This document provides instruction on using the midpoint formula in coordinate geometry. It defines the midpoint M as the point lying equidistant between the endpoints of a line segment AB. The midpoint formula is given as: if P1(x1,y1) and P2(x2,y2) are the endpoints of the segment, then the midpoint M has coordinates (x1+x2)/2, (y1+y2)/2. Several examples are worked out applying the formula to find the coordinates of midpoints of various line segments. Additional practice problems are provided for students to find midpoints and to solve for the coordinates of one endpoint given the other endpoint and midpoint.
The document introduces the rectangular coordinate system and graphing utilities. It discusses plotting points in the four quadrants and finding the coordinates, distance, and midpoint between points. It also covers determining if points satisfy a given equation and solving linear equations for a variable.
Η αναφορά στον Vieta και στους τύπους του στο σχολικό βιβλίο της Άλγεβρας της Α’ Λυκείου, μπορεί μας να μας δώσει την ευκαιρία να μιλήσουμε στους μαθητές μας για το έργο του και τη συμβολή του στην ανάπτυξη της σύγχρονης Άλγεβρας.
The document introduces the three-dimensional coordinate system and methods for graphing points, finding the distance between two points, and calculating the midpoint between two points in three-dimensional space. It provides examples of graphing points in the octants of three-dimensional space, calculating the distance between two example points, and finding the midpoint between another two points. The document concludes by providing a whiteboard activity and assignment problems related to these three-dimensional coordinate concepts.
The document provides instructions for plotting points on a coordinate plane. It lists 17 points in the form (x,y) and instructs the reader to: 1) write their name and date, 2) locate and mark the points on the x and y axes, 3) connect the points in order from 1 to 17, 4) identify the diagram, and 5) color it while keeping the points visible.
The document discusses finding the roots of quadratic functions. It explains that the roots are where the parabola crosses the x-axis. It introduces the quadratic formula as a method to calculate the exact roots and provides examples of using the formula to find roots. It also discusses finding the axis of symmetry and turning point of quadratic functions.
This document is a mathematics exam consisting of 5 sections with multiple questions in each section:
1) The first section contains 4 questions involving operations on numbers in scientific notation, fractions, and proportions.
2) The second section contains 4 questions involving algebra, including developing and factorizing quadratic expressions and solving equations.
3) The third section contains 5 questions involving geometry, including plotting points, calculating lengths and coordinates, and properties of circles and triangles.
4) The fourth section contains 4 questions involving interpreting data from a cumulative frequency polygon including calculating frequencies, relative frequencies, and averages.
5) The fifth and final section contains 5 questions involving geometry relationships for circles and parallels involving lengths, centers,
1) The document contains a mathematics exam with multiple choice and free response questions covering topics like GCD, percentages, solving equations, factoring expressions, and geometry.
2) In part III, students are asked to factorize and simplify algebraic expressions, reduce expressions by combining like terms, and solve equations.
3) Part IV involves plotting points in the coordinate plane, determining properties of quadrilaterals formed by the points, calculating perimeters, and performing translations.
This document provides instruction on using the midpoint formula in coordinate geometry. It defines the midpoint M as the point lying equidistant between the endpoints of a line segment AB. The midpoint formula is given as: if P1(x1,y1) and P2(x2,y2) are the endpoints of the segment, then the midpoint M has coordinates (x1+x2)/2, (y1+y2)/2. Several examples are worked out applying the formula to find the coordinates of midpoints of various line segments. Additional practice problems are provided for students to find midpoints and to solve for the coordinates of one endpoint given the other endpoint and midpoint.
The document introduces the rectangular coordinate system and graphing utilities. It discusses plotting points in the four quadrants and finding the coordinates, distance, and midpoint between points. It also covers determining if points satisfy a given equation and solving linear equations for a variable.
Η αναφορά στον Vieta και στους τύπους του στο σχολικό βιβλίο της Άλγεβρας της Α’ Λυκείου, μπορεί μας να μας δώσει την ευκαιρία να μιλήσουμε στους μαθητές μας για το έργο του και τη συμβολή του στην ανάπτυξη της σύγχρονης Άλγεβρας.
