This document contains information about a mathematics exam for Form 5 students at Tunku Besar Burhanuddin Secondary School in Negeri Sembilan, Malaysia. The exam will take place in May 2010 and consists of 40 multiple choice questions to be completed in 1 hour and 15 minutes. The document provides formulas and concepts that may be useful for answering the questions. It also contains instructions for students on how to fill in the answer sheet.
The document contains a mathematics exam paper with 14 pages. It consists of two sections - Section A with 52 marks and Section B with 14 marks. Section A contains 12 multiple choice questions. Various formulas are provided that may help in answering the questions, including formulas for algebra, geometry, trigonometry and calculus.
[END SUMMARY]
Mathematics Form 1-Chapter 6-7 Linear Equalities Linear Inequalities KBSM of ...KelvinSmart2
This document contains notes for a mathematics chapter covering linear equations and inequalities. It introduces key topics like conversions between units of length, mass, time, and money. It also covers solving linear equations in two variables, simultaneous linear equations using substitution and elimination methods, and solving inequalities in one and two variables. Examples of each type of problem are provided.
A 8 100 C 8 099 and width (n + 3) cm. If the depth is 5 cm,
calculate the volume of the box in cm3.
B 8 101 D 8 098
34 Simplify: 6x + 3y - (4x - 2y) A 45n2 + 135n + 135 C 45n2 + 135n
B 45n2 + 135n D 45n2 + 135n + 15
A 2x + 5y C 10x + y
B 2x + 5y D 10x - y
39 The perimeter of a rectangle is 60 cm. If
This document provides instructions and questions for a Mathematics Form 4 exam. It consists of two sections, with Section A containing 12 multiple-choice and short-answer questions worth 52 marks total. Section B contains 4 long-answer questions worth 48 marks total. The questions cover topics such as sets, Venn diagrams, quadratic equations, geometry, statistics, and probability. Students are instructed to show their work and include units in their answers.
1. The document contains 10 mathematics word problems involving the calculation of areas and perimeters of circles, sectors, and composite shapes made of circles and lines. Various formulas involving pi, radii, arcs, and sectors are used.
2. The problems are presented with diagrams and given information such as lengths of arcs, radii, angles. Students are asked to use circle formulas to calculate perimeters and areas.
3. Detailed step-by-step working is shown for each problem, applying concepts like finding arc lengths, subtracting overlapping regions, and combining components of composite shapes.
The document contains examples and exercises on sets and Venn diagrams. It includes questions that ask the reader to:
1) Shade regions in Venn diagrams that represent given sets;
2) Find the number of elements in sets defined within Venn diagrams;
3) List elements that are the intersection or union of given sets; and
4) Draw additional sets in incomplete Venn diagrams based on defined conditions.
Mathematics Form 1-Chapter 8 lines and angles KBSM of form 3 chp 1 ...KelvinSmart2
This document contains notes on lines and angles from mathematics Form 3. It reviews concepts from Form 1 such as classifying angles and defining parallel and perpendicular lines. It then introduces new concepts like transversals, corresponding angles, interior angles, and alternate angles formed when a line crosses two parallel lines. It provides examples of using angle properties to solve problems involving triangles and quadrilaterals. Finally, it includes sample exercises involving finding missing angle measures using the properties of parallel lines crossed by a transversal.
Mathematics Form 1-Chapter 4 Ratio, Rates and Proportion KBSM of form 2 chp 5 KelvinSmart2
The document summarizes key concepts about ratios, rates, and proportions from a math chapter. It defines what a ratio is and how it can be written. It provides examples of how to use ratios to determine if quantities are proportional. It also discusses how to find ratios of three quantities or when multiple ratios are given. The remainder of the document consists of example problems for students to practice applying these ratio and proportion concepts.
The document contains a mathematics exam paper with 14 pages. It consists of two sections - Section A with 52 marks and Section B with 14 marks. Section A contains 12 multiple choice questions. Various formulas are provided that may help in answering the questions, including formulas for algebra, geometry, trigonometry and calculus.
[END SUMMARY]
Mathematics Form 1-Chapter 6-7 Linear Equalities Linear Inequalities KBSM of ...KelvinSmart2
This document contains notes for a mathematics chapter covering linear equations and inequalities. It introduces key topics like conversions between units of length, mass, time, and money. It also covers solving linear equations in two variables, simultaneous linear equations using substitution and elimination methods, and solving inequalities in one and two variables. Examples of each type of problem are provided.
A 8 100 C 8 099 and width (n + 3) cm. If the depth is 5 cm,
calculate the volume of the box in cm3.
B 8 101 D 8 098
34 Simplify: 6x + 3y - (4x - 2y) A 45n2 + 135n + 135 C 45n2 + 135n
B 45n2 + 135n D 45n2 + 135n + 15
A 2x + 5y C 10x + y
B 2x + 5y D 10x - y
39 The perimeter of a rectangle is 60 cm. If
This document provides instructions and questions for a Mathematics Form 4 exam. It consists of two sections, with Section A containing 12 multiple-choice and short-answer questions worth 52 marks total. Section B contains 4 long-answer questions worth 48 marks total. The questions cover topics such as sets, Venn diagrams, quadratic equations, geometry, statistics, and probability. Students are instructed to show their work and include units in their answers.
1. The document contains 10 mathematics word problems involving the calculation of areas and perimeters of circles, sectors, and composite shapes made of circles and lines. Various formulas involving pi, radii, arcs, and sectors are used.
2. The problems are presented with diagrams and given information such as lengths of arcs, radii, angles. Students are asked to use circle formulas to calculate perimeters and areas.
3. Detailed step-by-step working is shown for each problem, applying concepts like finding arc lengths, subtracting overlapping regions, and combining components of composite shapes.
The document contains examples and exercises on sets and Venn diagrams. It includes questions that ask the reader to:
1) Shade regions in Venn diagrams that represent given sets;
2) Find the number of elements in sets defined within Venn diagrams;
3) List elements that are the intersection or union of given sets; and
4) Draw additional sets in incomplete Venn diagrams based on defined conditions.
