This document presents a multi-part math problem involving a polygon with sides of decreasing length forming an arithmetic progression. It provides information about the polygon and asks the reader to analyze several propositions related to distances traveled by a formic along the polygon's path. It then asks the reader to identify which of the propositions are true.
The document contains 16 multiple choice questions about mathematics. The questions cover topics such as functions, geometry, trigonometry, probability, and sets. For each question, the correct answer is provided according to the key at the end.
This document contains 16 multiple choice questions from an exam on various math and logic topics:
1. The value of an expression involving sums and differences of powers of 2 is between 114 and 117.
2. One statement about graphs of two real functions f and g is correct.
3. For functions f, g, and h to have the composite function h∘g∘f have domain R, a condition on m must be met.
The document then provides the answers to each question.
This document contains a 16 question math exam covering topics such as functions, trigonometry, geometry, and linear systems. The questions involve solving equations, analyzing graphs, calculating areas and probabilities, and determining properties of functions and geometric shapes. The correct answers are provided at the end.
This document contains 25 math problems and their solutions. The problems cover a range of arithmetic topics like number properties, operations, sequences, and word problems. The correct answers to the problems are provided in a key at the end.
A tractor factory established a goal to produce 20,000 tractors by 2025, having produced increasing amounts from 2010 to 2017. Assuming continued growth at the same rate, the goal will be reached and surpassed by 150 tractors. Several word problems are presented involving functions, geometry, trigonometry, and other mathematical concepts. The document provides 20 multiple choice questions with answers for an exam.
This document contains 10 multi-part questions related to mathematics. The questions cover topics such as functions, probability, geometry, and trigonometry. For example, question 1 involves calculating values of functions, finding where two functions are equal, and sketching their graphs. Question 4 analyzes the distances traveled by two planes flying routes between cities.
The document contains a 14 question multiple choice exam covering topics in mathematics. The questions test concepts in arithmetic progressions, geometry, functions, probability, and algebra. Correct answer choices are provided for each question at the end.
The document contains a 14-question multiple choice exam on mathematics topics such as geometry, trigonometry, complex numbers, and functions. The exam includes questions about sets, progressions, matrices, volumes, ellipses, logarithms, and more. The key provided at the end of the document indicates the correct answer for each question is choice C for question 1, B for question 2, the answer is nullified for question 3, A for question 4, and so on, with the least number being choice C for the final question.
The document contains 16 multiple choice questions about mathematics. The questions cover topics such as functions, geometry, trigonometry, probability, and sets. For each question, the correct answer is provided according to the key at the end.
This document contains 16 multiple choice questions from an exam on various math and logic topics:
1. The value of an expression involving sums and differences of powers of 2 is between 114 and 117.
2. One statement about graphs of two real functions f and g is correct.
3. For functions f, g, and h to have the composite function h∘g∘f have domain R, a condition on m must be met.
The document then provides the answers to each question.
This document contains a 16 question math exam covering topics such as functions, trigonometry, geometry, and linear systems. The questions involve solving equations, analyzing graphs, calculating areas and probabilities, and determining properties of functions and geometric shapes. The correct answers are provided at the end.
This document contains 25 math problems and their solutions. The problems cover a range of arithmetic topics like number properties, operations, sequences, and word problems. The correct answers to the problems are provided in a key at the end.
A tractor factory established a goal to produce 20,000 tractors by 2025, having produced increasing amounts from 2010 to 2017. Assuming continued growth at the same rate, the goal will be reached and surpassed by 150 tractors. Several word problems are presented involving functions, geometry, trigonometry, and other mathematical concepts. The document provides 20 multiple choice questions with answers for an exam.
This document contains 10 multi-part questions related to mathematics. The questions cover topics such as functions, probability, geometry, and trigonometry. For example, question 1 involves calculating values of functions, finding where two functions are equal, and sketching their graphs. Question 4 analyzes the distances traveled by two planes flying routes between cities.
The document contains a 14 question multiple choice exam covering topics in mathematics. The questions test concepts in arithmetic progressions, geometry, functions, probability, and algebra. Correct answer choices are provided for each question at the end.
The document contains a 14-question multiple choice exam on mathematics topics such as geometry, trigonometry, complex numbers, and functions. The exam includes questions about sets, progressions, matrices, volumes, ellipses, logarithms, and more. The key provided at the end of the document indicates the correct answer for each question is choice C for question 1, B for question 2, the answer is nullified for question 3, A for question 4, and so on, with the least number being choice C for the final question.
The document contains 10 math problems from an exam. The assistant provides concise summaries of the solutions in 3 sentences or less for each problem:
1) The function f is applied twice to 2019, giving a value of 10.
2) The numbers 16, 24, 36, 54, 81 form a geometric progression with 5 terms.
3) There is a unique solution set that makes the sum of 5 functions equal to the zero function.
4) There are 9 configurations that guarantee victory, which is 90% of the total possible configurations.
5) It calculates the apothem and radius of a sphere tangent to a hexagonal cross-section of a cube.
6) It determines the complex
This document contains a mathematics professor's presentation of graphs and equations to students, along with true/false statements about them. It also contains 15 multiple choice questions related to mathematics, including equations, geometry, and probability. The correct answers to the questions are provided at the end.
Problemas resueltos de matemática_ preuniversitarioNklp Peláez
1. The maximum value of n is 3 based on the equations: m -2 = n +5 and n2 +5 = m+4.
2. The polynomial is reducible to a single term with coefficient 48.
3. Based on the equation 1239=1.92 +2.9+3, the value of a×b is 4×2=8.
This document contains a summary of a survey given to cadets at the AFA (Air Force Academy) regarding their participation in various sports. The survey found that:
- 66 cadets play volleyball, with 25 not playing another sport
- 68 cadets play swimming, with 29 not playing another sport
- 70 cadets play athletics, with 26 not playing another sport
- 6 cadets play all three sports
The number of cadets that play at least two of the sports is 59.