The document introduces the three-dimensional coordinate system and methods for graphing points, finding the distance between two points, and calculating the midpoint between two points in three-dimensional space. It provides examples of graphing points in the octants of three-dimensional space, calculating the distance between two example points, and finding the midpoint between another two points. The document concludes by providing a whiteboard activity and assignment problems related to these three-dimensional coordinate concepts.
The document provides instructions for plotting points on a coordinate plane. It lists 17 points in the form (x,y) and instructs the reader to: 1) write their name and date, 2) locate and mark the points on the x and y axes, 3) connect the points in order from 1 to 17, 4) identify the diagram, and 5) color it while keeping the points visible.
The document discusses finding the roots of quadratic functions. It explains that the roots are where the parabola crosses the x-axis. It introduces the quadratic formula as a method to calculate the exact roots and provides examples of using the formula to find roots. It also discusses finding the axis of symmetry and turning point of quadratic functions.
This document is a mathematics exam consisting of 5 sections with multiple questions in each section:
1) The first section contains 4 questions involving operations on numbers in scientific notation, fractions, and proportions.
2) The second section contains 4 questions involving algebra, including developing and factorizing quadratic expressions and solving equations.
3) The third section contains 5 questions involving geometry, including plotting points, calculating lengths and coordinates, and properties of circles and triangles.
4) The fourth section contains 4 questions involving interpreting data from a cumulative frequency polygon including calculating frequencies, relative frequencies, and averages.
5) The fifth and final section contains 5 questions involving geometry relationships for circles and parallels involving lengths, centers,
1) The document contains a mathematics exam with multiple choice and free response questions covering topics like GCD, percentages, solving equations, factoring expressions, and geometry.
2) In part III, students are asked to factorize and simplify algebraic expressions, reduce expressions by combining like terms, and solve equations.
3) Part IV involves plotting points in the coordinate plane, determining properties of quadrilaterals formed by the points, calculating perimeters, and performing translations.
Class 9 Cbse Maths Sample Paper Model 2Sunaina Rawat
The document is a sample test paper for Class 9 mathematics. It provides general instructions for a 3 hour exam with 37 questions divided into 4 sections. Section A contains 10 one-mark questions, Section B contains 9 two-mark questions, Section C contains 10 three-mark questions, and Section D contains 8 four-mark questions. The questions cover a range of mathematics topics including decimals, polynomials, geometry, trigonometry, and probability.
This document demonstrates how to find the midpoint M(x,y) of points on a coordinate plane. It provides examples of finding the midpoints of points A(10,2) and B(20,24), which is M(15,13); of points R(-12,-8) and C(16,12), which is M(2,2); and of points F(-9,3) and F(12,-6), which is M(-3,1). It also shows working through examples of finding the x- and y-coordinates that satisfy midpoint equations.
The document discusses Breadth First Search (BFS) and Depth First Search (DFS) algorithms for graphs. It defines key graph terminology and describes how to represent graphs using adjacency lists and matrices. It then explains how BFS and DFS work by exploring the graph in different ways, keeping track of vertex colors and paths/trees produced. Both algorithms run in O(V+E) time and have different applications like routing, sorting, and finding connected components.
This document contains 20 multiple choice questions about matrices and determinants. The questions cover topics like identifying symmetric matrices, matrix multiplication and addition, inverses, determinants, and solving systems of linear equations using matrices. An answer key is provided at the end to check the answers to the questions.
APEX INSTITUTE was conceptualized in May 2008, keeping in view the dreams of young students by the vision & toil of Er. Shahid Iqbal. We had a very humble beginning as an institute for IIT-JEE / Medical, with a vision to provide an ideal launch pad for serious JEE students . We actually started to make a difference in the way students think and approach problems.
This document contains a mathematics exam with 7 sections covering topics such as:
1) Choosing correct answers and justifications for systems of equations and inequalities.
2) Solving systems of equations, calculating proportions, and simplifying polynomials.
3) Graphing lines and finding intersections of lines and circles.
4) Calculating angles, similarities of triangles, and loci of points.
5) Conducting statistical analysis on survey data including calculating range, mean, and percentages.
