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.
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.
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.
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.
1. The document is a chemistry exam paper containing multiple choice and structured questions testing knowledge of chemistry concepts and skills such as writing chemical equations and calculations.
2. It includes questions testing knowledge of the periodic table, molecular and empirical formulas, chemical reactions like acid-base titration and electrolysis, and acid-base properties.
3. Diagrams and tables are provided to support questions about apparatus set-ups, chemical equations, and recording results of titration experiments.
This document provides a revision on form 4 chemistry topics, specifically focusing on section A which contains 42 marks worth of questions to be answered in 60 minutes. The questions cover various topics including the periodic table, ions, compounds, electrolysis, acids and bases, and concentration calculations. The document tests understanding of concepts like relative atomic mass, chemical formulas, half equations, and acid-base reactions through multiple choice and short answer questions referring to diagrams, tables, and chemical equations provided.
Koleksi soalan percubaan add math kertas 1
1. peperiksaan percubaan sekolah asrama penuh dan jawapan
2. pepriksaan percubaan negeri perak dan jawapan
3. peperiksaan percubaan negeri selangor dan jawapan
4. peperiksaan percubaan negeri terengganu dan jawapan
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.
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.
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.
1. The document is a chemistry exam paper containing multiple choice and structured questions testing knowledge of chemistry concepts and skills such as writing chemical equations and calculations.
2. It includes questions testing knowledge of the periodic table, molecular and empirical formulas, chemical reactions like acid-base titration and electrolysis, and acid-base properties.
3. Diagrams and tables are provided to support questions about apparatus set-ups, chemical equations, and recording results of titration experiments.
This document provides a revision on form 4 chemistry topics, specifically focusing on section A which contains 42 marks worth of questions to be answered in 60 minutes. The questions cover various topics including the periodic table, ions, compounds, electrolysis, acids and bases, and concentration calculations. The document tests understanding of concepts like relative atomic mass, chemical formulas, half equations, and acid-base reactions through multiple choice and short answer questions referring to diagrams, tables, and chemical equations provided.
Koleksi soalan percubaan add math kertas 1
1. peperiksaan percubaan sekolah asrama penuh dan jawapan
2. pepriksaan percubaan negeri perak dan jawapan
3. peperiksaan percubaan negeri selangor dan jawapan
4. peperiksaan percubaan negeri terengganu dan jawapan
This document provides notes on additional mathematics for Form 4 students. It includes definitions and examples of functions, inverse functions, quadratic equations, and logarithms. Some key points summarized:
1. A function f maps objects to images. To find the inverse function f-1, change f(x) to y and solve for x in terms of y.
2. To find the roots of a quadratic equation, one can use factorisation, the quadratic formula, or complete the square. The nature of the roots depends on the sign of b2 - 4ac.
3. To solve a system of equations involving one linear and one non-linear equation, one can substitute one equation into the other and solve
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.
1. The document describes 6 experiments involving chemical reactions and properties. It includes questions about the experiments and reactions.
2. Experiment 1 involves electrolysis of silver nitrate and copper sulfate solutions. Observations and half reactions are asked about.
3. Experiment 2 involves heating lead(II) carbonate and identifying the gas produced. Calculations of moles of gas are required.
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 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
1) The document provides guidance on answering physics questions involving experiments. It suggests including an inference, hypothesis, aim, variables, apparatus, procedure, data table, and graph in the answer.
2) A sample question involves stopping distance and relates mass to inertia. The suggested answer structure includes an inference about mass and inertia, a hypothesis testing their relationship, and an experiment using a jigsaw blade, plasticine balls of varying mass, and a stopwatch.
3) The procedure specifies controlling mass, measuring oscillation period, and repeating with different plasticine masses to obtain data for a graph analyzing the relationship between mass and period.
The composite function is gf(x) = 2x - 2. We are given f(x) = 2 - x. To find g, let f(x) = u in gf(x). Then u = 2 - x. Substitute u = 2 - x in gf(x) = 2u - 2. This gives g(x) = 2 - 2x. Therefore, fg(x) = f(2 - 2x) = (2 - (2 - 2x)) = 2x - 2.
1. The document provides a topical test with 6 questions about chemical equations and stoichiometric calculations. It asks the student to write chemical equations for reactions involving sodium, magnesium carbonate, aluminum, copper nitrate, and iron. It also asks the student to calculate relative molecular mass, mass of atoms, relative molecular mass of a gas, a combustion reaction of magnesium, and the volume and number of oxygen molecules from the decomposition of hydrogen peroxide.
