GAUTENG DEPARTMENT OF EDUCATION SENIOR SECONDARY INTERVENTION PROGRAMME. MATHEMATICS Grade 11 SESSION 17 LEARNER NOTES
|
|
- Matthew Booth
- 5 years ago
- Views:
Transcription
1 TRANSFORMATIONS Learner note: Transformations are easy to master and you can score well in questions involving this topic. Ensure that you know the different algebraic transformation rules. LESSON OVERVIEW 1. Introduction session 5 minutes. Typical exam questions: Question 1: 0 minutes 3. Discussion of solutions 35 minutes SECTION A: TYPICAL EXAM QUESTIONS Question 1 (0 minutes) (a) On the diagram below, represent the point A( 3; ). () Page 1 of 8
2 (b) Now represent the following points on the diagram provided on the previous page: Point B, the rotation of point A, 90 anticlockwise about the origin. Point C, the rotation of point A, 180 about the origin. Point D, the rotation of point A, 90 clockwise about the origin. (3) (c) Write down algebraic rules to describe the above transformations. (3) (d) (e) What type of quadrilateral is figure ABCD? Explain by referring to the properties of quadrilaterals. () Figure ABCD is enlarged by a scale factor of units through the origin to form its image A B C D. On the diagram provided on the previous page, sketch the image A B C D and indicate the coordinates of the vertices. () (f) (g) Determine the ratio: Area ABCD Area A B C D ABCD is reflected about the y-axis to form its image EFGH. Write down the coordinates of E. () Determine the ratio: Perimeter ABCD Perimeter EFGH (h) Describe, using words and algebraic notation, the single transformations involved if figure ABCD is transformed by the rule: 1 1 ( x; y) x ; y 1 (3) Page of 8
3 SECTION B: SOLUTIONS AND HINTS Question 1 (a), (b) D (4;6) A ( 6;4) A( 3;) D(;3) B( ; 3) C(3; ) C (6; 4) B ( 4; 6) (b) B( ; 3) C(3; ) D(;3) (c) 90 anticlockwise: ( x ; y) ( y ; x) 180 anti-clockwise or clockwise: ( x ; y) ( x ; y) 90 clockwise: ( x ; y) ( y ; x) (d) ABCD is a square since: Diagonals are equal in length Diagonals bisect each other at right angles B( ; 3) C(3; ) D(;3) (3) ( x ; y) ( y ; x) ( x ; y) ( x ; y) ( x ; y) ( y ; x) (3) square properties () Page 3 of 8
4 (e) A ( 6;4) (f) (g) (g)() B ( 4; 6) C (6; 4) D (4;6) See diagram Area ABCD 1 1 Area A B C D 4 E(3;) Perimeter ABCD 4side AB 1 Perimeter EFGH 4side EF (since AB EF) See Section C (Enlargement and reduction rules) (h) ( x; y) x; y reduction by a factor of x; y x; y reflection about x axis x; y x; y 1 translation of 1 unit downwards 1 1 ( x; y) x; y 1 correct coordinates indicated joining points to form enlarged square () 1 4 answer answer reduction reflection translation (3) Page 4 of 8
5 SECTION C: ADDITIONAL CONTENT NOTES The following is a summary of the algebraic transformation rules TRANSLATION RULES If the point ( x; y ) is translated to form the point ( x a ; y b) where a is a horizontal move and b is a vertical move, then the following rules apply: If a 0, the horizontal translation is to the right. If a 0, the horizontal translation is to the left. If b 0, the vertical translation is upward. If b 0, the vertical translation is downward REFLECTION RULES Reflection about the y-axis: ( x ; y) ( x ; y) Reflection about the x-axis: ( x ; y) ( x ; y) Reflection about the line y x: ( x ; y) ( y ; x) RULES OF ROTATION ABOUT THE ORIGIN Rotation of 90 anti-clockwise: ( x ; y) ( y ; x) Rotation of 90 clockwise: ( x ; y) ( y ; x) Rotation of 180 clockwise or anti-clockwise: ( x ; y) ( x ; y) ENLARGEMENT AND REDUCTION RULES ( x ; y) ( kx ; ky) If k 1, the image is an enlargement of the original figure. Multiply the original first and second coordinates by k units to get the coordinates of the image. The image will be k times larger than the original figure. If 0k 1, the image is a reduction of the original figure. Multiply the original first and second coordinates by k units to get the coordinates of the image. Page 5 of 8