This document contains a 20 question multiple choice exam covering topics in mathematics. The questions cover areas like functions, geometry, probability, sequences, and matrices. For each question there are 4 possible answer choices labeled a, b, c, or d. The exam also includes the answers to each question labeled with the corresponding letter choice.
The document contains 20 multiple choice questions about polynomials. The questions cover topics such as solving polynomial equations, finding the remainder of polynomial division, relationships between the coefficients and roots of polynomials, and interpreting graphs of polynomial functions. The correct answers to each question are provided in a key at the end.
The document discusses linear equations in three dimensions. It introduces the three-dimensional coordinate system using ordered triples (x, y, z) to represent points. Examples are given of graphing points and linear equations in three dimensions by finding intercepts on the x, y, and z axes. Applications to word problems involving points scored in a track meet and school supplies purchased are presented as examples of writing and solving linear equations with three variables.
The document contains 10 math problems from an exam:
1) Calculating probabilities of selecting balls from a box with different colors.
2) Finding the number of vertices of a polyhedron given information about its faces and edges.
3) Determining heights of solids formed by cutting a pyramid with parallel planes.
4-10) Additional math problems involving geometry, polynomials, exponents, and number theory.
This document presents information about a video game level where the character must reach the 20th floor of a building using one of three elevators to escape attacking monsters. The elevators stop at different floors according to their programming (even, multiples of 3, multiples of 5). Several propositions are then made about which elevators could stop at the same floor. Overall the level requires strategic use of the elevators to progress.
This document contains 15 multiple choice questions about matrices. The questions cover topics such as matrix multiplication, inverses, determinants, and properties of matrices. For each question there are 5 answer choices lettered a-e. The questions range in difficulty from relatively straightforward calculations to more conceptual questions about properties of matrices.
The document contains 20 multiple choice questions related to systems of linear equations. The questions cover topics such as determining the number of solutions to a system, properties of matrices, and using systems of equations to solve word problems. Sample questions ask the learner to determine the number of possible values for a variable that would make a given system possible and indeterminate, or to identify properties of matrices that would satisfy certain conditions.
The document contains 10 multiple choice questions about polynomials. The questions cover topics such as: properties of polynomial roots including multiplicity; determining coefficients given information about roots; representing polynomials in matrix form; evaluating polynomials; and solving systems of equations involving polynomial roots.
The document contains 16 multiple choice questions from an exam on various math and physics topics. The questions cover areas like functions, equations, geometry, ratios, and more. They require analyzing graphs, solving equations, making comparisons between values, and selecting the logically correct multiple choice response based on the information given in each question.
The document contains 20 multiple choice questions about functions. The questions cover topics such as: graphs of polynomial, quadratic and logarithmic functions; maximums and domains of functions; relationships between input and output values; intersections of graphs; and analyzing real world scenarios involving functional relationships.
The document contains 20 multiple choice questions about complex numbers. It tests concepts such as geometric representations of complex numbers and sets, properties of complex functions, solutions to complex equations, and calculations involving complex numbers. The questions range from identifying geometric shapes formed by complex roots to evaluating expressions and solving inequalities involving complex variables.
This document contains 10 mathematics questions from a practice exercise list. The questions cover topics such as quadratic functions, progressions, systems of equations, combinatorics involving selecting items from groups, geometry problems involving areas and volumes of shapes, and trigonometric equations. Each question has multiple parts asking to determine values, equations, areas, volumes, and other quantitative relationships presented in the figures or scenarios described. Solutions are provided in Portuguese for each part of each question.
The document contains 20 multiple choice questions about polynomials. The questions cover topics such as polynomial functions, roots of polynomials, graphs of polynomials, and solving polynomial equations.
The document contains 15 multiple choice questions about matrices. Some key details:
- Questions ask about properties of matrices like invertibility, multiplication, and Vandermonde matrices.
- Matrices represent things like pixel colors, employee pay, and encoded messages.
- Operations include finding determinants, inverses, eigenvalues, and using matrices to represent geometric transformations.
- The correct answers are usually specific numeric values or matrix expressions.
The document is a mathematics study guide for 7th grade students covering operations with integers, exponents, roots, and algebraic expressions over a 3 week period. It includes examples and exercises on calculating exponents and roots of integers, the rules for signs in exponents, and evaluating algebraic expressions using order of operations.
This document discusses algebraic expressions, factorization, and radicals. It defines algebraic expressions and outlines rules for multiplying, dividing, and factoring algebraic expressions using notable products such as the difference of squares, sum and difference of cubes, and binomial squares. It also covers simplifying fractional algebraic expressions and operations involving fractions. Finally, it discusses factoring polynomials using the Ruffini method and summarizes rules for adding, subtracting, multiplying, and dividing radicals.
The document contains 7 questions regarding geometry, functions, matrices, and probability. Question 1 involves finding angle measures given side lengths in a triangle under different progressions. Question 2 analyzes the graph and solutions of a piecewise function. Question 3 examines when a matrix is invertible and determines the absolute value of a complex number root of a cubic polynomial.
The document contains 16 multiple choice questions from an exam on various math and geometry topics. The questions cover topics like pyramid construction using blocks, functions, probability, geometry concepts like circles and rotations, and data analysis like median and frequency distributions.
The document contains 10 math problems from an exam. The assistant provides concise summaries of the solutions in 3 sentences or less for each problem:
1) The function f is applied twice to 2019, giving a value of 10.