Mathematics Form 1-Chapter 8 lines and angles KBSM of form 3 chp 1 ...KelvinSmart2
This document contains notes on lines and angles from mathematics Form 3. It reviews concepts from Form 1 such as classifying angles and defining parallel and perpendicular lines. It then introduces new concepts like transversals, corresponding angles, interior angles, and alternate angles formed when a line crosses two parallel lines. It provides examples of using angle properties to solve problems involving triangles and quadrilaterals. Finally, it includes sample exercises involving finding missing angle measures using the properties of parallel lines crossed by a transversal.
Mathematics Form 1-Chapter 4 Ratio, Rates and Proportion KBSM of form 2 chp 5 KelvinSmart2
The document summarizes key concepts about ratios, rates, and proportions from a math chapter. It defines what a ratio is and how it can be written. It provides examples of how to use ratios to determine if quantities are proportional. It also discusses how to find ratios of three quantities or when multiple ratios are given. The remainder of the document consists of example problems for students to practice applying these ratio and proportion concepts.
Mathematics form 1 - Chapter 9-12 By KelvinKelvinSmart2
1. The document is a revision guide for mathematics chapters 9-12 covering topics like angles, parallel and perpendicular lines, polygons, area, perimeter, and geometric solids.
2. It provides definitions, diagrams, and methods for determining properties of different shapes as well as calculating measures like area, perimeter, and volume.
3. Formulas and step-by-step processes are given for finding missing values of angles, lengths of sides, areas of triangles, parallelograms, trapezoids, and volumes of cubes and cuboids.
This document contains a mathematics revision exercise for Form 2 students with questions in three sections:
1) Simple calculation questions involving addition, subtraction, multiplication, and division of fractions, decimals, and integers. Students are asked to show their work.
2) Distance problems calculating the distance between points on a coordinate plane using the distance formula. Students are asked to use a calculator and show their steps.
3) Circumference and diameter problems for circles using pi and the circumference formula. Students are asked to calculate values and find values using the appropriate formulas, showing their work.
The final section contains word problems involving ratios, rates, and coordinate geometry finding the midpoint of a line segment. Students must show their
MATHEMATICS FORM 4 KSSM CHAPTER 6 LINEAR INEQUALITIES IN TWO VARIABLESMISS ESTHER
This mathematics test covers chapter 6 on linear inequalities in two variables. Students are asked to graphically shade the region satisfying the inequalities y + x ≤ 4, y ≥ -1, and y < x, and then write three linear inequalities representing the shaded region. They must also state the three inequalities for a shaded region in diagram 1 and show their steps.
Phileas Fogg makes a wager at the Reform Club that he can circumnavigate the world in 80 days. He travels by steamship and trains, crossing the Suez Canal, visiting India, Hong Kong, Japan, and the United States before returning to England. However, in Liverpool Fix arrests Fogg, believing he robbed the Bank of England. Fogg learns he has finished the journey in 79 days and wins the wager.
Mathematics Mid Year Form 4 Paper 1 Mathematicssue sha
This document provides a summary of key concepts in mathematics form 4, including:
1) Rounding numbers and expressing them in scientific notation.
2) Performing calculations with scientific notation numbers, such as addition/subtraction.
3) Factoring expressions and solving quadratic equations.
4) Calculating gradients of lines from graphs.
5) Working with sets, subsets, and Venn diagrams.
Peperiksaan pertengahan tahun t4 2012 (2)normalamahadi
This document contains 12 mathematics questions testing skills such as solving simultaneous linear equations, quadratic equations, calculating areas and perimeters of shapes, set theory, and logical reasoning. The questions cover topics like functions, sequences, proportions, geometry, and Venn diagrams. Students are required to show their work and provide answers for full marks.
Dokumen tersebut memberikan arahan untuk latihan unit tentang dunia yang indah yang meliputi 5 soalan tentang perbuatan yang baik atau tidak baik beserta pilihan jawapan ya atau tidak.
The document contains 7 multi-step word problems involving the calculation of volumes of various solids. Diagrams are provided with each problem showing the shapes involved. The solids include combinations of cubes, cylinders, cones, pyramids, and prisms. The problems require using formulas for volume, such as those for cubes, cylinders, cones, and pyramids, and performing calculations involving pi, areas, heights and radii. The final section provides the answers to each problem.
This document contains an English exam for third grade students. It has 40 questions across 5 sections - A, B, C, D and E. Section A contains questions that require choosing the best word or phrase to complete sentences. Section B requires choosing sentences that best fit pictures. Section C contains sentence completion questions. Section D and E involve reading passages and answering comprehension questions based on them. The exam is 50 minutes long and students are told not to open the paper until instructed to.
This document provides study materials for the Additional Mathematics SPM examination. It contains one-page notes and worksheets for 10 topics in Additional Mathematics, including functions. The purpose is to help both students and teachers master the concepts through compact graphics and intensive practice exercises. Doing practice questions and understanding concepts are emphasized as important for student success on the SPM exam.
This document contains a mathematics worksheet with multiple choice, fill-in-the-blank, and word problems. It covers skills like rounding numbers, addition, subtraction, multiplication, division, converting units, and analyzing data in tables. The worksheet is divided into sections for rounding, operations, word problems, shape identification, and data analysis. It is meant to assess a student's understanding of basic math concepts.
This document contains 39 multiple choice mathematics questions covering topics such as:
- Standard form
- Significant figures
- Linear equations
- Gradients of straight lines
- Coordinate geometry
- Sets and Venn diagrams
The questions range from basic calculations to more complex problems involving algebraic manipulation and geometric concepts.
This document contains a math skills assessment with 40 multiple choice questions testing various math concepts including:
- Addition
- Subtraction
- Multiplication
- Division
- Word problems
- Place value
- Telling time
- Fractions
- Decimals
- Money amounts
The questions require choosing the correct answer from 4 options to complete number sentences, perform calculations, or solve word problems on a range of math topics for different grade levels.