The document discusses the determinant of a matrix. It begins by providing historical context and a geometric interpretation of determinants. It then outlines several key properties of determinants, such as how exchanging rows changes the sign of the determinant. Formulas for calculating the determinant of matrices of various sizes are presented, including the general formula for an n×n matrix. Applications of determinants in fields like statistics and transformations are also mentioned.
This document provides information about the Cartesian plane and coordinates. It defines the x-axis and y-axis, which are the horizontal and vertical reference lines on a coordinate grid. Coordinates are represented as an ordered pair of numbers (x,y) that show the position on the grid by indicating the distance from the origin horizontally and vertically. For example, the point (3,2) is located 3 units to the right and 2 units up. The document includes a grid and asks the reader to plot two points, draw a line between them, and identify three other coordinate pairs that lie on that line.
The document provides instructions for graphing linear equations using the slope-intercept form. It includes graphing the equations y = 2/3x - 3 and y = -1/4x, finding the slope and y-intercept for each, and writing the equation 3x + 4y = 8 in slope-intercept form to graph it. Students are assigned problems 17 through 26 on page 248 and told to check their work with a graphing calculator.
The document discusses three forms of quadratic functions - standard form, vertex form, and intercept form - and provides examples of how to write quadratic functions in each form and the steps to graph each by finding the vertex, axis of symmetry, and intercepts. The standard form is ax^2 + bx + c, the vertex form is a(x-h)^2 + k, and the intercept form is a(x-p)(x-q), with each using different variables to indicate the features of the parabolic graph.
1. The document is a review for Chapter 6 that contains 15 multi-step math problems involving geometry and proportions.
2. It also includes a table with geometry terms and their definitions at the end for additional review.
3. The problems cover a range of concepts like similar triangles, alternate interior angles, proportions, geometric means, and using shadows to calculate heights.
Quadratic functions are polynomials of degree 2 with the general form f(x)=ax2+bx+c. The discriminant, ∆ =b2-4ac, determines the number of x-intercepts. Cubic functions are polynomials of degree 3 with the general form f(x)= ax3+bx2+cx+d. Quartic functions are polynomials of degree 4 with the general form f(x)=ax4+bx3+cx2+dx+e. Higher degree polynomial functions have more complex behaviors determined by their factors and coefficients.
This document is a math exam for class G7 consisting of 7 sections testing various math skills. Section I has 4 multiple choice questions testing equations and operations. Section II has 4 algebra questions involving developing, reducing, factorizing expressions. Section III has 4 equation solving questions. Section IV is a word problem about boys and marbles. Section V has 4 geometry questions involving triangle angles, perimeters. Section VI is a proof question about triangle congruence. Section VII has 4 coordinate geometry questions finding midpoints and projections of points on axes. The exam tests a wide range of math fundamentals over its 7 sections.
1) The document outlines a class agenda that includes reviewing quadratics and new solving methods in preparation for a Friday test. It also notes a third quarter exam on Friday covering quadratics, factoring, exponents, and polynomials.
2) The class will begin with warm-up problems reviewing graphing quadratics and finding axes of symmetry. Steps for graphing the equation y + 6x = x^2 + 9 are provided.
3) Additional examples are given for graphing a quadratic function modeling the height of a basketball after being shot, finding the maximum height and time to reach it by using the vertex of the parabola.
This document provides information about an exam for the Edexcel GCE Core Mathematics C3 Bronze Level B1 qualification. It lists the paper reference, time allowed, materials required and permitted calculators. It provides instructions for candidates on writing details on the front page and information about the structure of the paper. It also lists the 9 questions that make up the exam, covering topics like functions, graphs, derivatives, iterations and logarithms. The final section suggests grade boundaries for the exam.
This document provides instructions for graphing quadratic functions and examples worked through step-by-step. It begins with the general steps: 1) identify coefficients, 2) find the vertex, 3) draw the axis of symmetry, 4) find the y-intercept, 5) find roots, 6) reflect points over the axis, and 7) graph the parabola. An example graphs the function y = 3x^2 - 6x + 1. It then works through graphing the path of a basketball using the function f(x) = -16x^2 + 32x, finding that the maximum height is 16 feet reached at 1 second, and the basketball is in the air for 2 seconds. The document
1) Inverse trigonometric functions take an output value and return the corresponding input angle. They are written with "arc" before the trig function name, like arcsin, arccos, arctan.