2) The numbers 16, 24, 36, 54, 81 form a geometric progression with 5 terms.
3) There is a unique solution set that makes the sum of 5 functions equal to the zero function.
4) There are 9 configurations that guarantee victory, which is 90% of the total possible configurations.
5) It calculates the apothem and radius of a sphere tangent to a hexagonal cross-section of a cube.
6) It determines the complex
This document contains a mathematics professor's presentation of graphs and equations to students, along with true/false statements about them. It also contains 15 multiple choice questions related to mathematics, including equations, geometry, and probability. The correct answers to the questions are provided at the end.
Problemas resueltos de matemática_ preuniversitarioNklp Peláez
1. The maximum value of n is 3 based on the equations: m -2 = n +5 and n2 +5 = m+4.
2. The polynomial is reducible to a single term with coefficient 48.
3. Based on the equation 1239=1.92 +2.9+3, the value of a×b is 4×2=8.
This document contains a summary of a survey given to cadets at the AFA (Air Force Academy) regarding their participation in various sports. The survey found that:
- 66 cadets play volleyball, with 25 not playing another sport
- 68 cadets play swimming, with 29 not playing another sport
- 70 cadets play athletics, with 26 not playing another sport
- 6 cadets play all three sports
The number of cadets that play at least two of the sports is 59.
This document contains a 20 question multiple choice exam covering topics in mathematics. The questions cover areas like functions, geometry, probability, sequences, and matrices. For each question there are 4 possible answer choices labeled a, b, c, or d. The exam also includes the answers to each question labeled with the corresponding letter choice.
The document contains 20 multiple choice questions about polynomials. The questions cover topics such as solving polynomial equations, finding the remainder of polynomial division, relationships between the coefficients and roots of polynomials, and interpreting graphs of polynomial functions. The correct answers to each question are provided in a key at the end.
The document discusses linear equations in three dimensions. It introduces the three-dimensional coordinate system using ordered triples (x, y, z) to represent points. Examples are given of graphing points and linear equations in three dimensions by finding intercepts on the x, y, and z axes. Applications to word problems involving points scored in a track meet and school supplies purchased are presented as examples of writing and solving linear equations with three variables.
The document contains 10 math problems from an exam:
1) Calculating probabilities of selecting balls from a box with different colors.
2) Finding the number of vertices of a polyhedron given information about its faces and edges.
3) Determining heights of solids formed by cutting a pyramid with parallel planes.
4-10) Additional math problems involving geometry, polynomials, exponents, and number theory.
This document presents information about a video game level where the character must reach the 20th floor of a building using one of three elevators to escape attacking monsters. The elevators stop at different floors according to their programming (even, multiples of 3, multiples of 5). Several propositions are then made about which elevators could stop at the same floor. Overall the level requires strategic use of the elevators to progress.
This document contains 15 multiple choice questions about matrices. The questions cover topics such as matrix multiplication, inverses, determinants, and properties of matrices. For each question there are 5 answer choices lettered a-e. The questions range in difficulty from relatively straightforward calculations to more conceptual questions about properties of matrices.
The document contains 20 multiple choice questions related to systems of linear equations. The questions cover topics such as determining the number of solutions to a system, properties of matrices, and using systems of equations to solve word problems. Sample questions ask the learner to determine the number of possible values for a variable that would make a given system possible and indeterminate, or to identify properties of matrices that would satisfy certain conditions.
The document contains 10 multiple choice questions about polynomials. The questions cover topics such as: properties of polynomial roots including multiplicity; determining coefficients given information about roots; representing polynomials in matrix form; evaluating polynomials; and solving systems of equations involving polynomial roots.
The document contains 16 multiple choice questions from an exam on various math and physics topics. The questions cover areas like functions, equations, geometry, ratios, and more. They require analyzing graphs, solving equations, making comparisons between values, and selecting the logically correct multiple choice response based on the information given in each question.
The document contains 20 multiple choice questions about functions. The questions cover topics such as: graphs of polynomial, quadratic and logarithmic functions; maximums and domains of functions; relationships between input and output values; intersections of graphs; and analyzing real world scenarios involving functional relationships.
The document contains 20 multiple choice questions about complex numbers. It tests concepts such as geometric representations of complex numbers and sets, properties of complex functions, solutions to complex equations, and calculations involving complex numbers. The questions range from identifying geometric shapes formed by complex roots to evaluating expressions and solving inequalities involving complex variables.
This document contains 10 mathematics questions from a practice exercise list. The questions cover topics such as quadratic functions, progressions, systems of equations, combinatorics involving selecting items from groups, geometry problems involving areas and volumes of shapes, and trigonometric equations. Each question has multiple parts asking to determine values, equations, areas, volumes, and other quantitative relationships presented in the figures or scenarios described. Solutions are provided in Portuguese for each part of each question.
The document contains 20 multiple choice questions about polynomials. The questions cover topics such as polynomial functions, roots of polynomials, graphs of polynomials, and solving polynomial equations.
The document contains 15 multiple choice questions about matrices. Some key details:
- Questions ask about properties of matrices like invertibility, multiplication, and Vandermonde matrices.
- Matrices represent things like pixel colors, employee pay, and encoded messages.
- Operations include finding determinants, inverses, eigenvalues, and using matrices to represent geometric transformations.
- The correct answers are usually specific numeric values or matrix expressions.
The document is a mathematics study guide for 7th grade students covering operations with integers, exponents, roots, and algebraic expressions over a 3 week period. It includes examples and exercises on calculating exponents and roots of integers, the rules for signs in exponents, and evaluating algebraic expressions using order of operations.