This document contains instructions for several graph theory problems. It asks the student to:
1) Identify the vertices, edges, and degrees of graphs and calculate the sum of degrees.
2) Calculate the shortest path between two vertices in a graph.
3) Construct two possible subgraphs from a given graph.
4) Calculate the number of handshakes that would occur if five students sat at a circular table and shook hands with each other.
5) Draw a directed weighted graph representing airline routes and flight times and find the fastest route between two cities.
The document contains information about solving equations and calculating values based on ratios, percentages, areas, perimeters, and other geometric concepts. It provides 14 math word problems and questions with multiple choice answers to choose from. The high-level information is that it tests a variety of basic math and geometry skills through multi-step word problems.
The document is the cover page for a confidential mathematics exam for Form Four students in Terengganu, Malaysia. It provides information for candidates taking the exam, including that the exam consists of 40 questions to be answered on the answer sheet provided, and formulas that may be useful are listed on pages 4-5. Candidates are allowed to use a scientific calculator and a booklet of 4-figure mathematical tables.
The document is a mathematics exam paper for Form 4 students in Malaysia. It contains instructions for the exam, mathematical formulas that may be helpful, and 14 multiple choice questions related to mathematics. The questions cover topics like geometry, trigonometry, standard form, and algebraic simplification. The document provides the necessary information and context for students taking the exam to answer the questions.
Mathematics form 1 - Chapter 9-12 By KelvinKelvinSmart2
1. The document is a revision guide for mathematics chapters 9-12 covering topics like angles, parallel and perpendicular lines, polygons, area, perimeter, and geometric solids.
2. It provides definitions, diagrams, and methods for determining properties of different shapes as well as calculating measures like area, perimeter, and volume.
3. Formulas and step-by-step processes are given for finding missing values of angles, lengths of sides, areas of triangles, parallelograms, trapezoids, and volumes of cubes and cuboids.
This document contains a mathematics revision exercise for Form 2 students with questions in three sections:
1) Simple calculation questions involving addition, subtraction, multiplication, and division of fractions, decimals, and integers. Students are asked to show their work.
2) Distance problems calculating the distance between points on a coordinate plane using the distance formula. Students are asked to use a calculator and show their steps.
3) Circumference and diameter problems for circles using pi and the circumference formula. Students are asked to calculate values and find values using the appropriate formulas, showing their work.
The final section contains word problems involving ratios, rates, and coordinate geometry finding the midpoint of a line segment. Students must show their
MATHEMATICS FORM 4 KSSM CHAPTER 6 LINEAR INEQUALITIES IN TWO VARIABLESMISS ESTHER
This mathematics test covers chapter 6 on linear inequalities in two variables. Students are asked to graphically shade the region satisfying the inequalities y + x ≤ 4, y ≥ -1, and y < x, and then write three linear inequalities representing the shaded region. They must also state the three inequalities for a shaded region in diagram 1 and show their steps.
Phileas Fogg makes a wager at the Reform Club that he can circumnavigate the world in 80 days. He travels by steamship and trains, crossing the Suez Canal, visiting India, Hong Kong, Japan, and the United States before returning to England. However, in Liverpool Fix arrests Fogg, believing he robbed the Bank of England. Fogg learns he has finished the journey in 79 days and wins the wager.
Mathematics Mid Year Form 4 Paper 1 Mathematicssue sha
This document provides a summary of key concepts in mathematics form 4, including:
1) Rounding numbers and expressing them in scientific notation.
2) Performing calculations with scientific notation numbers, such as addition/subtraction.
3) Factoring expressions and solving quadratic equations.
4) Calculating gradients of lines from graphs.
5) Working with sets, subsets, and Venn diagrams.
Peperiksaan pertengahan tahun t4 2012 (2)normalamahadi
This document contains 12 mathematics questions testing skills such as solving simultaneous linear equations, quadratic equations, calculating areas and perimeters of shapes, set theory, and logical reasoning. The questions cover topics like functions, sequences, proportions, geometry, and Venn diagrams. Students are required to show their work and provide answers for full marks.
Dokumen tersebut memberikan arahan untuk latihan unit tentang dunia yang indah yang meliputi 5 soalan tentang perbuatan yang baik atau tidak baik beserta pilihan jawapan ya atau tidak.
The document contains 7 multi-step word problems involving the calculation of volumes of various solids. Diagrams are provided with each problem showing the shapes involved. The solids include combinations of cubes, cylinders, cones, pyramids, and prisms. The problems require using formulas for volume, such as those for cubes, cylinders, cones, and pyramids, and performing calculations involving pi, areas, heights and radii. The final section provides the answers to each problem.
This document contains an English exam for third grade students. It has 40 questions across 5 sections - A, B, C, D and E. Section A contains questions that require choosing the best word or phrase to complete sentences. Section B requires choosing sentences that best fit pictures. Section C contains sentence completion questions. Section D and E involve reading passages and answering comprehension questions based on them. The exam is 50 minutes long and students are told not to open the paper until instructed to.
This document provides study materials for the Additional Mathematics SPM examination. It contains one-page notes and worksheets for 10 topics in Additional Mathematics, including functions. The purpose is to help both students and teachers master the concepts through compact graphics and intensive practice exercises. Doing practice questions and understanding concepts are emphasized as important for student success on the SPM exam.
This document contains a mathematics worksheet with multiple choice, fill-in-the-blank, and word problems. It covers skills like rounding numbers, addition, subtraction, multiplication, division, converting units, and analyzing data in tables. The worksheet is divided into sections for rounding, operations, word problems, shape identification, and data analysis. It is meant to assess a student's understanding of basic math concepts.
This document contains 39 multiple choice mathematics questions covering topics such as:
- Standard form
- Significant figures
- Linear equations
- Gradients of straight lines
- Coordinate geometry
- Sets and Venn diagrams
The questions range from basic calculations to more complex problems involving algebraic manipulation and geometric concepts.
