If a quadrilateral is not a square (then) the four sides of the quadrilateral are not equal. Note: Award (A1) for if (then), (A1) for the correct phrases in the correct order. If the four sides of the quadrilateral are equal (then) the quadrilateral is a square. 1)(ft) Note: Award (A1) for if (then), (A1)(ft) for the correct phrases in the correct order. (C2) Note: Follow through in if the inverse and converse in (a) and are correct and reversed. IB Questionbank Mathematical Studies 3rd edition 9
10 The converse is not always true, for example a rhombus (diamond) is a quadrilateral with four equal sides, but it is not a square. (A1)(R Note: Do not award (A1)(R0). IB Questionbank Mathematical Studies 3rd edition 10
IB Practice Chi Squared Test of Independence
1. A university required all Science students to study one language for one year. A survey was carried out at the university amongst the 150 Science students. These students all studied one of either French,
Logic Appendix. Section 1 Truth Tables CONJUNCTION EXAMPLE 1
Logic Appendix T F F T Section 1 Truth Tables Recall that a statement is a group of words or symbols that can be classified collectively as true or false. The claim 5 7 12 is a true statement, whereas
CSL105: Discrete Mathematical Structures. Ragesh Jaiswal, CSE, IIT Delhi
Propositional Logic: logical operators Negation ( ) Conjunction ( ) Disjunction ( ). Exclusive or ( ) Conditional statement ( ) Bi-conditional statement ( ): Let p and q be propositions. The biconditional
CHAPTER 2. Logic. 1. Logic Definitions. Notation: Variables are used to represent propositions. The most common variables used are p, q, and r.
CHAPTER 2 Logic 1. Logic Definitions 1.1. Propositions. Definition 1.1.1. A proposition is a declarative sentence that is either true (denoted either T or 1) or false (denoted either F or 0). Notation:
Handout #1: Mathematical Reasoning
Math 101 Rumbos Spring 2010 1 Handout #1: Mathematical Reasoning 1 Propositional Logic A proposition is a mathematical statement that it is either true or false; that is, a statement whose certainty or
Propositional Logic. A proposition is a declarative sentence (a sentence that declares a fact) that is either true or false, but not both.
irst Order Logic Propositional Logic A proposition is a declarative sentence (a sentence that declares a fact) that is either true or false, but not both. Are the following sentences propositions? oronto
Direct Translation is the process of translating English words and phrases into numbers, mathematical symbols, expressions, and equations.
Section 1 Mathematics has a language all its own. In order to be able to solve many types of word problems, we need to be able to translate the English Language into Math Language. is the process of translating
CHAPTER 3. Methods of Proofs. 1. Logical Arguments and Formal Proofs
CHAPTER 3 Methods of Proofs 1. Logical Arguments and Formal Proofs 1.1. Basic Terminology. An axiom is a statement that is given to be true. A rule of inference is a logical rule that is used to deduce
3. Logical Reasoning in Mathematics
3. Logical Reasoning in Mathematics Many state standards emphasize the importance of reasoning. We agree disciplined mathematical reasoning is crucial to understanding and to properly using mathematics.
Math 3000 Section 003 Intro to Abstract Math Homework 2
Math 3000 Section 003 Intro to Abstract Math Homework 2 Department of Mathematical and Statistical Sciences University of Colorado Denver, Spring 2012 Solutions (February 13, 2012) Please note that these
Discrete Mathematics and Probability Theory Fall 2009 Satish Rao, David Tse Note 2
CS 70 Discrete Mathematics and Probability Theory Fall 2009 Satish Rao, David Tse Note 2 Proofs Intuitively, the concept of proof should already be familiar We all like to assert things, and few of us
8 Square matrices continued: Determinants
8 Square matrices continued: Determinants 8. Introduction Determinants give us important information about square matrices, and, as we ll soon see, are essential for the computation of eigenvalues. You
(b) (i) How much is to be paid as a deposit under this option? (1) Find the cost of the loan under Friendly Credit Terms.
1. Angela needs $4000 to pay for a car. She was given two options by the car seller. Option A: Outright Loan A loan of $4000 at a rate of 12% per annum compounded monthly. Find (i) (ii) the cost of this
Geometry of 2D Shapes
Name: Geometry of 2D Shapes Answer these questions in your class workbook: 1. Give the definitions of each of the following shapes and draw an example of each one: a) equilateral triangle b) isosceles
A Quick Algebra Review
1. Simplifying Epressions. Solving Equations 3. Problem Solving 4. Inequalities 5. Absolute Values 6. Linear Equations 7. Systems of Equations 8. Laws of Eponents 9. Quadratics 10. Rationals 11. Radicals
Section 1.5 Exponents, Square Roots, and the Order of Operations
Section 1.5 Exponents, Square Roots, and the Order of Operations Objectives In this section, you will learn to: To successfully complete this section, you need to understand: Identify perfect squares.