2) To graph inverse trig functions, they are reflections of the original trig functions over the line y = x. Their domains are the ranges of the original functions, and their ranges are the domains of the original functions.
3) Students are assigned practice problems evaluating and graphing inverse trig functions, with a quiz scheduled for the following Monday.
This document contains 5 multiple choice questions about geometry and trigonometry concepts: (1) Finding a length on a figure, (2) Determining the number of possible triangles given angle and side lengths, (3) Solving a trigonometric equation, (4) Calculating a reference angle, (5) Using trigonometry to calculate distances and heights from two observation points of an airplane.
Geographic Information Systems (Question Paper) [May – 2018 | CBSGS - 75:25 P...Mumbai B.Sc.IT Study
Q.1 ATTEMPT ANY TWO QUESTIONS: (10 MARKS)
(A) Write a short note Eon Geospatial Data.
(B) List and explain various types of Map Projections.
(C) Explain the Data Structure of a Polygon Coverage.
(D) Explain any two types of Raster Data.
Q.2 ATTEMPT ANY TWO QUESTIONS: (10 MARKS)
(A) List and explain various Data Creation Techniques.
(B) Write a short note on Data Conversion.
(C) Explain the Map to Map and Image to Map Transformation.
(D) List and explain different types of Geometric Transformation.
Q.3 ATTEMPT ANY TWO QUESTIONS: (10 MARKS)
(A) Explain various relationship between tables.
(B) Explain the concept of Normalization.
(C) List and explain different types of Map.
(D) What is Data Classification? Explain.
Q.4 ATTEMPT ANY TWO QUESTIONS: (10 MARKS)
(A) Write a short note on Attribute Data Query.
(B) Explain Descriptive Statistics.
(C) What is the output of the following for a statement (slope=1) AND (NOT (Aspect=4)).
[IMAGE -> ]
(D) What do you understand by Spatial Data Query?
Q.5 ATTEMPT ANY TWO QUESTIONS: (10 MARKS)
(A) What is Buffering? Write down the applications of Buffering.
(B) What do you mean by pattern analysis? Explain Nearest Neighbour Analysis.
(C) Write the purpose of the following Map Manipulation Operations with example.
(i) Erase
(ii) Update
(iii) Select
(iv) Eliminate
(v) Clip
(D) What is Local Operation? Explain Local Operation with a Single Raster.
Q.6 ATTEMPT ANY TWO QUESTIONS: (10 MARKS)
(A) List and explain the elements of Spatial Interpolation.
(B) Explain the Thin-Plate Splines Local Method.
(C) What is Spatial Interpolation? What are Spatial Interpolation types? Explain any one type.
(D) What is Kriging? Explain Universal Kriging.
Q.7 ATTEMPT ANY THREE QUESTIONS: (15 MARKS)
(A) Explain the following with example:
(i) Association
(ii) Aggregation
(B) Write the importance of control points in Affine Transformation.
(C) Write a short note on Map Production.
(D) Explain different types of Graphs.
(E) Explain the Density Estimation Local Method.
(F) Explain the Thiessen Polygons Local Method.
1. The document contains a mock test with 30 multiple choice questions covering various topics like patterns, codes, spatial reasoning, logical reasoning, and data interpretation.
2. The first section contains questions on patterns, codes to form words, identifying words that cannot be formed from given letters, and interpreting coded messages.
3. The later sections include questions involving diagrams of trees, balls in a row, points in a grid, relationships between figures, identifying symmetric and embedded figures, and puzzles involving directions and seating arrangements.
Class 9 Cbse Maths Sample Paper Model 2Sunaina Rawat
The document is a sample test paper for Class 9 mathematics. It provides general instructions for a 3 hour exam with 37 questions divided into 4 sections. Section A contains 10 one-mark questions, Section B contains 9 two-mark questions, Section C contains 10 three-mark questions, and Section D contains 8 four-mark questions. The questions cover a range of mathematics topics including decimals, polynomials, geometry, trigonometry, and probability.