This document contains a math skills assessment with 40 multiple choice questions testing various math concepts including:
- Addition
- Subtraction
- Multiplication
- Division
- Word problems
- Place value
- Telling time
- Fractions
- Decimals
- Money amounts
The questions require choosing the correct answer from 4 options to complete number sentences, perform calculations, or solve word problems on a range of math topics for different grade levels.
This document contains instructions for several graph theory problems. It asks the student to:
1) Identify the vertices, edges, and degrees of graphs and calculate the sum of degrees.
2) Calculate the shortest path between two vertices in a graph.
3) Construct two possible subgraphs from a given graph.
4) Calculate the number of handshakes that would occur if five students sat at a circular table and shook hands with each other.
5) Draw a directed weighted graph representing airline routes and flight times and find the fastest route between two cities.
The document contains information about solving equations and calculating values based on ratios, percentages, areas, perimeters, and other geometric concepts. It provides 14 math word problems and questions with multiple choice answers to choose from. The high-level information is that it tests a variety of basic math and geometry skills through multi-step word problems.
The document is the cover page for a confidential mathematics exam for Form Four students in Terengganu, Malaysia. It provides information for candidates taking the exam, including that the exam consists of 40 questions to be answered on the answer sheet provided, and formulas that may be useful are listed on pages 4-5. Candidates are allowed to use a scientific calculator and a booklet of 4-figure mathematical tables.
The document is a mathematics exam paper for Form 4 students in Malaysia. It contains instructions for the exam, mathematical formulas that may be helpful, and 14 multiple choice questions related to mathematics. The questions cover topics like geometry, trigonometry, standard form, and algebraic simplification. The document provides the necessary information and context for students taking the exam to answer the questions.
The document is a mathematics exam paper for Form 4 students in Malaysia. It contains instructions for the exam, mathematical formulas that may be helpful, and 14 multiple choice questions related to mathematics. The questions cover topics like geometry, trigonometry, standard form, and algebraic simplification. The document provides the necessary information and context for students taking the exam to answer the questions.
The document is a mathematics exam paper for Form Four students in Negeri Sembilan, Malaysia. It consists of 40 multiple choice questions testing various mathematical concepts. The questions cover topics like rounding, standard form, algebraic expressions, sets, probability, geometry, trigonometry, and more. The document provides mathematical formulas that may be helpful in answering the questions.
This document contains information for candidates regarding a mathematics exam paper. It provides instructions that candidates should answer all 40 questions, blacken only one answer for each question on the answer sheet, and may use a non-programmable scientific calculator. It also lists several mathematical formulae that may be helpful in answering the questions. The exam paper contains 21 pages and consists of multiple choice questions testing various mathematics concepts.
The document is a mathematics exam paper for Form 4 students in Malaysia. It contains 22 pages with questions in two sections - Section A and Section B. Section A contains 13 multiple choice questions worth a total of 52 marks. Section B contains 4 questions worth a total of 64 marks. The paper provides formulas that may be helpful in answering the questions covering topics such as algebra, geometry, trigonometry, and statistics.
This document is the first paper of a diagnostic exam in mathematics for Form 4 students in Malaysia. It contains 40 multiple choice questions about mathematical concepts. The first few pages provide information for students on the structure of the exam and a list of mathematical formulae that may be useful in answering the questions. Then the questions begin, covering topics such as operations with scientific notation, solving equations, geometry, and other common areas of mathematics.
The document is the cover page for a mathematics exam paper for Form 4 students in Malaysia. It provides instructions for students, including the time allotted (1 hour and 15 minutes), a reminder not to open the paper until instructed, and information that the paper contains 40 questions. It also lists some common mathematical formulas that may be useful for answering the questions.
JAWAPAN BUKU PEPERIKSAAN MATEMATIK SPM.pdfPuvaVari1
This document contains the answers and explanations for a mathematics SPM exam paper from 2021. It provides the correct answers for 37 multiple choice questions from the exam, labeled Questions 1 through 37. For each question, it explains the reasoning behind the correct answer and why the other answer choices are incorrect. The document is written in both English and Malay.
1. The question provides a table of mathematical formulae that may be helpful in answering questions, including formulae for relations, shapes and space, and trigonometric ratios.
2. A graphing question asks the student to graph an equation, find the value of y for a given x, and draw a line to find the values of x that satisfy a second equation.
3. A probability question provides two boxes with cards and asks the student to calculate the probability of picking certain combinations of cards from the two boxes.
1. The document contains mathematical formulas and definitions that may be helpful in answering questions on a Mathematics exam. It includes formulas for shapes, space, averages, probabilities, and other topics.
2. The document consists of 5 pages of mathematical formulas presented in both Malay and English. Formulas are provided for areas, volumes, averages, probabilities, geometry shapes and other concepts.
3. The formulas are presented with commonly used symbols to help students answer exam questions efficiently. Definitions of key terms are also included to aid understanding.
This document is a mathematics exam paper from the Malaysian Ministry of Education for the 2012 Pentaksiran Diagnostik Akademik Sekolah Berasrama Penuh assessment. It contains 40 multiple choice questions testing various mathematics concepts. The questions are in Malay and include diagrams. Formulas that may be useful for answering the questions are provided.
This document provides information about a mathematics higher exam, including:
1) It is a non-calculator paper for section A and calculators may be used for section B.
2) Section A contains 20 multiple choice questions worth 40 marks. Section B contains 3 longer form questions worth 30 marks.
3) The document provides standard formulas, derivatives, and integrals that may be useful for the exam questions. It also includes worked examples of completing the answer sheet for section A.
Midyearform5paper22010mathematics 100730001403-phpapp01Ragulan Dev
This document contains a mathematics exam paper for Form 5 students. It consists of two sections - Section A with 12 multiple choice questions worth a total of 52 marks, and Section B with 4 structured questions worth a total of 48 marks. The paper tests students on topics including algebra, geometry, trigonometry, statistics and probability. It provides various diagrams to accompany the questions. Several formulae are also listed that may help students to answer the questions.