Show all work for credit. Attach paper as needed to keep work neat & organized.
Geometry Semester 1 Review Part 2 Name Show all work for credit. Attach paper as needed to keep work neat & organized. Determine the reflectional (# of lines and draw them in) and rotational symmetry (order
Likewise, we have contradictions: formulas that can only be false, e.g. (p p).
CHAPTER 4. STATEMENT LOGIC 59 The rightmost column of this truth table contains instances of T and instances of F. Notice that there are no degrees of contingency. If both values are possible, the formula
p: I am elected q: I will lower the taxes
Implication Conditional Statement p q (p implies q) (if p then q) is the proposition that is false when p is true and q is false and true otherwise. Equivalent to not p or q Ex. If I am elected then I
Beyond Propositional Logic Lukasiewicz s System
Beyond Propositional Logic Lukasiewicz s System Consider the following set of truth tables: 1 0 0 1 # # 1 0 # 1 1 0 # 0 0 0 0 # # 0 # 1 0 # 1 1 1 1 0 1 0 # # 1 # # 1 0 # 1 1 0 # 0 1 1 1 # 1 # 1 Brandon
Tom wants to find two real numbers, a and b, that have a sum of 10 and have a product of 10. He makes this table.
Sum and Product This problem gives you the chance to: use arithmetic and algebra to represent and analyze a mathematical situation solve a quadratic equation by trial and improvement Tom wants to find
GCSE Mathematics. Foundation Tier Unit 3 Geometry and Algebra Mark scheme. 43603F November 2015. Version 1.1 Final
GCSE Mathematics Foundation Tier Unit 3 Geometry and Algebra Mark scheme 43603F November 20 Version 1.1 Final Mark schemes are prepared by the Lead Assessment Writer and considered, together with the relevant
Lesson 21. Circles. Objectives
Student Name: Date: Contact Person Name: Phone Number: Lesson 1 Circles Objectives Understand the concepts of radius and diameter Determine the circumference of a circle, given the diameter or radius Determine
A Second Course in Mathematics Concepts for Elementary Teachers: Theory, Problems, and Solutions
A Second Course in Mathematics Concepts for Elementary Teachers: Theory, Problems, and Solutions Marcel B. Finan Arkansas Tech University c All Rights Reserved First Draft February 8, 2006 1 Contents 25
Mathematical Induction
Mathematical Induction In logic, we often want to prove that every member of an infinite set has some feature. E.g., we would like to show: N 1 : is a number 1 : has the feature Φ ( x)(n 1 x! 1 x) How
Verbal Phrases to Algebraic Expressions
Student Name: Date: Contact Person Name: Phone Number: Lesson 13 Verbal Phrases to s Objectives Translate verbal phrases into algebraic expressions Solve word problems by translating sentences into equations
26 Integers: Multiplication, Division, and Order
26 Integers: Multiplication, Division, and Order Integer multiplication and division are extensions of whole number multiplication and division. In multiplying and dividing integers, the one new issue
Pre-Algebra - Order of Operations
0.3 Pre-Algebra - Order of Operations Objective: Evaluate expressions using the order of operations, including the use of absolute value. When simplifying expressions it is important that we simplify them
Grade 8 Mathematics Geometry: Lesson 2
Grade 8 Mathematics Geometry: Lesson 2 Read aloud to the students the material that is printed in boldface type inside the boxes. Information in regular type inside the boxes and all information outside
Using the Area Model to Teach Multiplying, Factoring and Division of Polynomials
visit us at www.cpm.org Using the Area Model to Teach Multiplying, Factoring and Division of Polynomials For more information about the materials presented, contact Chris Mikles mikles@cpm.org From CCA
Investigating Quadrilaterals Grade Four
Ohio Standards Connection Geometry and Spatial Sense Benchmark A Provide rationale for groupings and comparisons of two-dimensional figures and three-dimensional objects. Indicator 3 Identify similarities
Mathematics for Computer Science/Software Engineering. Notes for the course MSM1F3 Dr. R. A. Wilson
Mathematics for Computer Science/Software Engineering Notes for the course MSM1F3 Dr. R. A. Wilson October 1996 Chapter 1 Logic Lecture no. 1. We introduce the concept of a proposition, which is a statement
Lesson 18: Introduction to Algebra: Expressions and Variables
LESSON 18: Algebra Expressions and Variables Weekly Focus: expressions Weekly Skill: write and evaluate Lesson Summary: For the Warm Up, students will solve a problem about movie tickets sold. In Activity
UNIT 2 Braille Lesson Plan 1 Braille
Codes and Ciphers Activity Mathematics Enhancement Programme Lesson Plan 1 Braille 1 Introduction T: What code, designed more than 150 years ago, is still used extensively today? T: The system of raised
In January 2008 Larry had 90 000 USD to invest for his retirement in January 2011.
