№ lp_2_3_00998
File format: docx Character count: 2356 File size: 66 KB
Note: Year
Subject: Mathematics
Document Type: Educational material
Target Audience: Students
Contextual description: This educational document provides various problems and examples related to proportional relationships, requiring students to analyze tables and graphs to identify such relationships and solve related questions.
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Why did Western Europe Adopt Proportional Representation? A Political Geography Explanation
Year: 2009
Region / city: Western Europe
Topic: Electoral Systems, Proportional Representation, Political Parties
Document Type: Academic Paper
Institution: Stanford University
Author: Jonathan Rodden
Target Audience: Political Scientists, Academics
Period of Effect: Late 19th to Early 20th Century
Approval Date: 2009
Date of Revisions: December 30, 2009
Annual Giving | Proportional Giving Charts
Year: 2023
Region / City: Diocese of Virginia
Topic: Stewardship, Church Giving
Document Type: Chart, Guide
Organization / Institution: Diocese of Virginia
Author: Not specified
Target Audience: Church members, Congregational leaders
Period of Validity: Not specified
Approval Date: Not specified
Date of Changes: Not specified
Multiple-Choice Questions on Ratios, Unit Rates, and Proportional Reasoning
Subject: Mathematics
Topic: Ratios, Unit Rates, Proportions
Type of document: Multiple-choice question set
Educational level: Middle school (Grade 6)
Question format: Four-option multiple choice
Number of questions: 8
Skills assessed: Ratio interpretation, unit rate calculation, proportional reasoning, basic division
Political Studies: First Past the Post vs Proportional Representation
Note: Year
Theme: Electoral Systems
Document Type: Article
Author: Voting Counts, The Week
Target Audience: General Public
Proportional Relationships in Tables and Unit Rate Exercises
Grade Level: Middle School
Subject: Mathematics
Topic: Proportional Relationships, Unit Rates, Tables
Document Type: Educational Worksheet
Author: Unknown
Intended Audience: Students
Skills Practiced: Calculating unit rates, identifying proportional relationships, writing equations from tables
Number of Exercises: 7
Content Includes: Tables of costs, time, calories, ingredients, book prices, coffee prices, polygon perimeters
The Architecture of Ratio: Evolution of Proportional Law and Applications in Hydraulic Control Systems
Year: Not specified
Region / City: Not specified
Subject: History of mathematics and engineering; proportional law; control systems
Document Type: Treatise / Technical report
Institution: Not specified
Author: Not specified
Target Audience: Engineers, mathematicians, historians of science
Period Covered: From ancient Greece to modern industrial control
Date of Publication: Not specified
Technical Focus: Proportional law in PID controllers, high-pressure hydraulic systems
Ratios and Proportional Relationships Exercises
Year: 2026
Region / City: Not specified
Subject: Mathematics
Document Type: Educational Worksheet
Author: Not specified
Target Audience: Students
Skills: Ratio calculation, proportional reasoning, rate conversion
Number of Problems: 15 plus bonus
Required Materials: Calculator
Electoral Systems: Majoritarian, Proportional Representation, and Mixed Models
Document type: Educational worksheet
Subject: Electoral systems and democratic representation
Topic: Political science and democratic institutions
Educational level: Secondary education / civic education
Country reference: Germany (example of personalized proportional representation system)
Key concepts: Majoritarian electoral system, first-past-the-post system, absolute majority system, proportional representation system, mixed electoral systems
Structure: Explanatory text, multiple-choice questions, short-answer tasks, space for student questions
Purpose: Learning and assessment material on how votes are converted into political representation
Audience: Students studying civics or political science