Q1Perform the two basic operations of multiplication and divisio.docxamrit47
Q1
Perform the two basic operations of multiplication and division to a complex number in both rectangular and polar form, to demonstrate the different techniques.
· Dividing complex numbers in rectangular and polar forms.
· Converting complex numbers between polar and rectangular forms and vice versa.
Q2
Calculate the mean, standard deviation and variance for a set of ungrouped data
· Completing a tabular approach to processing ungrouped data.
Q3
Calculate the mean, standard deviation and variance for a set of grouped data
· Completing a tabular approach to processing grouped data having selected an appropriate group size.
Q4
Sketch the graph of a sinusoidal trig function and use it to explain and describe amplitude, period and frequency.
· Calculate various features and coordinates of a waveform and sketch a plot accordingly.
· Explain basic elements of a waveform.
Q5
Use two of the compound angle formulae and verify their results.
· Simplify trigonometric terms and calculate complete values using compound formulae.
Q6
Find the differential coefficient for three different functions to demonstrate the use of function of a function and the product and quotient rules
· Use the chain, product and quotient rule to solve given differentiation tasks.
Q7
Use integral calculus to solve two simple engineering problems involving the definite and indefinite integral.
· Complete 3 tasks; one to practise integration with no definite integrals, the second to use definite integrals, the third to plot a graph and identify the area that relates to the definite integrals with a calculated answer for the area within such.
Q8
Use the laws of logarithms to reduce an engineering law of the type y = axn to a straight line form, then using logarithmic graph paper, plot the graph and obtain the values for the constants a and n.
· See Task.
Q9
Use complex numbers to solve a parallel arrangement of impedances giving the answer in both Cartesian and polar form
· See Task.
Q10
Use differential calculus to find the maximum/minimum for an engineering problem.
· See Task.
Q11
Using a graphical technique determine the single wave resulting from a combination of two waves of the same frequency and then verify the result using trig formulae.
· See Task.
Q12
Use numerical integration and integral calculus to analyse the results of a complex engineering problem
· See Task.
Level of Detail in
Solution
s: Need to show work leading to final answer
Need
Question 1
(a) Find:
(4 + i2)
(1 + i3)
Use the rules for multiplication and division of complex numbers in rectangular form.
(b) Convert the answer in rectangular form to polar form
(c) Repeat Q1a by first converting the complex numbers to polar form and then using the rules for multiplication and division of complex numbers in polar form.
(d) Convert the answer in polar form to rectangular form.
Question 2
The following data within the working area consists of measurements of resistor values from a producti ...
The document provides information about a seminar on excellence for the PMR examination, including its objectives to help students understand the exam requirements and marking scheme. It discusses key points about correctly writing answers and interpreting different types of questions. Examples of objective and subjective questions are also included to demonstrate the format and how to solve different math problems.
This document provides information and questions related to a UPSR mathematics exam consisting of 40 multiple choice questions. It includes instructions for answering the questions, diagrams related to some questions, and the questions themselves, which cover a range of mathematics topics including operations with whole numbers, decimals, percentages, time, measurement, geometry, and word problems.
This document contains information about a diagnostic mathematics exam for the Malaysian Certificate of Education (SPM) taken in August 2012. It provides instructions for the exam, including that it contains 40 multiple choice questions to be completed in 1 1/4 hours. It also lists several mathematical formulas that may be useful for answering the questions.
This document contains a 31 page mathematics examination paper for SPM 2013. It includes 19 multiple choice questions related to mathematical formulas, shapes and space, algebra, trigonometry, and coordinate geometry. The questions require calculations, applying formulas, analyzing diagrams, and expressing algebraic expressions in simplest form.
This document contains a 31 page mathematics examination paper for SPM 2013. It includes 19 multiple choice questions related to mathematical formulas, shapes and space, algebra, trigonometry, and coordinate geometry. The questions require calculations, applying formulas, analyzing diagrams, and expressing algebraic expressions in simplest form.
Similar to Mathematics Mid Year Form 5 Paper 1 2010 (20)
This document contains 11 math word problems involving ratios, rates, and proportions. The problems cover a variety of topics including sharing money, comparing weights and distances, dividing groups of students or shares into ratios, and finding missing values in ratio relationships. Students are asked to show the step-by-step work to solve each problem and find the requested value, such as a total amount, difference, or individual share.
This document contains 10 math word problems involving geometry concepts like triangles, rectangles, trapezoids, and squares. The problems involve calculating areas, perimeters, lengths and distances. Readers are asked to solve each problem and show their work. The high-level goal is to practice applying geometric formulas and reasoning skills to calculate values related to 2D shapes.
This document appears to be a math test for a student containing 6 word problems involving linear equations. The first problem involves finding a number such that adding 3 to 4 times the number equals subtracting 7 from 5 times the number. The second problem asks the student to find the value of x given the perimeter and side lengths of a square. The third problem involves finding the height y of a triangle given its base and area. The fourth problem asks the student to find Khamis's weight given the sum of her weight and her sister's weight. The fifth problem involves finding the length of a parallelogram given its height and area. The sixth problem involves solving for the variable y in an equation involving fractions and addition/sub
Dokumen tersebut merupakan kertas soalan untuk ujian akhir tahun mata pelajaran Pendidikan Moral Tingkatan 2. Terdiri daripada lima bahagian yang meliputi soalan pilihan ganda, benar atau salah, lengkapkan kata kosong, dan nyatakan nilai. Soalan terakhir meminta senarai dan cadangan serta kesan kemalangan jalan raya.
Latihan Pendidikan Moral Ting.1 - Kebebasan Beragamasue sha
Dokumen tersebut membahas perayaan Thaipusam di Malaysia dimana penganut agama Hindu akan berkumpul untuk melakukan upacara keagamaan seperti berdoa, menunaikan hajat, dan menaiki tangga sambil mengusung kavadi. Dokumen juga menyentuh tentang kebebasan beragama di Malaysia dimana berbagai kepercayaan dan amalan dapat dijalankan secara harmonis.