This document demonstrates how to find the midpoint M(x,y) of points on a coordinate plane. It provides examples of finding the midpoints of points A(10,2) and B(20,24), which is M(15,13); of points R(-12,-8) and C(16,12), which is M(2,2); and of points F(-9,3) and F(12,-6), which is M(-3,1). It also shows working through examples of finding the x- and y-coordinates that satisfy midpoint equations.
The document discusses Breadth First Search (BFS) and Depth First Search (DFS) algorithms for graphs. It defines key graph terminology and describes how to represent graphs using adjacency lists and matrices. It then explains how BFS and DFS work by exploring the graph in different ways, keeping track of vertex colors and paths/trees produced. Both algorithms run in O(V+E) time and have different applications like routing, sorting, and finding connected components.
This document contains 20 multiple choice questions about matrices and determinants. The questions cover topics like identifying symmetric matrices, matrix multiplication and addition, inverses, determinants, and solving systems of linear equations using matrices. An answer key is provided at the end to check the answers to the questions.
APEX INSTITUTE was conceptualized in May 2008, keeping in view the dreams of young students by the vision & toil of Er. Shahid Iqbal. We had a very humble beginning as an institute for IIT-JEE / Medical, with a vision to provide an ideal launch pad for serious JEE students . We actually started to make a difference in the way students think and approach problems.
This document contains a mathematics exam with 7 sections covering topics such as:
1) Choosing correct answers and justifications for systems of equations and inequalities.
2) Solving systems of equations, calculating proportions, and simplifying polynomials.
3) Graphing lines and finding intersections of lines and circles.
4) Calculating angles, similarities of triangles, and loci of points.
5) Conducting statistical analysis on survey data including calculating range, mean, and percentages.
The document discusses the determinant of a matrix. It begins by providing historical context and a geometric interpretation of determinants. It then outlines several key properties of determinants, such as how exchanging rows changes the sign of the determinant. Formulas for calculating the determinant of matrices of various sizes are presented, including the general formula for an n×n matrix. Applications of determinants in fields like statistics and transformations are also mentioned.
This document provides information about the Cartesian plane and coordinates. It defines the x-axis and y-axis, which are the horizontal and vertical reference lines on a coordinate grid. Coordinates are represented as an ordered pair of numbers (x,y) that show the position on the grid by indicating the distance from the origin horizontally and vertically. For example, the point (3,2) is located 3 units to the right and 2 units up. The document includes a grid and asks the reader to plot two points, draw a line between them, and identify three other coordinate pairs that lie on that line.
The document provides instructions for graphing linear equations using the slope-intercept form. It includes graphing the equations y = 2/3x - 3 and y = -1/4x, finding the slope and y-intercept for each, and writing the equation 3x + 4y = 8 in slope-intercept form to graph it. Students are assigned problems 17 through 26 on page 248 and told to check their work with a graphing calculator.
The document discusses three forms of quadratic functions - standard form, vertex form, and intercept form - and provides examples of how to write quadratic functions in each form and the steps to graph each by finding the vertex, axis of symmetry, and intercepts. The standard form is ax^2 + bx + c, the vertex form is a(x-h)^2 + k, and the intercept form is a(x-p)(x-q), with each using different variables to indicate the features of the parabolic graph.
1. The document is a review for Chapter 6 that contains 15 multi-step math problems involving geometry and proportions.
2. It also includes a table with geometry terms and their definitions at the end for additional review.
3. The problems cover a range of concepts like similar triangles, alternate interior angles, proportions, geometric means, and using shadows to calculate heights.
Quadratic functions are polynomials of degree 2 with the general form f(x)=ax2+bx+c. The discriminant, ∆ =b2-4ac, determines the number of x-intercepts. Cubic functions are polynomials of degree 3 with the general form f(x)= ax3+bx2+cx+d. Quartic functions are polynomials of degree 4 with the general form f(x)=ax4+bx3+cx2+dx+e. Higher degree polynomial functions have more complex behaviors determined by their factors and coefficients.