This document contains the instructions for three experiments:
1) To compare the reactivity of alkali metals towards oxygen by observing their reactions in different sets. Students are asked to record observations, make predictions, and analyze pH changes.
2) To determine the reaction between barium chloride and potassium chromate solutions by measuring precipitate formation at different volumes. Students must complete a table of results and draw a graph to identify the reacting quantities.
3) To investigate the effect of zinc size on its reaction rate with sulfuric acid by developing a full experiment plan outlining the problem, hypothesis, variables, materials, procedure, and method of collecting data.
This document contains a 2010 Additional Mathematics exam paper from the Sijil Pelajaran Malaysia (SPM). It consists of 25 multiple choice and short answer questions covering topics like:
- Relations and functions
- Quadratic equations
- Geometric and arithmetic progressions
- Trigonometry
- Probability and statistics
The questions require students to apply concepts like domain and range, inverse functions, maximum/minimum values, and normal distributions to solve problems involving graphs, equations, and word problems.
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
The document contains 3 examples of SPM (Malaysian public exam) questions on sets. The first question involves finding the complement of a set R defined in terms of digit sums. The second uses a Venn diagram to represent the complement of a union of sets P and Q. The third is a word problem using a table and Venn diagram about TV viewership data. The examples are intended to help students practice set theory concepts for the SPM exam.
This document contains a mathematics exam for Secondary School students in Perak, Malaysia. It covers topics like sets, Venn diagrams, linear inequalities, simultaneous linear equations, quadratic equations and expressions, solid geometry, and mathematical reasoning. There are 10 multiple choice questions for each topic area testing students' understanding of key concepts and ability to solve related problems. The document is in Malay and contains diagrams to illustrate the questions.
The document provides examples of calculating angles between lines and planes in 3 dimensions. It includes calculating angles between a line and plane using tangent, and between two planes. It also provides practice questions involving finding angles between lines and planes given dimensional information about the lines and planes.
This document provides notes on additional mathematics for Form 4 students. It includes definitions and examples of functions, inverse functions, quadratic equations, and logarithms. Some key points summarized:
1. A function f maps objects to images. To find the inverse function f-1, change f(x) to y and solve for x in terms of y.
2. To find the roots of a quadratic equation, one can use factorisation, the quadratic formula, or complete the square. The nature of the roots depends on the sign of b2 - 4ac.
3. To solve a system of equations involving one linear and one non-linear equation, one can substitute one equation into the other and solve
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.
1. The document describes 6 experiments involving chemical reactions and properties. It includes questions about the experiments and reactions.
2. Experiment 1 involves electrolysis of silver nitrate and copper sulfate solutions. Observations and half reactions are asked about.
3. Experiment 2 involves heating lead(II) carbonate and identifying the gas produced. Calculations of moles of gas are required.
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 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
1) The document provides guidance on answering physics questions involving experiments. It suggests including an inference, hypothesis, aim, variables, apparatus, procedure, data table, and graph in the answer.
2) A sample question involves stopping distance and relates mass to inertia. The suggested answer structure includes an inference about mass and inertia, a hypothesis testing their relationship, and an experiment using a jigsaw blade, plasticine balls of varying mass, and a stopwatch.
3) The procedure specifies controlling mass, measuring oscillation period, and repeating with different plasticine masses to obtain data for a graph analyzing the relationship between mass and period.
The composite function is gf(x) = 2x - 2. We are given f(x) = 2 - x. To find g, let f(x) = u in gf(x). Then u = 2 - x. Substitute u = 2 - x in gf(x) = 2u - 2. This gives g(x) = 2 - 2x. Therefore, fg(x) = f(2 - 2x) = (2 - (2 - 2x)) = 2x - 2.
1. The document provides a topical test with 6 questions about chemical equations and stoichiometric calculations. It asks the student to write chemical equations for reactions involving sodium, magnesium carbonate, aluminum, copper nitrate, and iron. It also asks the student to calculate relative molecular mass, mass of atoms, relative molecular mass of a gas, a combustion reaction of magnesium, and the volume and number of oxygen molecules from the decomposition of hydrogen peroxide.
This document contains the instructions for three experiments:
1) To compare the reactivity of alkali metals towards oxygen by observing their reactions in different sets. Students are asked to record observations, make predictions, and analyze pH changes.