Nota Pendidikan Moral Ting. 1 Unit 23 : Berkorban Untuk Negarasue sha
Dokumen tersebut membahas tentang pengorbanan untuk negara. Ia mendefinisikan pengorbanan sebagai kesediaan untuk menyerahkan hidup demi negara. Dokumen tersebut kemudian memberikan contoh tokoh-tokoh sejarah Malaysia yang berjuang untuk negara. Akhirnya dokumen tersebut menjelaskan peranan pasukan keamanan seperti angkatan darat, laut, dan udara dalam menjaga keamanan dan kedaulatan negara.
Nota Pendidikan Moral Ting.1 bagi Bidang 5 : Hak Asasi Manusiasue sha
Unit 24 membincangkan tentang perlindungan hak kanak-kanak untuk memastikan mereka mendapat makanan, tempat tinggal, pendidikan, perlindungan dan kasih sayang agar dapat membesar dengan sihat dan gembira. Unit 25 menekankan perlunya memberikan layanan yang adil kepada wanita dengan memberikan peluang pendidikan dan kerjaya serta mengiktiraf sumbangan mereka. Unit 28 membincangkan hak asasi pengguna untuk mendapat keperluan asas, membu
LINES AND PLANES IN 3 DIMENSION - SET INDUCTIONsue sha
This document discusses various places and things without providing many details, asking questions about similarities between pictures and who lives in a particular place. It touches on looking at different things, visiting places, and does not seem to have a clear topic or message that can be succinctly summarized in 3 sentences or less.
Analisa SPM 2011 2012 SMK Tunku Besar Burhanuddinsue sha
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The document summarizes the 2012 and 2011 examination results for SMK Tunku Besar Burhanuddin in Negeri Sembilan, Malaysia. It shows the pass rates and grade distributions for each subject. The overall pass rates were 64.3% in 2012 and 69.7% in 2011. Most subjects had high pass rates above 90% except for English and Arabic. The top students for the religious stream were Nurshamila Natasya bt. Shamsuddin and for the normal stream were Fatin Najiha bt. Abdul Hamid.
SMK Tunku Besar Burhanuddin melaksanakan program 5 bintang yang memberi peluang kepada semua pelajar untuk mencapai target prestasi tinggi dan mengiktiraf serta menghargai pelajar berprestasi.
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Chapter wise All Notes of First year Basic Civil Engineering.pptxDenish Jangid
Chapter wise All Notes of First year Basic Civil Engineering
Syllabus
Chapter-1
Introduction to objective, scope and outcome the subject
Chapter 2
Introduction: Scope and Specialization of Civil Engineering, Role of civil Engineer in Society, Impact of infrastructural development on economy of country.
Chapter 3
Surveying: Object Principles & Types of Surveying; Site Plans, Plans & Maps; Scales & Unit of different Measurements.
Linear Measurements: Instruments used. Linear Measurement by Tape, Ranging out Survey Lines and overcoming Obstructions; Measurements on sloping ground; Tape corrections, conventional symbols. Angular Measurements: Instruments used; Introduction to Compass Surveying, Bearings and Longitude & Latitude of a Line, Introduction to total station.
Levelling: Instrument used Object of levelling, Methods of levelling in brief, and Contour maps.
Chapter 4
Buildings: Selection of site for Buildings, Layout of Building Plan, Types of buildings, Plinth area, carpet area, floor space index, Introduction to building byelaws, concept of sun light & ventilation. Components of Buildings & their functions, Basic concept of R.C.C., Introduction to types of foundation
Chapter 5
Transportation: Introduction to Transportation Engineering; Traffic and Road Safety: Types and Characteristics of Various Modes of Transportation; Various Road Traffic Signs, Causes of Accidents and Road Safety Measures.
Chapter 6
Environmental Engineering: Environmental Pollution, Environmental Acts and Regulations, Functional Concepts of Ecology, Basics of Species, Biodiversity, Ecosystem, Hydrological Cycle; Chemical Cycles: Carbon, Nitrogen & Phosphorus; Energy Flow in Ecosystems.
Water Pollution: Water Quality standards, Introduction to Treatment & Disposal of Waste Water. Reuse and Saving of Water, Rain Water Harvesting. Solid Waste Management: Classification of Solid Waste, Collection, Transportation and Disposal of Solid. Recycling of Solid Waste: Energy Recovery, Sanitary Landfill, On-Site Sanitation. Air & Noise Pollution: Primary and Secondary air pollutants, Harmful effects of Air Pollution, Control of Air Pollution. . Noise Pollution Harmful Effects of noise pollution, control of noise pollution, Global warming & Climate Change, Ozone depletion, Greenhouse effect
Text Books:
1. Palancharmy, Basic Civil Engineering, McGraw Hill publishers.
2. Satheesh Gopi, Basic Civil Engineering, Pearson Publishers.
3. Ketki Rangwala Dalal, Essentials of Civil Engineering, Charotar Publishing House.
4. BCP, Surveying volume 1
Philippine Edukasyong Pantahanan at Pangkabuhayan (EPP) CurriculumMJDuyan
(𝐓𝐋𝐄 𝟏𝟎𝟎) (𝐋𝐞𝐬𝐬𝐨𝐧 𝟏)-𝐏𝐫𝐞𝐥𝐢𝐦𝐬
𝐃𝐢𝐬𝐜𝐮𝐬𝐬 𝐭𝐡𝐞 𝐄𝐏𝐏 𝐂𝐮𝐫𝐫𝐢𝐜𝐮𝐥𝐮𝐦 𝐢𝐧 𝐭𝐡𝐞 𝐏𝐡𝐢𝐥𝐢𝐩𝐩𝐢𝐧𝐞𝐬:
- Understand the goals and objectives of the Edukasyong Pantahanan at Pangkabuhayan (EPP) curriculum, recognizing its importance in fostering practical life skills and values among students. Students will also be able to identify the key components and subjects covered, such as agriculture, home economics, industrial arts, and information and communication technology.