This document is a math exam for class G7 consisting of 7 sections testing various math skills. Section I has 4 multiple choice questions testing equations and operations. Section II has 4 algebra questions involving developing, reducing, factorizing expressions. Section III has 4 equation solving questions. Section IV is a word problem about boys and marbles. Section V has 4 geometry questions involving triangle angles, perimeters. Section VI is a proof question about triangle congruence. Section VII has 4 coordinate geometry questions finding midpoints and projections of points on axes. The exam tests a wide range of math fundamentals over its 7 sections.
1) The document outlines a class agenda that includes reviewing quadratics and new solving methods in preparation for a Friday test. It also notes a third quarter exam on Friday covering quadratics, factoring, exponents, and polynomials.
2) The class will begin with warm-up problems reviewing graphing quadratics and finding axes of symmetry. Steps for graphing the equation y + 6x = x^2 + 9 are provided.
3) Additional examples are given for graphing a quadratic function modeling the height of a basketball after being shot, finding the maximum height and time to reach it by using the vertex of the parabola.
This document provides information about an exam for the Edexcel GCE Core Mathematics C3 Bronze Level B1 qualification. It lists the paper reference, time allowed, materials required and permitted calculators. It provides instructions for candidates on writing details on the front page and information about the structure of the paper. It also lists the 9 questions that make up the exam, covering topics like functions, graphs, derivatives, iterations and logarithms. The final section suggests grade boundaries for the exam.
This document provides instructions for graphing quadratic functions and examples worked through step-by-step. It begins with the general steps: 1) identify coefficients, 2) find the vertex, 3) draw the axis of symmetry, 4) find the y-intercept, 5) find roots, 6) reflect points over the axis, and 7) graph the parabola. An example graphs the function y = 3x^2 - 6x + 1. It then works through graphing the path of a basketball using the function f(x) = -16x^2 + 32x, finding that the maximum height is 16 feet reached at 1 second, and the basketball is in the air for 2 seconds. The document
1) Inverse trigonometric functions take an output value and return the corresponding input angle. They are written with "arc" before the trig function name, like arcsin, arccos, arctan.
2) To graph inverse trig functions, they are reflections of the original trig functions over the line y = x. Their domains are the ranges of the original functions, and their ranges are the domains of the original functions.
3) Students are assigned practice problems evaluating and graphing inverse trig functions, with a quiz scheduled for the following Monday.
This document contains 5 multiple choice questions about geometry and trigonometry concepts: (1) Finding a length on a figure, (2) Determining the number of possible triangles given angle and side lengths, (3) Solving a trigonometric equation, (4) Calculating a reference angle, (5) Using trigonometry to calculate distances and heights from two observation points of an airplane.
Geographic Information Systems (Question Paper) [May – 2018 | CBSGS - 75:25 P...Mumbai B.Sc.IT Study
Q.1 ATTEMPT ANY TWO QUESTIONS: (10 MARKS)
(A) Write a short note Eon Geospatial Data.
(B) List and explain various types of Map Projections.
(C) Explain the Data Structure of a Polygon Coverage.
(D) Explain any two types of Raster Data.
Q.2 ATTEMPT ANY TWO QUESTIONS: (10 MARKS)
(A) List and explain various Data Creation Techniques.
(B) Write a short note on Data Conversion.
(C) Explain the Map to Map and Image to Map Transformation.
(D) List and explain different types of Geometric Transformation.
Q.3 ATTEMPT ANY TWO QUESTIONS: (10 MARKS)
(A) Explain various relationship between tables.
(B) Explain the concept of Normalization.
(C) List and explain different types of Map.
(D) What is Data Classification? Explain.
Q.4 ATTEMPT ANY TWO QUESTIONS: (10 MARKS)
(A) Write a short note on Attribute Data Query.
(B) Explain Descriptive Statistics.
(C) What is the output of the following for a statement (slope=1) AND (NOT (Aspect=4)).
[IMAGE -> ]
(D) What do you understand by Spatial Data Query?
Q.5 ATTEMPT ANY TWO QUESTIONS: (10 MARKS)
(A) What is Buffering? Write down the applications of Buffering.
(B) What do you mean by pattern analysis? Explain Nearest Neighbour Analysis.
(C) Write the purpose of the following Map Manipulation Operations with example.