1. Give all answers in this question to the nearest whole currency unit. In January 2008 Larry had 90 000 USD to invest for his retirement in January 2011. He invested 40 000 USD in US government bonds
MATH 60 NOTEBOOK CERTIFICATIONS
MATH 60 NOTEBOOK CERTIFICATIONS Chapter #1: Integers and Real Numbers 1.1a 1.1b 1.2 1.3 1.4 1.8 Chapter #2: Algebraic Expressions, Linear Equations, and Applications 2.1a 2.1b 2.1c 2.2 2.3a 2.3b 2.4 2.5
9.2 Summation Notation
9. Summation Notation 66 9. Summation Notation In the previous section, we introduced sequences and now we shall present notation and theorems concerning the sum of terms of a sequence. We begin with a
Chapter 3. Cartesian Products and Relations. 3.1 Cartesian Products
Chapter 3 Cartesian Products and Relations The material in this chapter is the first real encounter with abstraction. Relations are very general thing they are a special type of subset. After introducing
Basic Proof Techniques
Basic Proof Techniques David Ferry dsf43@truman.edu September 13, 010 1 Four Fundamental Proof Techniques When one wishes to prove the statement P Q there are four fundamental approaches. This document
Elementary Number Theory and Methods of Proof. CSE 215, Foundations of Computer Science Stony Brook University http://www.cs.stonybrook.
Elementary Number Theory and Methods of Proof CSE 215, Foundations of Computer Science Stony Brook University http://www.cs.stonybrook.edu/~cse215 1 Number theory Properties: 2 Properties of integers (whole
1. I have 4 sides. My opposite sides are equal. I have 4 right angles. Which shape am I?
Which Shape? This problem gives you the chance to: identify and describe shapes use clues to solve riddles Use shapes A, B, or C to solve the riddles. A B C 1. I have 4 sides. My opposite sides are equal.
SOLVING EQUATIONS WITH RADICALS AND EXPONENTS 9.5. section ( 3 5 3 2 )( 3 25 3 10 3 4 ). The Odd-Root Property
498 (9 3) Chapter 9 Radicals and Rational Exponents Replace the question mark by an expression that makes the equation correct. Equations involving variables are to be identities. 75. 6 76. 3?? 1 77. 1
Performance Assessment Task Which Shape? Grade 3. Common Core State Standards Math - Content Standards
Performance Assessment Task Which Shape? Grade 3 This task challenges a student to use knowledge of geometrical attributes (such as angle size, number of angles, number of sides, and parallel sides) to
Compound Sentences and Coordination
Compound Sentences and Coordination Mary Westervelt Reference: Ann Hogue (2003) The Essentials of English: A Writer s Handbook. New York, Pearson Education, Inc. When two sentences are combined in a way
Multiplication and Division Properties of Radicals. b 1. 2. a Division property of radicals. 1 n ab 1ab2 1 n a 1 n b 1 n 1 n a 1 n b
488 Chapter 7 Radicals and Complex Numbers Objectives 1. Multiplication and Division Properties of Radicals 2. Simplifying Radicals by Using the Multiplication Property of Radicals 3. Simplifying Radicals
Mathematics tests. Mark schemes KEY STAGE 2. Test A, Test B and Mental mathematics LEVELS 3 5. National curriculum assessments
Ma KEY STAGE 2 LEVELS 3 5 Mathematics tests Mark schemes Test A, Test B and Mental mathematics 2009 National curriculum assessments QCA wishes to make its publications widely accessible. Please contact
FIRST GRADE MATH Summer 2011
Standards Summer 2011 1 OA.1 Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in
CHAPTER 7 GENERAL PROOF SYSTEMS
CHAPTER 7 GENERAL PROOF SYSTEMS 1 Introduction Proof systems are built to prove statements. They can be thought as an inference machine with special statements, called provable statements, or sometimes
How Old Are They? This problem gives you the chance to: form expressions form and solve an equation to solve an age problem. Will is w years old.