6 If k 0, the image is a rotation of 180of the original figure followed by an enlargement of the original figure. Multiply the original first and second coordinates by k units to get the coordinates of the image. Area of image k Area of original or Area of image k Area of original or Area of original 1 Area of image k SECTION D: HOMEWORK Question 1 (a) On the diagram below, draw figure ABCD with the coordinates of the vertices as follows: A( 6 ; 6); B( 4 ; ); C( ; 6) and D( 4 ; 8) Page 6 of 8
7 (b) On the diagram, draw the image A B C D if ABCD is rotated 90 anti-clockwise. Indicate the coordinates of B and C. () (c) State the general coordinates in terms of x and y of this rotation of 90 anti-clockwise using the notation ( x; y) (d) Now draw the image A B C D if ABCD is transformed under the rule: 1 1 ( x ; y) x ; y. () (e) Write down the value of the following ratio: Area ABCD Area A B C D () (f) Draw image A B C D if A B C D is rotated 180 clockwise. Indicate the coordinates of A () (g) Draw the image EFGH if A B C D is transformed under the rule ( x ; y) ( x ; y). Indicate the coordinates of E. () (h) Write down the single algebraic rule if ABCD is reflected about the x-axis, followed by a translation of 7 units right, followed by an enlargement by a scale factor of units. (4) SECTION E: SOLUTIONS TO SESSION 16 HOMEWORK 1 3xy 6.A 5x3y 11 B 9x6y A 3 10x 6y B x 4 x 4 3(4) y 6 y 6 y 3 Other methods are acceptable Multiplication of A by 3 Multiply B by - Adding to get x 4 x 4 3(4) y 6 y 3 (6) Page 7 of 8
8 (a) y 3 x x (3 x) x (3 x) x 3 x x 9 1x 4x 3x 11x 6 0 3x 11x 6 0 (3x )( x 3) 0 x 3 or x 3 5 y 3 or y 3 You may use the quadratic formula to solve this equation y3 x substitution multiplication standard form factors x-values y-values (8) (b) x 1 3 (1 3y) 1y 3y y 1 6y 9y (1 3y) y 9y 4y 16 0 y 4 0 y 6y (3y 4)( y 1) 0 4 y or y 1 3 x 3 or x 4 9y x1 3y substitution multiplication standard form factors x-values y-values (8) The SSIP is supported by Page 8 of 8
Chapters 7 & 8. Parallel and Perpendicular Lines/Triangles and Transformations
Chapters 7 & 8 Parallel and Perpendicular Lines/Triangles and Transformations 7-2B Lines I can identify relationships of angles formed by two parallel lines cut by a transversal. 8.G.5 Symbolic Representations
More informationUnit 5 Answers. Exercise 5.1. KS3 Maths Progress Delta 2. 2 a 1 left, 2 down b 6 right, 1 up c 7 right, 7 down d 6 left e 9 left, 3 up 3
Unit 5 Answers Exercise 5.1 1 2 a 1 left, 2 down b 6 right, 1 up c 7 right, 7 down d 6 left e 9 left, 3 up 3 4 5 a x = 0 b B is a reflection of T in the line x = 2 C is a reflection of T in the line y
More informationChapter 12 Transformations: Shapes in Motion
Name Geometry Honors Date Per. Teacher Chapter 12 Transformations: Shapes in Motion 1 Table of Contents Reflections Day 1.... Page 3 Translations Day 2....... Page 10 Rotations/Dilations Day 3.... Page
More informationUnit 3 Higher topic list
This is a comprehensive list of the topics to be studied for the Edexcel unit 3 modular exam. Beside the topics listed are the relevant tasks on www.mymaths.co.uk that students can use to practice. Logon
More informationLearning Log Title: CHAPTER 6: TRANSFORMATIONS AND SIMILARITY. Date: Lesson: Chapter 6: Transformations and Similarity
Chapter 6: Transformations and Similarity CHAPTER 6: TRANSFORMATIONS AND SIMILARITY Date: Lesson: Learning Log Title: Date: Lesson: Learning Log Title: Chapter 6: Transformations and Similarity Date: Lesson:
More informationStudent Name: Teacher: Date: Miami-Dade County Public Schools. Test: 9_12 Mathematics Geometry Exam 2
Student Name: Teacher: Date: District: Miami-Dade County Public Schools Test: 9_12 Mathematics Geometry Exam 2 Description: GEO Topic 5: Quadrilaterals and Coordinate Geometry Form: 201 1. If the quadrilateral
More information3.1 INTRODUCTION TO THE FAMILY OF QUADRATIC FUNCTIONS
3.1 INTRODUCTION TO THE FAMILY OF QUADRATIC FUNCTIONS Finding the Zeros of a Quadratic Function Examples 1 and and more Find the zeros of f(x) = x x 6. Solution by Factoring f(x) = x x 6 = (x 3)(x + )
More informationYear 7 Set 1 : Unit 1 : Number 1. Learning Objectives: Level 5