This document discusses algebraic expressions, factorization, and radicals. It defines algebraic expressions and outlines rules for multiplying, dividing, and factoring algebraic expressions using notable products such as the difference of squares, sum and difference of cubes, and binomial squares. It also covers simplifying fractional algebraic expressions and operations involving fractions. Finally, it discusses factoring polynomials using the Ruffini method and summarizes rules for adding, subtracting, multiplying, and dividing radicals.
The document contains 7 questions regarding geometry, functions, matrices, and probability. Question 1 involves finding angle measures given side lengths in a triangle under different progressions. Question 2 analyzes the graph and solutions of a piecewise function. Question 3 examines when a matrix is invertible and determines the absolute value of a complex number root of a cubic polynomial.
The document contains 16 multiple choice questions from an exam on various math and geometry topics. The questions cover topics like pyramid construction using blocks, functions, probability, geometry concepts like circles and rotations, and data analysis like median and frequency distributions.
This document contains a test with 16 multiple choice questions covering various topics in mathematics. The questions assess knowledge of functions, geometry, probability, matrices, and data analysis. The correct answers are provided at the end.
The document contains 20 multiple choice questions about mathematics topics such as functions, geometry, trigonometry, and algebra. The questions cover concepts like parabolas, areas, solid geometry, probability, combinatorics, and equations. The document provides a key with the correct answer for each question listed from A to E.
This document contains 15 multiple choice questions from an IME 2019 exam covering topics in trigonometry, functions, geometry, complex numbers, and algebra. The questions involve concepts like progressions, function definitions, probability, areas of shapes, coordinate transformations, inequalities, and solving equations. The answers to each question are provided in a key at the end.
This document contains 23 multiple choice questions about equations. The questions cover a range of topics including solving linear, quadratic, and absolute value equations; finding the number of real solutions of equations; determining the sum or product of the roots of equations; and identifying properties of the solutions sets of equations.
The document contains 20 multiple choice questions from an exam in Brazil (ITA 2018). The questions cover a range of math and geometry topics including: arithmetic and geometric progressions, matrices, polynomials, probability, triangles, circles, trigonometry and complex numbers.
This document contains 10 multi-part math problems from an exam. Problem 1 involves finding dimensions of a parallelepiped and calculating volume and surface area. Problem 2 determines the domain of a function. Problem 3 analyzes solutions to a system of equations based on parameter values. The remaining problems involve additional concepts like tetrahedrons, integrals, triangles, complex numbers, polynomials, and systems of equations.
The document contains a 20 question multiple choice exam covering various topics in mathematics and geometry. For each question, there are 5 potential answer choices labeled a-e. The questions cover topics such as functions, complex numbers, limits, integrals, geometry, and probability. At the end, a key is provided indicating the correct answer for each question.
The document contains 15 multiple choice questions from an exam in Brazil. The questions cover topics in mathematics including geometry, trigonometry, algebra, and calculus.
1) The document contains 10 math problems from a Brazilian entrance exam (Fuvest). The problems cover topics like functions, geometry, probability, and word problems.
2) Mafalda is frustrated that she cannot solve one of the math problems. The problem asks her to solve 291.
3) A transportation company received a request to make an additional delivery, which would require deviating from the most direct route. The question calculates the minimum price the company would need to charge for the extra time and fuel required.
This document contains 6 questions regarding mathematics from a Brazilian university entrance exam (UNICAMP).
The questions cover topics such as: solving equations for real numbers; geometric and arithmetic sequences; matrix operations; properties of triangles; percentages and rates of change.
The summary provides the key results and solutions for each question in less than 3 sentences per question.
This document contains a 16 question multiple choice test covering topics in mathematics. The questions involve solving word problems related to ratios, percentages, geometry, algebra and other mathematical concepts. Correct answers are provided for each question at the end.
This document contains 13 math problems related to geometry, algebra, and other topics. Some key details:
- Problem 1 involves finding parameters of linear functions relating shoe size and length for Brazil and the US.
- Problem 2 analyzes data from Felix Baumgartner's skydive record, calculating velocity at a given time and when he broke the sound barrier.
- Problem 3 involves matrix multiplication and finding the value of a parameter for a system of equations to have a solution.
- Problems 4-6 cover marketing discounts on course enrollments, volume calculations for a pool with dimensions in geometric progression, and nutrient content relationships in fertilizers.
- Later problems analyze triangles, polynomials,
1) The quadratic function f(x) is defined as f(x) = x^2 + cx. For c = 1 - √3, the vertex of the parabola's graph has an x-coordinate and y-coordinate that sum to zero.
2) Three circles are tangent to each other, with radii a = 1 cm, b = 4 cm, and c = 5 cm. For a = 2 cm and b = 3 cm, c must be 10 cm for the triangle formed by the circle centers to be a right triangle.
3) For the linear system defined, the values of m where the sum of squares of the matrix coefficients equals the sum of the matrix elements squared
The document contains 16 multiple choice questions from an exam (ACAFE 2016). The questions cover topics such as sequences, functions, systems of equations, geometry, probability, and other mathematical concepts.
This document contains a 12 question multiple choice exam covering topics in mathematics and geometry. The questions involve functions, graphs, probability, volumes, areas, and geometric relationships.
1) For question 1, the smallest values of n and k such that kS_n = 20 are n = 2 and k = 6. For any positive integer j, there exist integers n ≥ 1 and k ≥ 0 such that kS_n = j.
2) For question 2, the domain of f(x) is [-1,0) U [1,+∞) and f(x) = 0 when x = ±1/√2.
3) For question 5a, the cosine of angle ACB can be expressed in terms of α and β.