How Old Are They? This problem gives you the chance to: form expressions form and solve an equation to solve an age problem Will is w years old. Ben is 3 years older. 1. Write an expression, in terms of
The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION MATHEMATICS A. Monday, January 27, 2003 1:15 to 4:15 p.m.
The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION MATHEMATICS A Monday, January 27, 2003 1:15 to 4:15 p.m., only Print Your Name: Print Your School s Name: Print your name and the
Lecture Notes in Discrete Mathematics. Marcel B. Finan Arkansas Tech University c All Rights Reserved
Lecture Notes in Discrete Mathematics Marcel B. Finan Arkansas Tech University c All Rights Reserved 2 Preface This book is designed for a one semester course in discrete mathematics for sophomore or junior
ALGEBRA I (Common Core)
The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION ALGEBRA I (Common Core) Wednesday, June 17, 2015 1:15 to 4:15 p.m. MODEL RESPONSE SET Table of Contents Question 25..................
General Certificate of Secondary Education November 2012. Mathematics (Linear) B 4365 Paper 2 Higher Tier. Final. Mark Scheme
General Certificate of Secondary Education November 2012 Mathematics (Linear) B 4365 Paper 2 Higher Tier Final Mark Scheme Mark schemes are prepared by the Principal Examiner and considered, together with
7.5 Emphatic Verb Tense
Chapter 7 Verb Usage 211 7.5 Emphatic Verb Tense The emphatic tenses of a verb are used to add emphasis. In addition, the emphatic tense can be used with the word not in negative sentences and to form
Introduction to formal semantics -
Introduction to formal semantics - Introduction to formal semantics 1 / 25 structure Motivation - Philosophy paradox antinomy division in object und Meta language Semiotics syntax semantics Pragmatics
INTRODUCTORY SET THEORY
M.Sc. program in mathematics INTRODUCTORY SET THEORY Katalin Károlyi Department of Applied Analysis, Eötvös Loránd University H-1088 Budapest, Múzeum krt. 6-8. CONTENTS 1. SETS Set, equal sets, subset,
CALCULATIONS. Understand the operation of addition and the related vocabulary, and recognise that addition can be done in any order
CALCULATIONS Pupils should be taught to: Understand the operation of addition and the related vocabulary, and recognise that addition can be done in any order As outcomes, Year 1 pupils should, for example:
( ) which must be a vector
MATH 37 Linear Transformations from Rn to Rm Dr. Neal, WKU Let T : R n R m be a function which maps vectors from R n to R m. Then T is called a linear transformation if the following two properties are
Applied Liberal Arts Mathematics MAT-105-TE
Applied Liberal Arts Mathematics MAT-105-TE This TECEP tests a broad-based overview of mathematics intended for non-math majors and emphasizes problem-solving modeled on real-life applications. Topics
VISUAL GUIDE to. RX Scripting. for Roulette Xtreme - System Designer 2.0
VISUAL GUIDE to RX Scripting for Roulette Xtreme - System Designer 2.0 UX Software - 2009 TABLE OF CONTENTS INTRODUCTION... ii What is this book about?... iii How to use this book... iii Time to start...
WRITING PROOFS. Christopher Heil Georgia Institute of Technology
WRITING PROOFS Christopher Heil Georgia Institute of Technology A theorem is just a statement of fact A proof of the theorem is a logical explanation of why the theorem is true Many theorems have this
Predicate Logic. Example: All men are mortal. Socrates is a man. Socrates is mortal.