Year 7 Set 1 : Unit 1 : Number 1 I can place decimals in order of size I can place negative numbers in order of size I can add and subtract negative numbers I can set out and do addition, subtraction,
More informationDilations. Dilations. Enlarges or Reduces a figure using a scale factor. Name: Period: Date: Dilations. Scale Factor =
Name: Period: Date: Dilations Dilations Enlarges or Reduces a figure using a scale factor. Dilations B B B 6 2 2 C 6 C Scale Factor = B C BC has been enlarged by a scale factor of 3. What are the coordinates
More informationChapter 2: Transformations. Chapter 2 Transformations Page 1
Chapter 2: Transformations Chapter 2 Transformations Page 1 Unit 2: Vocabulary 1) transformation 2) pre-image 3) image 4) map(ping) 5) rigid motion (isometry) 6) orientation 7) line reflection 8) line
More informationBy: Caroline, Jenny, Jennifer, Jared, Kaleigh
By: Caroline, Jenny, Jennifer, Jared, Kaleigh 1) What are the coordinates of the image of (2, 5) after a counterclockwise rotation of 90º about the origin? 1) ( 2, 5) 2) (2, 5) 3) ( 5, 2) 4) (5, 2) A dilation
More informationName: Period: Unit 1. Modeling with Geometry: Transformations
Name: Period: Unit 1 Modeling with Geometry: Transformations 1 2017/2018 2 2017/2018 Unit Skills I know that... Transformations in general: A transformation is a change in the position, size, or shape
More informationGeometry Unit 5 Geometric and Algebraic Connections. Table of Contents
Geometry Unit 5 Geometric and Algebraic Connections Table of Contents Lesson 5 1 Lesson 5 2 Distance.p. 2-3 Midpoint p. 3-4 Partitioning a Directed Line. p. 5-6 Slope. p.7-8 Lesson 5 3 Revisit: Graphing
More informationGeometry R. Unit 12 Coordinate Geometry. Day Classwork Day Homework Wednesday 3/7 Thursday 3/8 Friday 3/9
Geometry R Unit 12 Coordinate Geometry Day Classwork Day Homework Wednesday 3/7 Thursday 3/8 Friday 3/9 Unit 11 Test Review Equations of Lines 1 HW 12.1 Perimeter and Area of Triangles in the Coordinate
More informationLesson 9: Coordinate Proof - Quadrilaterals Learning Targets
Lesson 9: Coordinate Proof - Quadrilaterals Learning Targets Using coordinates, I can find the intersection of the medians of a triangle that meet at a point that is two-thirds of the way along each median
More informationUnit 7. Transformations
Unit 7 Transformations 1 A transformation moves or changes a figure in some way to produce a new figure called an. Another name for the original figure is the. Recall that a translation moves every point
More information0,0 is referred to as the end point.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 Chapter 2: Radical Functions 2.1 Radical Functions and Transformations (Day 1) For the function y x, the radicand, x, must
More informationThis is called the vertex form of the quadratic equation. To graph the equation
Name Period Date: Topic: 7-5 Graphing ( ) Essential Question: What is the vertex of a parabola, and what is its axis of symmetry? Standard: F-IF.7a Objective: Graph linear and quadratic functions and show
More informationTransformations Geometry
Transformations Geometry Preimage the original figure in the transformation of a figure in a plane. Image the new figure that results from the transformation of a figure in a plane. Example: If function
More informationTransformations with Quadratic Functions KEY
Algebra Unit: 05 Lesson: 0 TRY THIS! Use a calculator to generate a table of values for the function y = ( x 3) + 4 y = ( x 3) x + y 4 Next, simplify the function by squaring, distributing, and collecting
More informationUnit 6: Connecting Algebra and Geometry Through Coordinates
Unit 6: Connecting Algebra and Geometry Through Coordinates The focus of this unit is to have students analyze and prove geometric properties by applying algebraic concepts and skills on a coordinate plane.
More informationWarm-up. Translations Using arrow notation to write a rule. Example: 1) Write a rule that would move a point 3 units to the right and 5 units down.