4) For question 9a, g(f−1(α)) = cos(1−α
This document contains a series of exercises related to vectors in a plane. It begins with exercises involving vector operations like finding scalar multiples that satisfy equations and vector addition and subtraction. Later questions involve vector properties such as parallelism of vectors, orthogonality, vector lengths, and linear combinations of vectors. Geometric representations of vectors are also explored through problems finding points and line segments. The document aims to reinforce concepts of vector algebra and geometry through multiple practice problems.
This document contains 20 multiple choice questions related to mathematics:
1. The number of digits in the integer part of 7x is 288, where x is a natural number with 2015 digits.
2. Statements I and II are true - I being that a certain function is strictly increasing, and II that a quadratic equation has one real solution.
3. Statements I, II, and III are true - I and II regarding a decreasing sequence being bounded above and below by 0 and 1, respectively, and III regarding being less than 1.
4. The value of T is a particular fraction involving matrices M and N.
O documento apresenta 17 questões do Exame Nacional do Ensino Médio (ENEM) sobre diversos assuntos como: corrida de regularidade, monitoramento de substâncias no sangue, crescimento populacional de médicos, modelos predador-presa, crescimento exponencial de bactérias, ativação de rádio automotivo por código secreto e frequências de transmissão de aparelhos sem fio. As questões envolvem cálculos, interpretação de gráficos e tabelas e raciocínio sobre probabilidades.
O documento apresenta três questões sobre um teste realizado com um novo modelo de carro. A primeira questão descreve que 50 litros de combustível foram colocados no tanque do carro e ele foi dirigido em uma pista de testes até o combustível acabar. A segunda questão fornece um gráfico que relaciona a quantidade de combustível no tanque com a distância percorrida. A terceira questão pede a expressão algébrica que relaciona essas duas grandezas.
O documento descreve um fabricante que decidiu contratar o plano B de uma empresa de entregas, ao invés do plano A que havia escolhido inicialmente. O plano B tem taxa fixa mensal menor, mas taxa variável maior por quilograma enviado. Com 650kg a serem enviados, o plano B terá custo total menor do que o plano A.
O documento apresenta 16 questões do Exame Nacional do Ensino Médio (ENEM) sobre diversos assuntos como: estatística, física, geometria e probabilidade. As questões envolvem interpretação e análise de gráficos, cálculos, resolução de problemas e relações entre grandezas geométricas.
Este documento apresenta 15 questões sobre diversos assuntos como: salário comissionado, interação predador-presa, doenças relacionadas ao saneamento, depreciação de veículos, probabilidades, geometria espacial e volumes de sólidos geométricos. As questões envolvem interpretação e análise de gráficos, cálculos, raciocínio lógico e resolução de problemas.
O documento apresenta 19 questões do ENEM PPL de 2014 sobre diversos assuntos como física, química e matemática. As questões abordam tópicos como emissão de poluentes em veículos, crescimento bacteriano, probabilidade, geometria espacial e outros.
1) O documento apresenta 15 questões do ENEM PPL de 2013 sobre diversos assuntos como matemática, probabilidade e estatística.
2) As questões envolvem cálculos, interpretação de gráficos e tabelas para analisar problemas relacionados a produção industrial, vendas, financiamentos, jogos de azar e outros.
3) As respostas variam entre letras que indicam o resultado correto de cada questão após realizar os procedimentos matemáticos necessários.
1) O documento apresenta 15 questões do ENEM PPL de 2012 sobre diversos assuntos como probabilidades, estatística, geometria e física.
2) As questões envolvem cálculos e análises de gráficos, tabelas e figuras para responder sobre tópicos como produção de resíduos, vendas de produtos, taxas de abandono escolar, capacidade de lixeiras e propriedades geométricas de figuras.
3) São abordados também conceitos como acomodação ocular, convergência de lentes, á
Este documento contém 18 questões do Exame Nacional do Ensino Médio (ENEM) de 2017 sobre diversos assuntos como geometria, funções, probabilidade e estatística. As questões envolvem cálculos, interpretação de gráficos e tabelas e raciocínio lógico.
O documento relata sobre o Exame Nacional do Ensino Médio (ENEM) de 2009 que foi cancelado e traz 15 questões objetivas sobre diversos assuntos como probabilidade, geometria, estatística e análise combinatória.
O documento apresenta 18 questões do ENEM 2010 sobre diversos assuntos como: planejamento de treinos, estimativa de quantidade de estrelas para um painel, volumes de leite em reservatórios, desperdício de água por torneiras, uso de bicicletas compartilhadas, consumo de sacolas plásticas, escolha de estacionamentos, conta de água, necessidade diária de ferro e zinco por meio de alimentos, escolha de museus a visitar, estatísticas de chutes a gol, probabilidade em teste para detecção de
O documento apresenta 16 questões do Enem 2016 sobre diversos assuntos como matemática, física, probabilidade e estatística. As questões abordam tópicos como cálculo de áreas, sistemas lineares, funções exponenciais e probabilidades.
O documento contém 15 questões do Exame Nacional do Ensino Médio (ENEM) da segunda aplicação de 2014. As questões abordam tópicos como matemática, física, biologia, história e língua portuguesa.
O documento descreve os tipos sanguíneos e os resultados de um teste em 200 pessoas. 100 pessoas tinham o antígeno A, 110 o antígeno B e 20 nenhum. Portanto, o número de pessoas com tipo sanguíneo A é igual a 100.
O documento discute um problema de trânsito no Brasil relacionado ao consumo de bebidas alcoólicas por motoristas. Dados mostram que após mudanças no código de trânsito em 2013, como redução do limite de álcool no sangue e aumento de multas, houve queda no número de acidentes entre 2013 e 2015.
The document provides information about 12 multiple choice questions that appeared on the 2018 Brazilian National High School Exam (ENEM). The questions cover topics such as mathematics, statistics, geometry, probability, and other subjects. Specifically, the document provides the questions, answer options, and sometimes additional context or information needed to solve each question.