Predicate Logic Example: All men are mortal. Socrates is a man. Socrates is mortal. Note: We need logic laws that work for statements involving quantities like some and all. In English, the predicate is
Independent samples t-test. Dr. Tom Pierce Radford University
Independent samples t-test Dr. Tom Pierce Radford University The logic behind drawing causal conclusions from experiments The sampling distribution of the difference between means The standard error of
Negative Integral Exponents. If x is nonzero, the reciprocal of x is written as 1 x. For example, the reciprocal of 23 is written as 2
4 (4-) Chapter 4 Polynomials and Eponents P( r) 0 ( r) dollars. Which law of eponents can be used to simplify the last epression? Simplify it. P( r) 7. CD rollover. Ronnie invested P dollars in a -year
2015 School Competition Target Round Problems 1 & 2
2015 School Competition Target Round Problems 1 & 2 Name DO NOT BEGIN UNTIL YOU ARE INSTRUCTED TO DO SO. This section of the competition consists of eight problems, which will be presented in pairs. Work
Solutions to Homework 6 Mathematics 503 Foundations of Mathematics Spring 2014
Solutions to Homework 6 Mathematics 503 Foundations of Mathematics Spring 2014 3.4: 1. If m is any integer, then m(m + 1) = m 2 + m is the product of m and its successor. That it to say, m 2 + m is the
Toothpick Squares: An Introduction to Formulas
Unit IX Activity 1 Toothpick Squares: An Introduction to Formulas O V E R V I E W Rows of squares are formed with toothpicks. The relationship between the number of squares in a row and the number of toothpicks
1. True or False? A voltage level in the range 0 to 2 volts is interpreted as a binary 1.
File: chap04, Chapter 04 1. True or False? A voltage level in the range 0 to 2 volts is interpreted as a binary 1. 2. True or False? A gate is a device that accepts a single input signal and produces one
MAT-71506 Program Verication: Exercises
MAT-71506 Program Verication: Exercises Antero Kangas Tampere University of Technology Department of Mathematics September 11, 2014 Accomplishment Exercises are obligatory and probably the grades will
Order of Operations More Essential Practice
Order of Operations More Essential Practice We will be simplifying expressions using the order of operations in this section. Automatic Skill: Order of operations needs to become an automatic skill. Failure
SAMPLE BOOKLET Published July 2015
National curriculum tests Key stage 2 Mathematics Mark schemes SAMPLE BOOKLET Published July 2015 This sample test indicates how the national curriculum will be assessed from 2016. Further information
Mathematics Practice for Nursing and Midwifery Ratio Percentage. 3:2 means that for every 3 items of the first type we have 2 items of the second.
Study Advice Service Student Support Services Author: Lynn Ireland, revised by Dave Longstaff Mathematics Practice for Nursing and Midwifery Ratio Percentage Ratio Ratio describes the relationship between
WOLLONGONG COLLEGE AUSTRALIA. Diploma in Information Technology
First Name: Family Name: Student Number: Class/Tutorial: WOLLONGONG COLLEGE AUSTRALIA A College of the University of Wollongong Diploma in Information Technology Mid-Session Test Summer Session 008-00
Data Analysis, Statistics, and Probability
Chapter 6 Data Analysis, Statistics, and Probability Content Strand Description Questions in this content strand assessed students skills in collecting, organizing, reading, representing, and interpreting
Practice Book. Practice. Practice Book
Grade 10 Grade 10 Grade 10 Grade 10 Grade 10 Grade 10 Grade 10 Exam CAPS Grade 10 MATHEMATICS PRACTICE TEST ONE Marks: 50 1. Fred reads at 300 words per minute. The book he is reading has an average of
Writing Interesting, Grammatically Correct Sentences This Workshop is Brought to You by the NVCC-Annandale RWC
Writing Interesting, Grammatically Correct Sentences This Workshop is Brought to You by the NVCC-Annandale RWC OBJECTIVES o o o In this workshop we will talk about the four kinds of sentences. We will
Mathematics Georgia Performance Standards
Mathematics Georgia Performance Standards K-12 Mathematics Introduction The Georgia Mathematics Curriculum focuses on actively engaging the students in the development of mathematical understanding by
The theory of the six stages of learning with integers (Published in Mathematics in Schools, Volume 29, Number 2, March 2000) Stage 1
The theory of the six stages of learning with integers (Published in Mathematics in Schools, Volume 29, Number 2, March 2000) Stage 1 Free interaction In the case of the study of integers, this first stage
Learning Objectives 9.2. Media Run Times 9.3
Unit 9 Table of Contents Unit 9: Factoring Video Overview Learning Objectives 9.2 Media Run Times 9.3 Instructor Notes 9.4 The Mathematics of Factoring Polynomials Teaching Tips: Conceptual Challenges
Conjunction is true when both parts of the statement are true. (p is true, q is true. p^q is true)
Mathematical Sentence - a sentence that states a fact or complete idea Open sentence contains a variable Closed sentence can be judged either true or false Truth value true/false Negation not (~) * Statement
Mathematics mark schemes
Ma KEY STAGE 2 Mathematics tests LEVEL 6 Mathematics mark schemes Paper 1 and Paper 2 2015 National curriculum tests 2 2015 key stage 2 level 6 mathematics tests mark schemes [BLANK PAGE] This page is
GEOMETRIC SEQUENCES AND SERIES
4.4 Geometric Sequences and Series (4 7) 757 of a novel and every day thereafter increase their daily reading by two pages. If his students follow this suggestion, then how many pages will they read during
Algebra 1. Practice Workbook with Examples. McDougal Littell. Concepts and Skills
McDougal Littell Algebra 1 Concepts and Skills Larson Boswell Kanold Stiff Practice Workbook with Examples The Practice Workbook provides additional practice with worked-out examples for every lesson.