Write your solutions in this sheet below the problem statement. Mark clearly your solutions by corresponding letters A, B, C, D and separate visually each solution from the other ones by empty space or by a line. Use the other side of the sheet or ask for an additional blank sheeet if necessary. Each problem 1. – 4. is worth 0 – 4 points, each answer to a particular question A, B, C, D contributes at most 1 point to the total. 1. Four algorithms process a square matrix M of size nn. The indices of rows and columns of M start with 1. Each of the algorithms processes all matrix elements. Determine the asymptotic complexity of each algorithm.A. Algorithm A processes each element of M in time proportional to log(nn).B. Algorithm B processes each element in the row r in time k∙r, where k is a positive constant.C. Algorithm C processes each element at position [r][c] (r and c are row and column indices, respectively) in time k∙r∙c, where k is a positive constant.D. Algorithm D processes each element in constant time. However, before processing the element, the algorithm checks the value of each element in the row in which the processed element is located. Each check takes constant time to complete. 2. Insert sort processes an array A with an even number of values, array length is N. The array contains elements of only two values, 10 and 20. The first value in the array is 10 and the values in the array strictly alternate: 10, 20, 10, 20, 10, etc.A. Determine how many comparisons between two element values are performed when the length of the array is 8: 10 20 10 20 10 20 10 20 B. Determine how many comparisons between two element values are performed when the last element with value 10 is being inserted to its final position in array A. Solve the problem for the general value of N ≥ 4. C. Write a function f(N) which returns the total number of comparisons made during the sort of array A. Suppose N  ≥  4. Explain how did you derive f(N). D. Decide to which complexity class belongs f(N). The available classes are (1), (log N), (N), (N ∙ log N), (N2). 3. AVL tree T is in the picture. The four particular subtrees with roots in D, E, F, G are shown schematically and the value given in the subtrees represents the depth of the subtree. The depth is the number of edges on the path from the subtree root to the deepest node in the subtree.A. T is depicted immediately after a new key (not depicted) was inserted into the tree. To complete correctly the insert operation, a rotation hast to be applied in T. Draw the shape of T after this rotation and determine the type of the rotation (L, R, LR or RL). B. Insert keys 10, 30, 20, 50, 40, in this order, into an originally empty AVL tree, using Insert operation. Draw the resulting AVL tree and determine the number and the type (L, R, LR, RL) of each rotation used in the process.C. Delete the key 10 from the AVL tree built in C. Which rotation, if any, was applied in the deletion process?D. Suppose that an AVL tree contains n2 keys and that another n keys are inserted, one by one, into the tree using the Insert operation. Use the asymptotic notation (O//) to specify the maximum number of simple (L or R) rotations which are performed during the whole process. Explain your reasoning. 4. A binary heap is given in the picture.A. Determine all possible integer values of element Z in the heap.B. Substitute Z by its smallest possible value (calculated in the answer to question A) .Next, use the Insert operation to insert values 55, 45, 35 into the heap, in the given order. Draw the resulting heap.C. Apply twice operation ExtractMin to the heap obtained in B. Draw the resulting heap.D. Suppose that a binary heap H contains exactly 2n leaves. Operation ExtractMin is applied n times on H. What is the asymptotic complexity of the whole process? Explain your reasoning.
Year: Not provided
Region / city: Not provided
Subject: Computer science
Document type: Problem set
Organization / institution: Not provided
Author: Not provided
Target audience: Students of computer science
Period of validity: Not provided
Approval date: Not provided
Date of changes: Not provided
Comparing straight-line graphs
Year: 2022
Region / City: New South Wales
Topic: Mathematics / Linear Graphs
Document Type: Lesson Plan
Institution: NSW Education Standards Authority
Author: Not specified
Target Audience: Students (grades K-10)
Period of validity: Not specified
Approval Date: Not specified
Date of Changes: Not specified
Distance–time graphs
Year: 2022
Region / city: New South Wales
Topic: Mathematics, Distance–time Graphs
Document type: Educational resource