𝐄𝐱𝐩𝐥𝐚𝐢𝐧 𝐭𝐡𝐞 𝐍𝐚𝐭𝐮𝐫𝐞 𝐚𝐧𝐝 𝐒𝐜𝐨𝐩𝐞 𝐨𝐟 𝐚𝐧 𝐄𝐧𝐭𝐫𝐞𝐩𝐫𝐞𝐧𝐞𝐮𝐫:
-Define entrepreneurship, distinguishing it from general business activities by emphasizing its focus on innovation, risk-taking, and value creation. Students will describe the characteristics and traits of successful entrepreneurs, including their roles and responsibilities, and discuss the broader economic and social impacts of entrepreneurial activities on both local and global scales.
Beyond Degrees - Empowering the Workforce in the Context of Skills-First.pptxEduSkills OECD
Iván Bornacelly, Policy Analyst at the OECD Centre for Skills, OECD, presents at the webinar 'Tackling job market gaps with a skills-first approach' on 12 June 2024
1. SULIT
1
1449/1
SULIT
1449/1
Kertas 1
Matematik
Kertas 1
Mei 2010
1 jam
UNIT PEPERIKSAAN & PENILAIAN
SEKOLAH MENENGAH KEBANGSAAN TUNKU BESAR BURHANUDDIN
71550 SERI MENANTI, NEGERI SEMBILAN
PEPERIKSAAN PERTENGAHAN TAHUN
TINGKATAN 5 2010
MATEMATIK
Kertas 1
Satu jam lima belas minit
JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU
1. Kertas soalan ini mengandungi 40 soalan.
2. Jawab semua soalan.
3. Jawab dengan menghitamkan ruangan yang betul pada kertas jawapan.
4. Bagi setiap soalan hitamkan satu ruangan sahaja.
5. Sekiranya anda hendak menukarkan jawapan, padamkan tanda yang telah
dibuat. Kemudian hitamkan jawapan yang baru.
6. Rajah yang mengiringi soalan tidak dilukiskan mengikut skala kecuali
dinyatakan.
7. Anda dibenarkan menggunakan kalkulator saintifik yang tidak boleh diprogram.
Di Sediakan Oleh Di Semak Oleh
__________________________
(Sunita binti Mukhtar )
Kertas soalan ini mengandungi 15 halaman bercetak
1449/1@2010 [Lihat sebelah
SULIT
2. Rumus-rumus berikut boleh membantu anda menjawab soalan. Simbol-simbol yang
diberi adalah yang biasa digunakan.
PERKAITAN
m+n
1. a ×a = a
m n
.
2. am ÷ an = am−n
3. (a )
m n
= a mn
1 d − b
4. A−1 =
ad − bc − c a
n( A)
5. P ( A) =
n( S )
6. P ( A' ) = 1 − P ( A)
7. Jarak = ( x1 − x2 ) 2 + ( y1 − y2 ) 2
8. Titik Tengah
( x, y ) = x1 + x2 , y1 + y2
2 2
jarak yang dilalui
9. Purata laju =
masa yang diambil
hasil tambah nilai data
10. Min =
bilangan data
hasil tambah( nilai titik tengah × ke ker apan )
11. Min =
hasil tambah ke ker apan
12. Teorem Pithagoras
c 2 = a 2 + b2
y2 − y1
13. m=
x2 − x1
p int asan − y
14. m=−
p int asan − x
BENTUK DAN RUANG
2
3. 1
1. Luas trapezium = × hasil tambah dua sisi selari × tinggi
2
2. Lilitan bulatan = πd = 2πj
3. Luas bulatan = πj2
4. Luas permukaan melengkung silinder = 2πjt
5. Luas permukaan sfera = 4πj2
6. Isipadu prisma tegak = luas keratan rentas × panjang
7. Isipadu silinder = πj2t
1 2
8. Isipadu kon = πj t
3
4 3
9. Isipadu sfera = πj
3
1
10. Isipadu piramid tegak = × luas tapak × tinggi
3
11. Hasil tambah sudut pedalaman poligon = ( n − 2 ) × 180 0
panjang lengkok sudut pusat
12. =
lili tan bula tan 360 0
luas sektor sudut pusat
13. =
luas bula tan 360 0
PA '
14. Faktor skala, k =
PA
15. Luas imej = k 2 × luas objek
3
4. Answer All Questions
1 Round of 0.0040055 to three significant figures
A 0.004 C 0.00401
B 0.0040 D 0.004006
2 8.11 × 10 −4 =
A 0.0000811 C 81100
B 0.000811 D 811000
3 Express 351 000 in standard form
A 3.51 × 10 3 C 3.51 × 10 -3
B 3.51 × 10 5 D 3.51 × 10 -5
4 The area of rectangular plot is 7.2km2. Its width is 2 400m. The length, in m, of the
nursery plot is
A 3 × 103 C 4.8 × 103
B 3 × 104 D 4.8 × 104
5 Express 1768 as a number in base five
A 1015 C 2315
B 1265 D 10015
6 111012 + 11102 =
A 1000112 C 1011112
B 1110012 D 1010112
P T
7 y
Q S
R
W
x U
V
Diagram 1
4
5. In Diagram 1, PQRST is a regular octagon. QRUVW is a regular pentagon . Find the
value of x + y
A 153 C 175.5
B 165.5 D 243
8
P Q
T
yo
30
°
S R
Diagram 2
In Diagram 2, PQRS is a square and RQT is a isosceles. Find the value of y.