O documento apresenta 16 questões do Exame Nacional do Ensino Médio (ENEM) de 2017, cobrindo diversos assuntos como geometria, física, probabilidade e estatística. As questões envolvem interpretação e análise de gráficos, cálculos e resolução de problemas.
O documento descreve um problema de engenharia sobre a construção de uma galeria subterrânea para transporte de água entre uma fonte e um reservatório em uma cidade. Dois projetos são apresentados: um segmento de reta ou uma semicircunferência. Após cálculos, o projeto da semicircunferência levaria menos tempo para ser concluído.
Este documento apresenta 16 questões do Exame Nacional do Ensino Médio (ENEM) de 2015 sobre diversos assuntos como física, matemática, probabilidade e estatística. As questões envolvem cálculos, interpretação de gráficos e tabelas para analisar situações problemas.
[1] Um professor alterou as notas de uma prova usando uma função polinomial para compensar questões difíceis. [2] Uma pessoa recebeu propostas de planos de telefonia e pretende gastar R$30,00. [3] A figura mostra a trajetória de um balanço e a equação que a descreve.
This presentation includes basic of PCOS their pathology and treatment and also Ayurveda correlation of PCOS and Ayurvedic line of treatment mentioned in classics.
This slide is special for master students (MIBS & MIFB) in UUM. Also useful for readers who are interested in the topic of contemporary Islamic banking.
Executive Directors Chat Leveraging AI for Diversity, Equity, and InclusionTechSoup
Let’s explore the intersection of technology and equity in the final session of our DEI series. Discover how AI tools, like ChatGPT, can be used to support and enhance your nonprofit's DEI initiatives. Participants will gain insights into practical AI applications and get tips for leveraging technology to advance their DEI goals.
MATATAG CURRICULUM: ASSESSING THE READINESS OF ELEM. PUBLIC SCHOOL TEACHERS I...NelTorrente
In this research, it concludes that while the readiness of teachers in Caloocan City to implement the MATATAG Curriculum is generally positive, targeted efforts in professional development, resource distribution, support networks, and comprehensive preparation can address the existing gaps and ensure successful curriculum implementation.
Biological screening of herbal drugs: Introduction and Need for
Phyto-Pharmacological Screening, New Strategies for evaluating
Natural Products, In vitro evaluation techniques for Antioxidants, Antimicrobial and Anticancer drugs. In vivo evaluation techniques
for Anti-inflammatory, Antiulcer, Anticancer, Wound healing, Antidiabetic, Hepatoprotective, Cardio protective, Diuretics and
Antifertility, Toxicity studies as per OECD guidelines
How to Manage Your Lost Opportunities in Odoo 17 CRMCeline George
Odoo 17 CRM allows us to track why we lose sales opportunities with "Lost Reasons." This helps analyze our sales process and identify areas for improvement. Here's how to configure lost reasons in Odoo 17 CRM
Introduction to AI for Nonprofits with Tapp NetworkTechSoup
Dive into the world of AI! Experts Jon Hill and Tareq Monaur will guide you through AI's role in enhancing nonprofit websites and basic marketing strategies, making it easy to understand and apply.
How to Fix the Import Error in the Odoo 17Celine George
An import error occurs when a program fails to import a module or library, disrupting its execution. In languages like Python, this issue arises when the specified module cannot be found or accessed, hindering the program's functionality. Resolving import errors is crucial for maintaining smooth software operation and uninterrupted development processes.
Macroeconomics- Movie Location
This will be used as part of your Personal Professional Portfolio once graded.
Objective:
Prepare a presentation or a paper using research, basic comparative analysis, data organization and application of economic information. You will make an informed assessment of an economic climate outside of the United States to accomplish an entertainment industry objective.
1. AFA 2019
1
01. (Epcar (Afa) 2019) Considere, no plano cartesiano, a figura abaixo, em que os segmentos horizontais são paralelos ao
eixo Ox
e os segmentos verticais são paralelos ao eixo Oy.
Sabe-se que:
- os comprimentos de segmentos consecutivos da poligonal, que começa na origem O (0, 0) e termina em Q, formam
uma progressão aritmética decrescente de razão r e primeiro termo 1
a , em que
1
r 0 ;
15
− < <
- dois comprimentos consecutivos da poligonal são sempre perpendiculares;
- 1
OA a ,
= 2
AB a ,
= 3
BC a ,
= e, assim sucessivamente, até 16
PQ a .
=
Suponha que uma formiga parta da origem O (0, 0), e percorra a trajetória descrita pela poligonal até chegar ao ponto Q.
Com base nas informações acima, analise as proposições abaixo.
I. Se 1
a 1
= e
1
r ,
16
= − então a distância d percorrida pela formiga até chegar ao ponto Q é tal que 1
17
d a .
2
=
II. Quando a formiga estiver na posição do ponto L (x, y), então x 6r.
= −
III. Se 1
a 1,
= então de A até C, a formiga percorrerá a distância d 2 3r.
= +
Quanto a veracidade das proposições, tem-se
a) apenas uma delas é verdadeira.
b) apenas duas são verdadeiras.
c) todas são verdadeiras.
d) nenhuma delas é verdadeira.
2. AFA 2019
2
02. (Epcar (Afa) 2019) Para angariar fundos para a formatura, os alunos do 3º ano do CPCAR vendem bombons no horário
do intervalo das aulas. Inicialmente, começaram vendendo cada bombom por R$ 4,00. Assim, perceberam que vendiam,
em média, 50 bombons por dia. A partir dos conhecimentos que os alunos tinham sobre função, estimaram que para
cada 5 centavos de desconto no preço de cada bombom (não podendo conceder mais que 70 descontos), seria possível
vender 5 bombons a mais por dia.