(i) Erase
(ii) Update
(iii) Select
(iv) Eliminate
(v) Clip
(D) What is Local Operation? Explain Local Operation with a Single Raster.
Q.6 ATTEMPT ANY TWO QUESTIONS: (10 MARKS)
(A) List and explain the elements of Spatial Interpolation.
(B) Explain the Thin-Plate Splines Local Method.
(C) What is Spatial Interpolation? What are Spatial Interpolation types? Explain any one type.
(D) What is Kriging? Explain Universal Kriging.
Q.7 ATTEMPT ANY THREE QUESTIONS: (15 MARKS)
(A) Explain the following with example:
(i) Association
(ii) Aggregation
(B) Write the importance of control points in Affine Transformation.
(C) Write a short note on Map Production.
(D) Explain different types of Graphs.
(E) Explain the Density Estimation Local Method.
(F) Explain the Thiessen Polygons Local Method.
1. The document contains a mock test with 30 multiple choice questions covering various topics like patterns, codes, spatial reasoning, logical reasoning, and data interpretation.
2. The first section contains questions on patterns, codes to form words, identifying words that cannot be formed from given letters, and interpreting coded messages.
3. The later sections include questions involving diagrams of trees, balls in a row, points in a grid, relationships between figures, identifying symmetric and embedded figures, and puzzles involving directions and seating arrangements.
This page is vert helpful those students they prepare junior engineer exam like.. SSC JEn, PWD, PHED, RSEB, BSNL JTO, TTA, WRD, DMRC, JMRC, RIICO etc exam
This document contains a solved sample paper for the SSC JE 2015 exam in electrical engineering. It consists of 50 multiple choice questions testing general intelligence and reasoning abilities, as well as electrical engineering concepts. The questions cover topics like patterns and series, coding and decoding, data interpretation, and electrical/plant science facts. The document also provides the answers to all questions.
This document contains 30 multiple choice mathematics questions covering topics such as statistics, probability, algebra and number theory. The questions test objectives related to calculating the standard deviation, mean, median, mode and range of data sets. Other concepts assessed include factorizing algebraic expressions, simplifying fractions, solving equations, working with number bases, and interpreting tables, charts and graphs to solve probability problems.
This document contains a quantitative aptitude practice test with 53 multiple choice questions. The questions cover topics such as geometry, algebra, arithmetic, number theory, and word problems. For each question there are 4 possible answer choices labeled a, b, c, or d. The test is 90 minutes long with 3 marks awarded for each correct answer and 1 mark deducted for each incorrect answer.
The document provides instructions and information for a 2-hour written examination in mathematics. It includes:
1. Instructions for students to follow such as opening the question paper when instructed and writing their name and registration number.
2. A list of common mathematical formulae that may be helpful in answering questions such as relations, shapes and space, Pythagoras theorem.
3. Ten mathematics questions testing topics like operations, algebra, geometry, trigonometry and statistics. Each question is broken down into parts with multiple steps.
4. Spaces provided for students to show their working and write their answers.
5. Information at the end about who prepared, verified and approved the question paper.
CREST Mathematics Olympiad exam sample paper for class 1. Get an overview of the exam pattern of CMO Class 1 exam with the questions and prepare early for the exam.
This pdf is free to download. This document is prepared by tutor Kundan sir from Vista's Learning.Keep learning CBSE Class 1 0 maths by signing up in Vista's Learning portal here
https://v-learning.in/live-course/1114/ncert-solutions-for-maths-chapter-2-polynomials-part-8-vistas-learning
This document contains 48 permutation and combination problems with multiple choice answers. It provides an introduction and contact information for Sthitpragya Science Classes, which offers advanced mathematics preparation courses. The problems cover a range of topics including factorials, permutations, combinations, and arrangements of objects.
This document contains a sample paper for the Crest Mathematics Olympiad (CMO) exam. The sample paper includes 10 multiple choice questions covering topics like integers, geometry, ratios, and word problems. It also provides the class-wise question distribution and marking scheme for the CMO exam. The syllabus for the CMO can be found online at the provided URL. The document seeks to enhance students' practical mathematics knowledge through this digital exam initiative.