Translations Using arrow notation to write a rule. Example: 1) Write a rule that would move a point 3 units to the right and 5 units down. (x, y) 2) Write a rule that would move a point 6 units down. (x,
More informationGRADE 12 MATHEMATICS LEARNER NOTES
SENIOR SECONDARY,059(0(7 PROGRAMME 0 GRADE LEARNER NOTES The SSIP is supported by c) Gauteng Department of Education, 0 TABLE OF CONTENTS LEARNER NOTES SESSION TOPIC Revision of Analytical Geometry (Grade
More informationLesson 9 Reflections Learning Targets :
Reflections Learning Targets : I can construct the line of reflection using the compass and a straightedge I can draw the reflected figure using a compass and a straightedge and on coordinate grid Opening
More informationAQA GCSE Further Maths Topic Areas
AQA GCSE Further Maths Topic Areas This document covers all the specific areas of the AQA GCSE Further Maths course, your job is to review all the topic areas, answering the questions if you feel you need
More information9.1: GRAPHING QUADRATICS ALGEBRA 1
9.1: GRAPHING QUADRATICS ALGEBRA 1 OBJECTIVES I will be able to graph quadratics: Given in Standard Form Given in Vertex Form Given in Intercept Form What does the graph of a quadratic look like? https://www.desmos.com/calculator
More informationMATHEMATICS DEPARTMENT COURSE OUTLINE TERM 1/2/3 YEAR 7
MATHEMATICS DEPARTMENT COURSE OUTLINE 2016-17 TERM 1/2/3 YEAR 7 Week Topic YEAR 7- Mathematics Term 1 plan 2016-2017 Learning outcomes 1/2 Numbers and the number system Recall prime numbers up to 50 Know
More informationUNIT 1 SIMILARITY, CONGRUENCE, AND PROOFS Lesson 1: Investigating Properties of Dilations Instruction
Prerequisite Skills This lesson requires the use of the following skills: operating with fractions, decimals, and percents converting among fractions, decimals, and percents Introduction A figure is dilated
More informationSYMMETRY, REFLECTION AND ROTATION EDULABZ. (i) (ii) (iii) (iv) INTERNATIONAL. (i) (one) (ii) (none) (iii) (one) (iv) (one)
6 SMMETR, REFLECTION AND ROTATION. Draw the line or lines of symmetry. (i) (ii) (iii) (iv) (v) (vi) (vii) (viii) (ix) (i) (one) (ii) (none) (iii) (one) (iv) (one) (v) (one) (vi) (none) (vii) (four) (viii)
More information4-1 Congruence and Transformations
4-1 Congruence and Transformations Warm Up Lesson Presentation Lesson Quiz Holt Geometry McDougal Geometry Objectives Draw, identify, and describe transformations in the coordinate plane. Use properties
More informationDISTANCE FORMULA: to find length or distance =( ) +( )
MATHEMATICS ANALYTICAL GEOMETRY DISTANCE FORMULA: to find length or distance =( ) +( ) A. TRIANGLES: Distance formula is used to show PERIMETER: sum of all the sides Scalene triangle: 3 unequal sides Isosceles
More informationModule Four: Connecting Algebra and Geometry Through Coordinates
NAME: Period: Module Four: Connecting Algebra and Geometry Through Coordinates Topic A: Rectangular and Triangular Regions Defined by Inequalities Lesson 1: Searching a Region in the Plane Lesson 2: Finding
More informationLesson 20: Four Interesting Transformations of Functions
Student Outcomes Students apply their understanding of transformations of functions and their graphs to piecewise functions. Lesson Notes In Lessons 17 19 students study translations and scalings of functions
More informationUnit #3: Quadratic Functions Lesson #13: The Almighty Parabola. Day #1
Algebra I Unit #3: Quadratic Functions Lesson #13: The Almighty Parabola Name Period Date Day #1 There are some important features about the graphs of quadratic functions we are going to explore over the
More information8 Quadrilaterals. Before
8 Quadrilaterals 8. Find Angle Measures in Polygons 8. Use Properties of Parallelograms 8.3 Show that a Quadrilateral is a Parallelogram 8.4 Properties of Rhombuses, Rectangles, and Squares 8.5 Use Properties
More informationChapter 5. Transforming Shapes
Chapter 5 Transforming Shapes It is difficult to walk through daily life without being able to see geometric transformations in your surroundings. Notice how the leaves of plants, for example, are almost
More informationStage 7 Checklists Have you reached this Standard?
Stage 7 Checklists Have you reached this Standard? Main Criteria for the whole year. J K L Use positive integer powers and associated real roots Apply the four operations with decimal numbers Write a quantity
More informationMATHEMATICS PAPER 2 QUESTIONS. QUESTION 1 In the diagram alongside, quadrilateral EFGH has vertices E( 1; 3), F(4; 4), G(3; 1) and H( 2; 2).