Considere:
- p o preço de cada bombom;
- n o número de bombons vendidos, em média, por dia;
- 𝑥𝑥 ∈ ℕ o número de reduções de 5 centavos concedidas no preço unitário de cada bombom; e
- y a arrecadação diária com a venda dos bombons.
Com base nessas informações, analise as proposições abaixo.
(02) O gráfico que expressa n em função de p está contido no segmento AB do gráfico abaixo.
(04) A maior arrecadação diária possível com a venda dos bombons, considerando os descontos de 5 centavos, ocorre
quando concederem 35 descontos de 5 centavos.
(08) Se forem concedidos 20 descontos de 5 centavos, serão vendidos mais de 100 bombons por dia.
A soma das proposições verdadeiras é igual a
a) 6
b) 10
c) 12
d) 14
3. AFA 2019
3
03. (Epcar (Afa) 2019) Considere no plano cartesiano abaixo representadas as funções reais 𝑓𝑓: ]𝑚𝑚, −𝑚𝑚] → ℝ e
𝑔𝑔: [𝑚𝑚, −𝑚𝑚[−{𝑣𝑣} → ℝ.
Nas afirmativas abaixo, escreva V para verdadeira e F para falsa.
( ) O conjunto imagem da função g é dado por Im(g) ]p, m]
= −
( ) A função h definida por h(x) f(x) g(x)
= ⋅ assume valores não negativos somente se x [t, b] [r, 0]
∈ ∪
( ) A função j definida por j(x) g(x) p
= − é maior que zero para todo x ([m, m[ {v})
∈ − −
A sequência correta é
a) F – F – V
b) F – V – V
c) V – V – F
d) V – F – F
4. AFA 2019
4
04. (Epcar (Afa) 2019) Considere o sistema abaixo
2 2 2
2 2 2
2 2 2
1 2 1
9
a b c
2 1 1
3
a b c
3 1 2
4
a b c
+ + =
+ − =
− − =
−
. Sabendo-se que a, b e c são números reais não
nulos, é incorreto afirmar que
a) |𝑎𝑎| + |𝑏𝑏| + |𝑐𝑐| ∈ (ℝ − ℚ)
b) 2 2 2
a b c 2
+ + >
c) O determinante da matriz
2
2
2
a 1 3
0 b 4
0 0 c
é igual a
1
.
6
d) 2 2 2
1 1 1
a b c
+ + é par.
05. (Epcar (Afa) 2019) No ano de 2017, 22 alunos da EPCAR foram premiados na Olimpíada Brasileira de Matemática das
Escolas Públicas (OBMEP). Desses alunos, 14 ganharam medalhas, sendo 3 alunos do 3º esquadrão, 9 do 2º esquadrão
e 2 do 1º esquadrão. Os demais receberam menção honrosa, sendo 2 alunos do 3º esquadrão, 4 do 2º esquadrão e 2
do 1º esquadrão. Para homenagear os alunos premiados, fez-se uma fotografia para ser publicada pela Nascentv em uma
rede social. Admitindo-se que, na fotografia, os alunos que receberam menção honrosa ficaram agachados, sempre numa
única ordem, sem alteração de posição entre eles, à frente de uma fila na qual se posicionaram os alunos medalhistas, de
modo que, nesta fila:
- as duas extremidades foram ocupadas somente por alunos do 2º esquadrão que receberam medalha;
- os alunos do 1º esquadrão, que receberam medalha, ficaram um ao lado do outro; e
- os alunos do 3º esquadrão, que receberam medalha, ficaram, também, um ao lado do outro.
Marque a alternativa que contém o número de fotografias distintas possíveis que poderiam ter sido feitas.
a) (72) 9!
⋅
b) (144) 9!
⋅
c) (288) 9!
⋅
d) (864) 9!
⋅
5. AFA 2019
5
06. (Epcar (Afa) 2019) Pela legislação brasileira, atualmente, os ditos “Jogos de Azar” estão proibidos. Tais jogos são, na
maioria das vezes, sustentados pelas perdas dos jogadores que financiam os que vão ter sorte. Esses jogos têm por
condição de existência que, na diferença entre as probabilidades de sorte e azar, predomine o azar. Ainda que proibidos,
bancas de alguns desses jogos são comumente encontradas em festas populares Brasil afora. Exemplo desses jogos é
aquele em que o jogador tem 1 bolinha para lançar sobre uma rampa, levemente inclinada, e deverá acertar uma das
“casinhas” numeradas de 1 a 6. Geralmente, o dono da banca de jogo impõe condições para que o jogador ganhe um
prêmio. Suponha que uma condição de sorte seja, desconsiderando quaisquer outras influências, lançar a bolinha três
vezes sucessivas de modo que, ao final dos três lançamentos, seja observado que a soma dos números das casinhas é igual
a 12. Desse modo, a probabilidade de se ter sorte nesse jogo é
a) menor que 3%.
b) maior que 8% e menor que 10%.
c) maior que 11% e menor que 13%.
d) superior a 13%.
07. (Epcar (Afa) 2019) Um objeto de decoração foi elaborado a partir de sólidos utilizados na rotina de estudos de um
estudante de matemática. Inicialmente, partiu-se de um cubo sólido de volume igual a 3
19.683 cm . Do interior desse
cubo, retirou-se, sem perda de material, um sólido formado por dois troncos de pirâmide idênticos e um prisma reto,
como mostra o esquema da figura a seguir.