A 85 C 105
B 100 D 115
Q
9 C
A
O
12
8° xo
P B S
Diagram 3
In Diagram 3, PAQ dan PBS is a tangent to the circle centre
AC = BC. Value of x is
A 32 C 58
B 52 D 64
10 In Diagram 4 shows two vertical poles, PQ and YX , on the horizontal plane,
P
Y
25m
Q 10 m
X
Diagram 4 5
6. The angle of depression of vertex Y from vertecx P is 420. Calculate the angle
of elevation of vertex Y from vertex Q
A 32
B 410 59’
C 570 51’
D 680 11’
X
11 12 cm
A B C
6 cm
Y
Diagram 5
In Diagram 5 , ABC is a straight line. BC is 10. Find the value cos ∠ABX
1 3
A − C −
5 5
2 4
B − D −
5 5
12 Which one of the following graphs represents y = cos xo for 0° ≤ x ≤ 180 ° ?
A B
y y
1 1
x x
0 90° 180° 0 90° 180°
-1 -1
C D
y
y
1
1
x
x 0 90° 180°
0 90° 180°
-1
-1
6
7. 13 Diagram 6 shows a right prism with a horizontol base ELKG.
F J
E L
G K
DIAGRAM 6
Name the angle between line FK and the plane EFG.
A ∠KFE C ∠KFG
B ∠KEF D ∠KGF
14 110112 + 1112 =
A 1000102 C 1100112
B 1011002 D 1111012
15 Diagram 7 , M’ is the image of M under a translation. T’ is the image of T under a same
translation.
Diagram 7
A (-4, 7) C (4, 1)
B (-2, 5) D (6, -1)
16 In Diagram 8, the triangle PQR is the image of the triangle SQT under an enlargement
7
8. Diagram 8
Find the scale of the enlargemet
1 1
A C
3 2
B 2 D 3
17 Diagram 9 shows two straight lines, ST and S’T’ drawn on a square grid
S’T’ is the image of ST under a rotation. Which of points A, B, C, D is the centre
of the rotation
Diagram 9
18 (2 x)(3 y ) − 2( x − 3 y ) 2 =
A − 2x 2 + 18 xy + 18 y 2
B − 2x 2 + 18 xy − 18 y 2
C − 2x 2 + 6 xy − 18 y 2
D − 2x 2 − 6 xy + 18 y 2
2
19 − 3 = 5, then p =
p
1 1
A C
16 4
1 1
B D
8 2
4u − v 8 − v
20 − =
uv 2v
1
A
2u
u−2
B
2u
u+2
C
2u
−u −2
D
2u
8
9. r 5
21 Given that − = 3r. Express r in terms of s.
s 3s
5 5
A C
3(1 − 3s ) 3(1 + 3s)
5 3(3s − 1)
B D
3(3s − 1) 5
( )
4
22 Simplify m 2 ÷ m5
A m C m11
13
B m3 D m
23 The gradient of the straight line 4x - 2y = 3
A -4 C 2
B -2 D 4
9
Given that 3 =
x
24 2x , find the value of x
3
2
A 2 C
3
1
B 1 D
2
25 List all the integers of t that saticfy the inequlities 3t − 8 < t ≤ 5 + 4t
A 0, 1, 2, 3 C -1, 0, 1,2,3,4
B -1, 0, 1, 2 ,3 D -2, -1, 0, 1, 2,3,4
1 2 − 1
26 +3 − =
4 5 6
4 8
A
3 C
1
6 8
B
13 D
13
27 The region defined by the inequalities y ≥ 2 x + 4 .
A B
y y
4 x
2 9
x
-2 -4
10. C y D
y
4 4
x x
2 2
4 − 4 12
28 If ( − 1 q ) =
p 2 , then p + q =
− 6
A -5 C 1
B -1 D 2
4 4 2 3
29 =
2 2 −1 2
8 16 4 16
A C
−2 10 2 10
14 2 4 8
B
3 0 D
9 10
30 Which graph represents y = x3 + 4?
A y B y
4
4
x x
O O
C D
y y
x
O x
O
-4
-4
31 Find the x-intercept of the straight line 3 y + 5 x = 5
A −2 C 1
10
11. B −1 D 2
32 Given that P ∪ Q = Q, R ∩ Q = R, and P '∩ R = R. the Venn diagram that represents
these relationships is
A B
R Q
P R P
Q
C D
Q R
P P
R Q
33 Diagram 10 is a venn diagram which shows the universal set ξ = P and set Q
ξ P Q
Diagram 10
The shaded region in the venn diagram represents the sets
A P’ ∩ Q’ C P ∩ Q’
B P’ ∩ Q D P ∩Q
34 Diagram 11 is venn diagram which shows the elements of sets P,Q and R
11
12. .5 .6 .4 .3 .1
Diagram 11 2
If the universal set ξ = P ∪ Q ∪ R, then set Q ' . is
A { 1,2 } C {1,2,5 }
B { 3, 6 } D {3,4,6 }
x2
35 It is given that T ∝ and T = 32 when x = 4 and w = 6. Express T in terms of w and
w
x.
3x 2 24 x 2
A B
w w
x2 12 x 2
C D
12 w w
1 1
36 Given that Q ∝ and Q = 45 when R = and S = 6 . Calculate value of S when
RS 2
1
R= and Q = 27.
3
A 9 C 36
B 15 D 135
37 Diagram 12 shows some number cards
1321 27 29 33 35
Diagram 12
A card is picked at random. State the probability that a prime number is picked
A 3/2 C 1/2
B 1/3 D 1/6
38 Class 5 Bestari consists of male students and female srudents. The number of male
students in the class is 16. If one student is chosen at random, find the probability of
choosing a male student is 4 / 9. Determine the number of female in 5 Bestari ?
A 20 C 28
B 24 D 36
12
13. 39 Table 1 shows the number of cars that visited a service centre for 5 consecutive
days
Days Number of cars
Monday 20
Tuesday 40
Wednesday 50
Thursday 30
Friday 40
Table 1
The mean is
A 35 C 40
B 36 D 50
40 Table 2 shows the distribution of the scores of 40 students in a health quiz
Score 1 2 3 4
Frequency 6 17 13 4
Table 2
If the above data is represented using a pie chart, then the angle of the
sector of the modal score is
A 900 C 1530
B 1170 D 2700
END OF THE QUESTIONS PAPER
13