MATHEMATICS PAPER 2 QUESTIONS MARKS: 150 TIME: 3 hours QUESTION 1 In the diagram alongside, quadrilateral EFGH has vertices E( 1; 3), F(4; 4), G(3; 1) and H( 2; 2) 6 y 4 F(4;4) E(-1;3) 2-5 5 H(-2;-2) -2
More information12.4 Rotations. Learning Objectives. Review Queue. Defining Rotations Rotations
12.4. Rotations www.ck12.org 12.4 Rotations Learning Objectives Find the image of a figure in a rotation in a coordinate plane. Recognize that a rotation is an isometry. Review Queue 1. Reflect XY Z with
More information8.2 Graph and Write Equations of Parabolas
8.2 Graph and Write Equations of Parabolas Where is the focus and directrix compared to the vertex? How do you know what direction a parabola opens? How do you write the equation of a parabola given the
More information1.8 Coordinate Geometry. Copyright Cengage Learning. All rights reserved.
1.8 Coordinate Geometry Copyright Cengage Learning. All rights reserved. Objectives The Coordinate Plane The Distance and Midpoint Formulas Graphs of Equations in Two Variables Intercepts Circles Symmetry
More informationYear 8 Set 2 : Unit 1 : Number 1
Year 8 Set 2 : Unit 1 : Number 1 Learning Objectives: Level 5 I can order positive and negative numbers I know the meaning of the following words: multiple, factor, LCM, HCF, prime, square, square root,
More informationProperties of Quadrilaterals
MIAP Chapter 6: Linear functions Master 6.1a Activate Prior Learning: Properties of Quadrilaterals A quadrilateral is a polgon with 4 sides. A trapezoid is a quadrilateral that has eactl one pair of parallel
More informationBand Topic Mastery Statements - I can Essential Knowledge - I know Whole order decimals and negative numbers.
Year 7 Maths Assessment Criteria Assessment 1 Band Topic Mastery Statements - I can Essential Knowledge - I know Whole order decimals and negative numbers. know and understand place value in Numbers and
More informationPeriod: Date Lesson 13: Analytic Proofs of Theorems Previously Proved by Synthetic Means
: Analytic Proofs of Theorems Previously Proved by Synthetic Means Learning Targets Using coordinates, I can find the intersection of the medians of a triangle that meet at a point that is two-thirds of
More informationShuters PLANNING & TRACKING PHOTOCOPIABLE. Grade. Also available for download from Premier.
PLANNING & TRACKING Also available for download from www.shuters.com Premier Mathematics Grade 9 PHOTOCOPIABLE OS1001303 CUSTOMER SERVICES THIS SERIES IS ALSO AVAILABLE AS E-BOOKS www.shuters.com Tel:
More informationUnit 14: Transformations (Geometry) Date Topic Page
Unit 14: Transformations (Geometry) Date Topic Page image pre-image transformation translation image pre-image reflection clockwise counterclockwise origin rotate 180 degrees rotate 270 degrees rotate
More informationCHAPTER 2 REVIEW COORDINATE GEOMETRY MATH Warm-Up: See Solved Homework questions. 2.2 Cartesian coordinate system
CHAPTER 2 REVIEW COORDINATE GEOMETRY MATH6 2.1 Warm-Up: See Solved Homework questions 2.2 Cartesian coordinate system Coordinate axes: Two perpendicular lines that intersect at the origin O on each line.
More informationHomework for Section 5.1
Homework for Section 5.1 1. reate the rotation R(T) 2. reate the reflection F(T) of the triangle T shown below 90 degrees of the triangle T shown below across clockwise about the center point of rotation.