2) To determine the reaction between barium chloride and potassium chromate solutions by measuring precipitate formation at different volumes. Students must complete a table of results and draw a graph to identify the reacting quantities.
3) To investigate the effect of zinc size on its reaction rate with sulfuric acid by developing a full experiment plan outlining the problem, hypothesis, variables, materials, procedure, and method of collecting data.
This document contains a 2010 Additional Mathematics exam paper from the Sijil Pelajaran Malaysia (SPM). It consists of 25 multiple choice and short answer questions covering topics like:
- Relations and functions
- Quadratic equations
- Geometric and arithmetic progressions
- Trigonometry
- Probability and statistics
The questions require students to apply concepts like domain and range, inverse functions, maximum/minimum values, and normal distributions to solve problems involving graphs, equations, and word problems.
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
The document contains 3 examples of SPM (Malaysian public exam) questions on sets. The first question involves finding the complement of a set R defined in terms of digit sums. The second uses a Venn diagram to represent the complement of a union of sets P and Q. The third is a word problem using a table and Venn diagram about TV viewership data. The examples are intended to help students practice set theory concepts for the SPM exam.
This document contains a mathematics exam for Secondary School students in Perak, Malaysia. It covers topics like sets, Venn diagrams, linear inequalities, simultaneous linear equations, quadratic equations and expressions, solid geometry, and mathematical reasoning. There are 10 multiple choice questions for each topic area testing students' understanding of key concepts and ability to solve related problems. The document is in Malay and contains diagrams to illustrate the questions.
The document provides examples of calculating angles between lines and planes in 3 dimensions. It includes calculating angles between a line and plane using tangent, and between two planes. It also provides practice questions involving finding angles between lines and planes given dimensional information about the lines and planes.
1. The document presents an exercise on mathematical reasoning with 5 questions.
2. The questions test a variety of mathematical logic skills, including determining if statements are true or false, writing implications, completing arguments with valid premises, and using quantifiers to form true statements.
3. The final section provides a diagnostic test to further assess skills in mathematical statements, implications, argument structures, and applying properties of shapes and numbers.
0580 s14 qp_43,IB,HL,SL,Studies,MYP,PYP Maths Tutor in Exploration(IA) Help S...kondal reddy
This document consists of a mathematics exam paper with 10 questions covering various topics in mathematics. The exam is 2 hours and 30 minutes long and contains 130 total marks. The questions cover topics such as algebra, geometry, trigonometry, statistics, and probability. Some of the questions involve solving equations, calculating areas and lengths, sketching graphs, working with vectors, and finding probabilities. The document provides the necessary figures, diagrams, and space for students to show their working and write their answers.
The document provides instructions and information for a mathematics exam. It instructs students to use black ink, fill in personal details, and answer all questions. It notes the total mark is 100 and marks for each question are shown in brackets. Questions marked with an asterisk assess written communication. The document advises students to read questions carefully, keep track of time, and check answers.
This document contains 20 multiple choice questions testing mathematical concepts and problem solving skills. The questions cover topics such as simultaneous linear equations, quadratic equations, functions, graphs, volumes, and other geometry topics. Students are required to show their working and solutions to receive full marks for each question. The final question indicates that this marks the end of the test paper.
The document provides instructions for an ICSE X Mathematics exam. It consists of 2 sections with a total of 80 marks. Section A is worth 40 marks and contains all compulsory questions. Section B is worth 40 marks and students must attempt any 4 questions. Working must be shown and rough work done on the same sheet. The questions assess a range of mathematical concepts through multiple choice and multi-part questions. Section A contains 15 multiple choice questions assessing topics like quadratic equations, probability, geometry and trigonometry. Sample multi-part questions in Section A include determining the value of 'a' if x-a is a factor of a given polynomial, and calculating interest earned and rate of interest based on deposits in a recurring account.
This document is a unit test review covering exponents, order of operations, variables and expressions, translating between words and math, equations and solutions. It contains 25 questions testing these concepts. The questions include writing expressions, evaluating expressions, defining math terms, solving equations, and performing calculations.
The document contains a math exam with 25 multiple choice questions. It tests concepts including functions, equations, logarithms, probability, and statistics. The questions range in difficulty from basic to advanced mathematical topics. An answer key is provided with the step-by-step work shown for partial credit questions. The exam covers a wide breadth of standard high school and introductory college level math materials.