- as bases maiores dos troncos estão contidas em faces opostas do cubo;
- as bases dos troncos são quadradas;
- a diagonal da base maior de cada tronco está contida na diagonal da face do cubo que a contém e mede a sua terça
parte;
- a diagonal da base menor de cada tronco mede a terça parte da diagonal da base maior do tronco; e
- os troncos e o prisma têm alturas iguais.
Assim, o volume do objeto de decoração obtido da diferença entre o volume do cubo e o volume do sólido esquematizado
na figura acima, em 3
cm , é um número do intervalo
a) [17.200,17.800]
b) ]17.800,18.400]
c) ]18.400,19.000]
d) ]19.000,19.600]
6. AFA 2019
6
08. (Epcar (Afa) 2019) Considere no plano cartesiano os pontos A (2, 0) e B (6, 4)
− que são simétricos em relação à reta
r. Se essa reta r determina na circunferência 2 2
x y 12x 4y 32 0
+ − − + =uma corda que mede n unidades de
comprimento, então n pertence ao intervalo
a) [4, 5[
b) [3, 4[
c) [2, 3[
d) [1, 2[
09. (Epcar (Afa) 2019) No plano cartesiano, os focos 1
F e 2
F da elipse
2 2
x y
: 1
36 32
α + =
são pontos diametralmente opostos
da circunferência λ e coincidem com as extremidades do eixo real de uma hipérbole equilátera .
β É incorreto afirmar que
a) α β λ
∩ ∩ =
∅
b) 1 2
{F , F }
λ β
∩ =
c) {A, B, C, D},
α β
∩ = sendo A, B, C, D pontos distintos
d) α λ
∩ ≠ ∅
10. (Epcar (Afa) 2019) O domínio mais amplo da função real f definida por 2
a
f(x) log (x 3),
= − em que a ]0,1[,
∈ é
a) [ 2, 2]
−
b) ] 2, 2[
−
c) ] , 2] [2, [
− ∞ − ∪ + ∞
d) [ 2, 3[ ] 3, 2]
− − ∪
11. (Epcar (Afa) 2019) Sobre a inequação
2
3
3x 2x
x ,
x
+
≥ considerando o conjunto universo 𝑈𝑈 ⊂ ℝ, é incorreto afirmar
que possui conjunto solução
a) unitário se 𝑈𝑈 = {𝑥𝑥 ∈ ℝ|𝑥𝑥 > 0 𝑒𝑒 𝑥𝑥 = 2𝑘𝑘, 𝑘𝑘 ∈ ℤ+
∗
}
b) vazio se U [2, [
= + ∞
c) com infinitas soluções se 𝑈𝑈 = {𝑥𝑥 ∈ ℝ|𝑥𝑥 = 2𝑘𝑘 + 1, 𝑘𝑘 ∈ ℤ}
d) com infinitas soluções se 𝑈𝑈 = {𝑥𝑥 ∈ ℝ ∗ |𝑥𝑥 ≤ 2}
12. (Epcar (Afa) 2019) Considere, no plano de Argand-Gauss, os números complexos A e B, sendo 𝐴𝐴
̄ = 𝑥𝑥 − 2𝑖𝑖, 𝑥𝑥 ∈ ℝ e
B 1 i.
= + . Se no produto A B
⋅ tem-se Re(A B) Im(A B),
⋅ ≥ ⋅ então, sobre todos os números complexos A, é correto afirmar
que
a) seus afixos formam uma reta.
b) nenhum deles é imaginário puro.
c) o que possui menor módulo é o que tem o maior argumento principal.
d) existe A tal que | A | | B | .
=
7. AFA 2019
7
13. (Epcar (Afa) 2019) Considere 𝑎𝑎 ∈ ℝ e os polinômios 6 3
a
P(x) x 26x 27
2
= − − e 2
A(x) 2x 4x a,
= + + tais que seus
gráficos se intersectam em um único ponto de ordenada nula. Sabendo também que, graficamente, A(x) tangencia o eixo
Ox,
analise as afirmativas abaixo e escreva V para verdadeira e F para falsa.
( ) O gráfico de P(x) corta o eixo Ox
em dois pontos.
( ) Os afixos das raízes de P(x) que possuem menor módulo formam um triângulo cujo perímetro mede 3 3 unidades
de comprimento.
( ) A soma das raízes imaginárias de P(x) é igual a 2.
−
A sequência correta é
a) V – V – V
b) V – F – F
c) F – V – F
d) F – V – V
14. (Epcar (Afa) 2019) Considere as matrizes
sen x 1
A
1 sen x
−
=
−
e
sen x sen x
B
1 3
=
−
. Se o determinante do produto
matricial AB é um número real positivo ou nulo, então os valores de x, no ciclo trigonométrico, que satisfazem essa
condição estão representados em
a) b) c) d)
15. (Epcar (Afa) 2019) Seja a equação trigonométrica 3 2
tg x 2 tg x tgx 2 0,
− − + = com
3
x [0, 2 [ , .
2 2
π π
π
∈ −
Sobre a
quantidade de elementos distintos do conjunto solução dessa equação, é correto afirmar que são, exatamente,
a) três
b) quatro
c) cinco
d) seis
16. (Epcar (Afa) 2019) Em uma turma de 5 alunos, as notas de um teste de matemática são números inteiros tais que a
média aritmética e a mediana são iguais a 5, e nenhum aluno errou todas as questões. Sabendo que esse conjunto de
notas é unimodal, com moda igual a 8, então a diferença entre a maior nota e a menor nota é um número que é divisor
de
a) 14 b) 15 c) 16 d) 18
8. AFA 2019
8
GABARITO
1 - C 2 - D 3 - A 4 - B 5 - D
6 - C 7 - C 8 - A 9 - D 10 - D
11 - B 12 - C 13 - A 14 - B 15 - D
16 - A