More informationBirkdale High School - Higher Scheme of Work
Birkdale High School - Higher Scheme of Work Module 1 - Integers and Decimals Understand and order integers (assumed) Use brackets and hierarchy of operations (BODMAS) Add, subtract, multiply and divide
More informationNO CALCULATOR ON ANYTHING EXCEPT WHERE NOTED
Algebra II (Wilsen) Midterm Review NO CALCULATOR ON ANYTHING EXCEPT WHERE NOTED Remember: Though the problems in this packet are a good representation of many of the topics that will be on the exam, this
More informationIntroduction to Transformations. In Geometry
+ Introduction to Transformations In Geometry + What is a transformation? A transformation is a copy of a geometric figure, where the copy holds certain properties. Example: copy/paste a picture on your
More informationLevel 4 means that I can
Level 4 means that I can Describe number patterns Find multiples Find factors Work out the square numbers Use word formulae Use co-ordinates in the first quadrant Multiply and divide whole numbers by 10
More informationCecil Jones Academy Mathematics Fundamental Map
Fundamentals Year 7 (Core) Knowledge Unit 1 Unit 2 Solve problems involving prime numbers Use highest common factors to solve problems Use lowest common multiples to solve problems Explore powers and roots
More informationSimilar Polygons. 38 Stretching and Shrinking
! Similar Polygons In Shapes and Designs, you learned that some polygons can fit together to cover, or tile, a flat surface. For example, the surface of a honeycomb is covered with a pattern of regular
More informationChislehurst and Sidcup Grammar School Mathematics Department Year 9 Programme of Study
Chislehurst and Sidcup Grammar School Mathematics Department Year 9 Programme of Study Timings Topics Autumn Term - 1 st half (7 weeks - 21 lessons) 1. Algebra 1: Expressions, Formulae, Equations and Inequalities
More information5.5 Properties of Parallelogram
GEOMETRY Q2T6 5.5 Exam View WS Name: Class: Date: 5.5 Properties of Parallelogram True/False Indicate whether the statement is true or false. 1. In a parallelogram, the consecutive angles are congruent.
More informationName: 1) Which of the following properties of an object are not preserved under a rotation? A) orientation B) none of these C) shape D) size
Name: 1) Which of the following properties of an object are not preserved under a rotation? A) orientation B) none of these C) shape D) size 2) Under a certain transformation, A B C is the image of ABC.
More informationPart I. Problems in this section are mostly short answer and multiple choice. Little partial credit will be given. 5 points each.
Math 106/108 Final Exam Page 1 Part I. Problems in this section are mostly short answer and multiple choice. Little partial credit will be given. 5 points each. 1. Factor completely. Do not solve. a) 2x
More informationLesson #6: Basic Transformations with the Absolute Value Function
Lesson #6: Basic Transformations with the Absolute Value Function Recall: Piecewise Functions Graph:,, What parent function did this piecewise function create? The Absolute Value Function Algebra II with
More informationMaths. Formative Assessment/key piece of work prior to end of unit: Term Autumn 1
Term Autumn 1 3 weeks Negative numbers Multiples and factors Common factors Prime numbers Ordering decimal numbers Rounding Square numbers and square roots Prime factor decomposition LCM and HCF Square
More informationModule 1 Topic C Lesson 14 Reflections
Geometry Module 1 Topic C Lesson 14 Reflections The purpose of lesson 14 is for students to identify the properties of reflection, to use constructions to find line of reflection, get familiar with notations
More informationf( x ), or a solution to the equation f( x) 0. You are already familiar with ways of solving
The Bisection Method and Newton s Method. If f( x ) a function, then a number r for which f( r) 0 is called a zero or a root of the function f( x ), or a solution to the equation f( x) 0. You are already
More informationANNUAL NATIONAL ASSESSMENT 2014 ASSESSMENT GUIDELINES MATHEMATICS GRADE 7
ANNUAL NATIONAL ASSESSMENT 2014 ASSESSMENT GUIDELINES MATHEMATICS GRADE 7 INTRODUCTION The 2014 cycle of Annual National Assessment (ANA 2014) will be administered in all public and designated 1 independent
More information6.1.3 How can I describe it?
Name: Date: Per: A# 6.1.3 How can I describe it? Describing Transformations In Lesson 6.1.2, you used words and coordinate points to describe how a triangle moved on a graph. These expressions described
More informationFocus Questions How does the new shape compare to the old shape? How do the coordinates of the new shape compare to the coordinates of the old shape?