This document provides sample exam questions from SPM 2011 organized by topic and paper. It includes 25 questions from Additional Mathematics Paper 1 and 15 questions from Paper 2. For each question, the topic and number of marks are indicated. An answer key is provided that references a website for detailed solutions. The questions cover a range of Additional Mathematics concepts including quadratic equations, functions, trigonometry, calculus, vectors, probability and statistics.
1. The document is the question paper for a mathematics exam with 15 multi-part questions testing a variety of skills including algebra, geometry, trigonometry, and calculus.
2. The first page provides formulae that may be useful for solving problems on the exam. These include formulas for circles, vectors, trigonometric identities, derivatives, and integrals.
3. The questions cover topics like finding equations of lines and circles, solving equations, sketching graphs, vector and trigonometric calculations, and evaluating limits and derivatives. Working step-by-step through each question is required to earn full credit.
1. The document is a mathematics module on mathematical reasoning containing 10 questions testing concepts like quantifiers, logical statements, implications, sets, and number patterns.
2. The questions cover topics such as determining whether statements are true or false, completing arguments with missing premises, writing implications, forming conclusions by induction, and identifying quantifiers to make statements true.
3. The answers provided are concise, clearly explaining the logic and working for each short question and sub-question.
1. The document is a mathematics worksheet on mathematical reasoning containing 10 questions testing concepts like quantifiers, logical statements, implications, sets, and number patterns.
2. The questions cover topics such as determining whether statements are true or false, completing logical arguments with missing premises, writing implications, forming conclusions by induction, and identifying quantifiers to make statements true.
3. The answers provided are short responses identifying true/false statements, writing missing premises or conclusions, and briefly explaining logical implications and conclusions formed by induction.
1
Week 2 Homework for MTH 125
Name___________________________________ Date: ___July 20, 2021______________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Graph the equation by determining the missing values needed to plot the ordered pairs.
1) y + x = 3; ( 1, ), ( 3, ), ( 2, )
1) _______
A)
B)
C)
D)
2
Find the x- and y-intercepts. Then graph the equation.
2) 10y - 2x = -4
2) _______
A) ( -2, 0);
B) ; (0, -2)
3
C) ( 2, 0);
D) ; (0, 2)
Find the midpoint of the segment with the given endpoints.
4
3) ( 8, 4) and ( 7, 9) 3) _______
A) B) C) D)
Suppose that segment PQ has the given coordinates for one endpoint P and for its midpoint M. Find the coordinates
of the other endpoint Q.
4) P( 5, 5) and M 4) _______
A) Q( 4, 4) B) Q C) Q D) Q
Solve the problem.
5) The graphing calculator screen shows the graph of one of the equations below. Which equation is it?
5) _______
A) y + 3x = 15 B) y - 3x = 15 C) y = 3x + 3 D) y + 3x = 3
Find the slope.
6) m = 6) _______
A) -5 B) 5 C) 12 D) 8
Find the slope of the line through the given pair of points, if possible. Based on the slope, indicate whether the line
through the points rises from left to right, falls from left to right, is horizontal, or is vertical.
7) ( -3, -5) and ( 4, -4) 7) _______
A) - ; falls B) - 7; falls C) 7; rises D) ; rises
Find the slope of the line.
5
8)
8) _______
A) B) C) - D) -
Find the slope of the line and sketch the graph.
9) 2x + 3y = 10
9) _______
A) Slope:
6
B) Slope: -
C) Slope: -
7
D) Slope:
Decide whether the pair of lines is parallel, perpendicular, or neither.
10) 3x - 4y = 12 and 8x + 6y = -9 10) ______
A) Parallel B) Perpendicular C) Neither
Choose the graph that matches the equation.
11) y = 2x + 4 11) ______
A)
B)
C)
8
D)
Find the equation in slope-intercept form of the line satisfying the conditions.
12) m = 2, passes through ( 6, -3) 12) ______
A) y = 2x - 15 B) y = 3x + 16 C) y = 2x - 13 D) y = 2x + 14
Write the equation in slope-intercept form.
13) 17x + 5y = 7 13) ______
A) y = x + B) y = 17x - 7 C) y = - x + D) y = x -
Find the slope and the y-intercept of the line.
14) 7x + 5y = 48 14) ______
A) Slope - ; y-intercept B) Slope ; y-intercept
C) Slope ; y-intercept D) Slope - ; y-intercept
Find an equation of the line that satisfies the conditions. Write the equation in standard form.
9
15) Through ( 5, 4); m = - 15) ______
A) 4x - 9y = 56 B) 4x + 9y = -56 C) 4x + 9y = 56 D) 9x + 4y = -56
...