Institution: NSW Education Standards Authority (NESA)
Target audience: Students, Educators
Period of validity: 2022
Approval date: 2022
Modification date: N/A
Tobin’s Spirit Guide to Graphs of Motion
Year: Not specified
Region / city: Not specified
Topic: Motion graphs, velocity, acceleration
Document type: Educational text
Organization / institution: Not specified
Author: Not specified
Target audience: Students, educators in physics
Period of validity: Not specified
Approval date: Not specified
Date of amendments: Not specified
Flaws and fakes in data collection: Understanding misleading statistics and graphs in educational contexts
Year: 2024
Region / city: New South Wales
Topic: Education, Data Literacy, Statistics
Document Type: Educational Curriculum
Author: NSW Education Standards Authority (NESA)
Target Audience: Educators, Secondary School Students
Period of Application: 2024 and beyond
Approval Date: Not specified
Date of Amendments: Not specified
Algebra 1 Unit 5 Lesson 6: Features of Graphs
Year: 2024
Region / City: N/A
Subject: Algebra
Document Type: Educational Material
Organization / Institution: Illustrative Mathematics
Author: N/A
Target Audience: Students, Educators
Period of Validity: N/A
Approval Date: N/A
Modification Date: N/A
Quadratic Relations and Properties of Graphs
Year: 2026
Region / City: Southern Alberta, Vancouver
Theme: Quadratic Functions, Algebra
Document Type: Educational Material
Institution: Math 20-2
Author: Not specified
Target Audience: Students of Algebra
Period of Action: Ongoing
Approval Date: Not specified
Date of Changes: Not specified
Note: Contextual description
Paraconsistent Existential Graphs Gamma Peirce System
Year: 2021
Region / City: Colombia
Subject: Logic, Paraconsistent Systems
Document Type: Academic Paper
Author: Manuel Sierra-Aristizabal
Target Audience: Scholars, Researchers in Logic and Philosophy
Period of Validity: Not Applicable
Approval Date: Not Applicable
Date of Changes: Not Applicable
Grade 12 Mathematics Common Test: Probability, Counting Principles, Graphs and Geometry – 13 August 2019
Grade: 12
Subject: Mathematics
Examination type: Common Test
Assessment title: Probability, Counting Principles, Graphs & Geometry Bookwork
Date: 13 August 2019
Validation status: Validation Test
Total marks: 70 Marks
Question 1 marks: 15 Marks
Question 2 marks: 5 Marks
Question 3 marks: 13 Marks
Question 4 marks: 8 Marks
Question 5 marks: 6 Marks
Question 6 marks: 7 Marks
Question 7 marks: 10 Marks
Question 8 marks: 6 Marks
Topics covered: Probability, Counting Principles, Permutations, Independent and Mutually Exclusive Events, Venn Diagrams, Logarithmic Functions, Graph Transformations, Calculus, Optimisation, Euclidean Geometry
Answer format: Answer sheet provided for Question 8; all other questions to be answered on lined paper
Topic 21 – Graphs and equations of motion – Questions
Year: 2023
Region / City: Not specified
Subject: Physics
Document Type: Educational material
Institution: Not specified
Author: Not specified
Target audience: Students studying motion and physics
Period of validity: Not specified
Approval date: Not specified
Modification date: Not specified
Understanding Graphs of Motion
Note: Year
Mathematics Form 4 Lesson Plan: Chapter 3 Quadratic Functions and Their Graphs, 23rd Mei 2014
Subject: Mathematics
Form: 4 Al-Farabi
Date: 23rd Mei 2014 (Tuesday)
Time: 10 minutes
Topic: Chapter 3 : Quadratic Functions
Sub-Topic: 3.1 : Quadratic Functions and Their Graphs
General Objective: Understand the concept of quadratic functions and their graphs
Specific Objectives: At the end of this lesson, students should be able to recognize quadratic functions, recognize shapes of graphs of quadratic functions, and find the value at parabola’s vertex
Lesson Content: General form of quadratic functions; shape of quadratic functions as parabola; condition of a > 0 and a < 0; completing the square method to determine vertex
Reference: Textbook: Additional Mathematics Form 4; Additional Mathematics SPM (Fajar Bakti)
Inculcation of Values: Self interest, Courage, Proactive, Motivated
Teaching Materials: Whiteboard, Marker, Textbook, Worksheets
Activities: Set Induction, Lesson Development, Conclusion, Evaluation, Follow up Activities
Homework: Exercises from textbook and workbook
Topics: Proportional graphs Relationships