WSMC High School Competition The Pros and Cons Credit Cards Project Problem 2007
WSMC High School Competition The Pros and Cons Credit Cards Project Problem 2007 Soon, all of you will be able to have credit cards and accounts. They are an important element in the fabric of the United
Using row reduction to calculate the inverse and the determinant of a square matrix
Using row reduction to calculate the inverse and the determinant of a square matrix Notes for MATH 0290 Honors by Prof. Anna Vainchtein 1 Inverse of a square matrix An n n square matrix A is called invertible
GRAVITATIONAL FIELDS PHYSICS 20 GRAVITATIONAL FORCES. Gravitational Fields (or Acceleration Due to Gravity) Symbol: Definition: Units:
GRAVITATIONAL FIELDS Gravitational Fields (or Acceleration Due to Gravity) Symbol: Definition: Units: Formula Description This is the formula for force due to gravity or as we call it, weight. Relevant
25 Integers: Addition and Subtraction
25 Integers: Addition and Subtraction Whole numbers and their operations were developed as a direct result of people s need to count. But nowadays many quantitative needs aside from counting require numbers
Lesson 4: Convert Fractions, Review Order of Operations
Lesson 4: Convert Fractions, Review Order of Operations LESSON 4: Convert Fractions, Do Order of Operations Weekly Focus: fractions, decimals, percent, order of operations Weekly Skill: convert, compute
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
ALGEBRA. sequence, term, nth term, consecutive, rule, relationship, generate, predict, continue increase, decrease finite, infinite
ALGEBRA Pupils should be taught to: Generate and describe sequences As outcomes, Year 7 pupils should, for example: Use, read and write, spelling correctly: sequence, term, nth term, consecutive, rule,
Calculating Perimeter
Calculating Perimeter and Area Formulas are equations used to make specific calculations. Common formulas (equations) include: P = 2l + 2w perimeter of a rectangle A = l + w area of a square or rectangle
3.1. RATIONAL EXPRESSIONS
3.1. RATIONAL EXPRESSIONS RATIONAL NUMBERS In previous courses you have learned how to operate (do addition, subtraction, multiplication, and division) on rational numbers (fractions). Rational numbers
/27 Intro to Geometry Review
/27 Intro to Geometry Review 1. An acute has a measure of. 2. A right has a measure of. 3. An obtuse has a measure of. 13. Two supplementary angles are in ratio 11:7. Find the measure of each. 14. In the
Learn How to Use The Roulette Layout To Calculate Winning Payoffs For All Straight-up Winning Bets
Learn How to Use The Roulette Layout To Calculate Winning Payoffs For All Straight-up Winning Bets Understand that every square on every street on every roulette layout has a value depending on the bet
Keywords: Forecasting, S&P CNX NIFTY 50, Fuzzy-logic, Fuzzy rule-base, Candlesticks, Fuzzycandlesticks, Figure 1.2: White Candle
American International Journal of Research in Science, Technology, Engineering & Mathematics Available online at http://www.iasir.net ISSN (Print): 2328-3491, ISSN (Online): 2328-3580, ISSN (CD-ROM): 2328-3629
MATH 10034 Fundamental Mathematics IV
MATH 0034 Fundamental Mathematics IV http://www.math.kent.edu/ebooks/0034/funmath4.pdf Department of Mathematical Sciences Kent State University January 2, 2009 ii Contents To the Instructor v Polynomials.
You know from calculus that functions play a fundamental role in mathematics.
CHPTER 12 Functions You know from calculus that functions play a fundamental role in mathematics. You likely view a function as a kind of formula that describes a relationship between two (or more) quantities.
Turing Machines, Part I
Turing Machines, Part I Languages The $64,000 Question What is a language? What is a class of languages? Computer Science Theory 2 1 Now our picture looks like Context Free Languages Deterministic Context