This document contains a final model test examination for mathematics. It includes questions in four groups - Algebra, Geometry, Trigonometry and Mensuration, and Statistics. The Algebra section contains three multi-part questions on topics like factoring polynomials, solving systems of linear equations, and finding terms in a geometric series. The Geometry section contains two multi-part questions involving constructions related to dividing a line segment into parts and constructing triangles. The Trigonometry and Mensuration section contains one multi-part question on trigonometric ratios and properties or on mensuration formulas. The Statistics section contains one multi-part question involving concepts like frequency distribution, mean, median and mode. The document also includes 40 multiple choice questions testing
This document contains a practice test for the NTSE Stage II exam with 46 multiple choice math questions. The questions cover topics like geometry, trigonometry, probability, arithmetic progressions, and algebra. For each question there are 4 possible answer choices labeled A, B, C, or D. The test is presented across 4 pages with around 10-12 questions per page.
This document appears to be an exam booklet for a test being administered by the Tara Institute. It provides instructions for test-takers, including how to fill out identifying information on the answer sheet, how long they have to complete the test, that it contains 200 multiple choice questions, and the scoring procedures. It notes there will be a penalty for wrong answers and advises test-takers not to open the booklet until instructed to do so.
This document contains a worksheet on permutation and combination problems with 40 multiple choice questions. It provides the total marks that can be scored, was compiled by Prashant Jain, and instructs students to attempt the worksheet in one sitting. It also contains the answer key and solutions to the problems at the end.
The document describes a mock CAT (Common Admission Test) exam with the following details:
- The test has 165 multiple choice questions divided into 3 sections with 55 questions each.
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- Correct answers receive 1 mark while incorrect answers receive a negative 1/4 mark deduction.
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CRO Olympiad Exam Sample Paper for Class 3
1. CLASS
3
SAMPLE PAPER
CREST Reasoning Olympiad (CRO)
1
1. Find the number which will be on the last sticker following the same pattern as the first
two follow:
(a) 24 (b) 23
(c) 32 (d) 33
2. Which two pieces of paper, when put together, will make the given shape?
(a) (b)
(c) (d)
Class Topic/Section No. of
Questions
Marks per Questions Total Marks
Logical Reasoning 25 1 25
1st
to 4th
Achiever’s Section 10 2 20
Grand Total 35 - 45
Logical Reasoning 40 1 40
5th
to 10th
Achiever’s Section 10 2 20
Grand Total 50 - 60
Syllabus for CRO is available at https://www.crestolympiads.com/cro-syllabus
Pattern and Marking Scheme
2. 2
3. Identify the missing number from the given alternatives that will complete the series.
(a) 36 (b) 49
(c) 51 (d) 64
4. Which of the following will be the correct mirror image of the given image?
(a) (b)
(c) (d)
CREST Olympiads – A digital initiative to
enhance practical knowledge
3. 3
5. There is a certain relationship between the pair of figures given on either side of (::);
identify the relationship of given pair and find the matching term.
Contamination : Food : : Infection : ?
(a) Germs (b) Disease
(c) Body (c) Microbes
6. Find the next letter of the following series:
D, G, J, M,?
(a) Q (b) O
(c) P (d) N
7. If A = BC, C = DE, then RN = ?
(a) TSPO (b) STOP
(c) PQOP (d) PQLM
8. How many triangles are there in the following figure?
(a) 8 (b) 6
(c) 4 (d) 7
CREST Olympiads – A digital initiative to
enhance practical knowledge
4. 4
9. If letter N represents North, E represent East, W represents West and S represents
South and dots represents the number of steps, then find the code for the path given
below:
(a) N2E2N3 (b) S3E2S2
(c) N2W2N3 (d) S3W2S3
10. In P, Q, R, S, T and U, R is taller than only P and U. S is shorter than only T and Q. If
each has different heights, then who will be at the third place when they are standing in
descending order of their height and the counting is done in the same order (tallest to
shortest)?
(a) R (b) S
(c) P (d) Q
1. (a), 2. (d), 3. (b), 4. (a), 5. (c), 6.(c), 7.(b), 8.(d), 9.(c), 10.(b)
Answers
Achiever’s Section