Learning Target: Extend their techniques for using integer expressions to record movement on a number line to using expressions to represent movement on the coordinate graph. Practice identifying whether
More informationWJEC MATHEMATICS INTERMEDIATE GRAPHS STRAIGHT LINE GRAPHS (PLOTTING)
WJEC MATHEMATICS INTERMEDIATE GRAPHS STRAIGHT LINE GRAPHS (PLOTTING) 1 Contents Some Simple Straight Lines y = mx + c Parallel Lines Perpendicular Lines Plotting Equations Shaded Regions Credits WJEC Question
More informationName: Date: Per: WARM UP
Name: Date: Per: 6.1.1-6.1.3 WARM UP 6-23. In the last three lessons, you have investigated rigid transformations: reflections, rotations, and translations. 1. What happens to a shape when you perform
More informationMath 3 - Lesson Title: Using the Coordinate Plane for Proofs
Targeted Content Standard(s): Use coordinates to prove simple geometric theorems algebraically. G.GPE.4 Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove
More informationL2 Translations, Reflections, and Rotations Pre-Assessment Per Date
L Translations, Reflections, and Rotations.1 - Pre-Assessment Per Date Have you ever wanted to rearrange the furniture in your room? First you might want to make sure that the furniture would fit in the
More informationFOUNDATION HIGHER. F Autumn 1, Yr 9 Autumn 2, Yr 9 Spring 1, Yr 9 Spring 2, Yr 9 Summer 1, Yr 9 Summer 2, Yr 9
Year: 9 GCSE Mathematics FOUNDATION F Autumn 1, Yr 9 Autumn 2, Yr 9 Spring 1, Yr 9 Spring 2, Yr 9 Summer 1, Yr 9 Summer 2, Yr 9 HIGHER Integers and place value Decimals Indices, powers and roots Factors,multiples
More informationMATH 021 UNIT 2 HOMEWORK ASSIGNMENTS
MATH 021 UNIT 2 HOMEWORK ASSIGNMENTS General Instructions You will notice that most of the homework assignments for a section have more than one part. Usually, the part (A) questions ask for explanations,
More informationForm 4 Syllabus Scheme B
Topic A revision of number work A revision of number work Indices Expressions: Expanding and Factorisation Form 4 Syllabus Scheme B Content 1. Directed Numbers 2. Factors and Multiples 3. Expressing a
More informationPark Forest Math Team. Meet #3. Self-study Packet
Park Forest Math Team Meet #3 Self-study Packet Problem Categories for this Meet (in addition to topics of earlier meets): 1. Mystery: Problem solving 2. : Properties of Polygons, Pythagorean Theorem 3.
More informationYear 7 Nov Grade : Year 7 Feb Grade : Year 7 May Grade :
Personal targets to help me achieve my grade : AFL Sheet Data 1 : Sampling, Averages and Diagrams ollecting Data I understand random sampling and bias Averages I can find the mean, median, mode and range
More informationS2 May Extension Test Checklist of Topics Length and Perimeter Learning Outcomes Revised Need Help
S2 May Extension Test Checklist of Topics Length and Perimeter Undersand the correct units to use in context Estimate lengths and Measure correctly Calculate the Perimeter of a shape Find missing lengths
More informationFormal Geometry Unit 9 Quadrilaterals
Name: Period: Formal Geometry Unit 9 Quadrilaterals Date Section Topic Objectives 2/17 9.5 Symmetry I can identify line and rotational symmetries in twodimensional figures. I can identify line and rotational
More informationYear 8 Unit 12 - shape properties
Year 8 Unit 12 - shape properties Foundation Able to recall the names of quadrilaterals, types of triangles and other simple polygons and to identify their properties. Secure Classify and name shapes Recognise
More informationTransformations. Write three rules based on what you figured out above: To reflect across the y-axis. (x,y) To reflect across y=x.
Transformations Geometry 14.1 A transformation is a change in coordinates plotted on the plane. We will learn about four types of transformations on the plane: Translations, Reflections, Rotations, and
More informationSection 18-1: Graphical Representation of Linear Equations and Functions
Section 18-1: Graphical Representation of Linear Equations and Functions Prepare a table of solutions and locate the solutions on a coordinate system: f(x) = 2x 5 Learning Outcome 2 Write x + 3 = 5 as
More informationAlgebra II Quadratic Functions
1 Algebra II Quadratic Functions 2014-10-14 www.njctl.org 2 Ta b le o f C o n te n t Key Terms click on the topic to go to that section Explain Characteristics of Quadratic Functions Combining Transformations
More informationQuadrilaterals & Transformations Study Guide
s & Transformations Study Guide What do I need to know for the upcoming Summative Assessment? s Classifications and Properties of: o o Trapezoid o Kite o Parallelogram o Rhombus o Rectangle o Square The
More informationYear 7 Key Performance Indicators Maths (Number)
Key Performance Indicators Maths (Number) M7.1 N1: I can use the four operations to answer calculations involving decimals. Use correct notation for recurring decimals, know the denominators of simple
More informationName Date Class. When the bases are the same and you multiply, you add exponents. When the bases are the same and you divide, you subtract exponents.
2-1 Integer Exponents A positive exponent tells you how many times to multiply the base as a factor. A negative exponent tells you how many times to divide by the base. Any number to the 0 power is equal
More informationAddition Properties. Properties something you cannot disprove always true. *You must memorize these properties!
Addition Properties Properties something you cannot disprove always true. *You must memorize these properties! 1) Commutative property of addition changing the order of addends will not change the sum
More information9 Transformations CHAPTER. Chapter Outline.
Chapter 9 www.ck12.org CHAPTER 9 Transformations Chapter Outline 9.1 EXPLORING SYMMETRY 9.2 TRANSLATIONS AND VECTORS 9.3 REFLECTIONS 9.4 ROTATIONS 9.5 COMPOSITION OF TRANSFORMATIONS 9.6 DILATIONS 9.7 TESSELLATIONS
More informationChapter 9 - Transformations. Transformation: operation that maps (or moves) a preimage onto an image.
Chapter 9 - Transformations Transformation: operation that maps (or moves) a preimage onto an image. 4 Types of transformations: I. Reflections II. Translations III. Rotations IV. Dilations 3 Parts of
More informationTerm Key topics What most pupils will learn (prior assessment may alter starting point & content) How might this learning be extended?
Learning overview for: Mathematics Term Key topics What most pupils will learn (prior assessment may alter starting point & content) Number Factors, multiples and primes HCF and LCM Calculate with negative
More informationUNIT 1 SIMILARITY, CONGRUENCE, AND PROOFS Lesson 6: Defining and Applying Similarity Instruction
Prerequisite Skills This lesson requires the use of the following skills: creating ratios solving proportions identifying congruent triangles calculating the lengths of triangle sides using the distance
More informationPractice Test (page 391) 1. For each line, count squares on the grid to determine the rise and the run. Use slope = rise
Practice Test (page 91) 1. For each line, count squares on the grid to determine the rise and the. Use slope = rise 4 Slope of AB =, or 6 Slope of CD = 6 9, or Slope of EF = 6, or 4 Slope of GH = 6 4,
More informationAdditional Practice. Name Date Class. 1. Refer to the rectangle at the right for the exercises below.
Additional Practice Investigation 1 1. Refer to the rectangle at the right for the eercises below. a. Give the length and width of a larger similar rectangle. Eplain your reasoning. cm cm b. Give the length
More informationUnit 5: Quadratic Functions
Unit 5: Quadratic Functions LESSON #5: THE PARABOLA GEOMETRIC DEFINITION DIRECTRIX FOCUS LATUS RECTUM Geometric Definition of a Parabola Quadratic Functions Geometrically, a parabola is the set of all
More informationMaths Homework Booklet Term 2
Maths Homework Booklet Term 2 Each week every student will be set piece of homework. This will be set on the first lesson of the week and due in on the last lesson of the week. Should students want to
More informationBeal High School. Mathematics Department. Scheme of Work for years 7 and 8
Beal High School Mathematics Department Scheme of Work for years 7 and 8 Version for web site March 2008 Note: This SoW covers levels 4 to 7. teachers will often dip in to level 8, especially as extension
More informationAlgebra Area of Parallelograms
Lesson 10.1 Reteach Algebra Area of Parallelograms The formula for the area of a parallelogram is the product of the base and height. The formula for the area of a square is the square of one of its sides.
More informationTo prove theorems using figures in the coordinate plane
6-9 s Using Coordinate Geometr Content Standard G.GPE.4 Use coordinates to prove simple geometric theorems algebraicall. bjective To prove theorems using figures in the coordinate plane Better draw a diagram!
More information1d Determining the derivative 1 Solving 2 First alternative: Determine the points where the graphs of and meet:
Marking scheme for the VWO Mathematics-B Exam of 3 July 04 Question. a. Determining the coordinates of point Taking the first derivative: Calculating the slope of the tangent line: Determining a formula
More informationGeometry Syllabus, First Semester (correlation with STAAR/EOC)
1 Geometry Syllabus, First Semester (correlation with STAAR/EOC) Legend: Example 3[R]-G.5(B) 3, The reporting category [R], Either Readiness or Supporting G.5, The TEKS (B) Expectation [P], indicates a
More informationYear 9 Key Performance Indicators Maths (Number)
Key Performance Indicators Maths (Number) M9.1 N1: I can apply the four operations to negative numbers. Raise negative numbers to a power Add and subtract negative numbers and know when the answer should
More informationReview Exercise. 1. Determine vector and parametric equations of the plane that contains the
Review Exercise 1. Determine vector and parametric equations of the plane that contains the points A11, 2, 12, B12, 1, 12, and C13, 1, 42. 2. In question 1, there are a variety of different answers possible,
More information