1 Week 2 Homework for MTH 125 Name_______________AbbyWhyte974
1
Week 2 Homework for MTH 125
Name___________________________________ Date: ___July 20, 2021______________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Graph the equation by determining the missing values needed to plot the ordered pairs.
1) y + x = 3; ( 1, ), ( 3, ), ( 2, )
1) _______
A)
B)
C)
D)
2
Find the x- and y-intercepts. Then graph the equation.
2) 10y - 2x = -4
2) _______
A) ( -2, 0);
B) ; (0, -2)
3
C) ( 2, 0);
D) ; (0, 2)
Find the midpoint of the segment with the given endpoints.
4
3) ( 8, 4) and ( 7, 9) 3) _______
A) B) C) D)
Suppose that segment PQ has the given coordinates for one endpoint P and for its midpoint M. Find the coordinates
of the other endpoint Q.
4) P( 5, 5) and M 4) _______
A) Q( 4, 4) B) Q C) Q D) Q
Solve the problem.
5) The graphing calculator screen shows the graph of one of the equations below. Which equation is it?
5) _______
A) y + 3x = 15 B) y - 3x = 15 C) y = 3x + 3 D) y + 3x = 3
Find the slope.
6) m = 6) _______
A) -5 B) 5 C) 12 D) 8
Find the slope of the line through the given pair of points, if possible. Based on the slope, indicate whether the line
through the points rises from left to right, falls from left to right, is horizontal, or is vertical.
7) ( -3, -5) and ( 4, -4) 7) _______
A) - ; falls B) - 7; falls C) 7; rises D) ; rises
Find the slope of the line.
5
8)
8) _______
A) B) C) - D) -
Find the slope of the line and sketch the graph.
9) 2x + 3y = 10
9) _______
A) Slope:
6
B) Slope: -
C) Slope: -
7
D) Slope:
Decide whether the pair of lines is parallel, perpendicular, or neither.
10) 3x - 4y = 12 and 8x + 6y = -9 10) ______
A) Parallel B) Perpendicular C) Neither
Choose the graph that matches the equation.
11) y = 2x + 4 11) ______
A)
B)
C)
8
D)
Find the equation in slope-intercept form of the line satisfying the conditions.
12) m = 2, passes through ( 6, -3) 12) ______
A) y = 2x - 15 B) y = 3x + 16 C) y = 2x - 13 D) y = 2x + 14
Write the equation in slope-intercept form.
13) 17x + 5y = 7 13) ______
A) y = x + B) y = 17x - 7 C) y = - x + D) y = x -
Find the slope and the y-intercept of the line.
14) 7x + 5y = 48 14) ______
A) Slope - ; y-intercept B) Slope ; y-intercept
C) Slope ; y-intercept D) Slope - ; y-intercept
Find an equation of the line that satisfies the conditions. Write the equation in standard form.
9
15) Through ( 5, 4); m = - 15) ______
A) 4x - 9y = 56 B) 4x + 9y = -56 C) 4x + 9y = 56 D) 9x + 4y = -56
...
This document provides instructions for a mathematics exam. It consists of 12 printed pages and contains 19 questions testing a variety of math skills. Candidates are to show their work, use a calculator or 3.142 for pi, and staple their pages together at the end. They have 1 hour and 30 minutes to complete the exam.
The document contains several mathematics problems involving:
1) Calculating values of expressions with directed numbers, integers, fractions, decimals, square roots, cubes, and algebraic expressions.
2) Solving equations and inequalities involving one or more variables.
3) Working with indices, statistics, functions, and graphs. Problems cover topics such as mean, median, mode, frequency tables, pie charts, and plotting points to graph functions.
This document contains a mathematics exam with 7 sections covering various topics:
1) Choosing the correct answers with justifications for questions about equations, inequalities, and trigonometric functions.
2) Verifying relationships between algebraic expressions.
3) Calculating relative frequencies, means, and number of buildings needed based on floor distributions.
4) Solving a system of equations and word problems about prices and discounts.
5) Working with polynomials including determining coefficients, evaluating, and solving equations.
6) Analyzing points, lines, triangles, and circles in a coordinate plane.
7) Proving geometric relationships involving circles, lines, and triangles.
This document provides a review of exercises for a Math 112 final exam. It contains 31 multi-part exercises covering topics like graphing, logarithms, trigonometry, and word problems. The review is intended to help students practice problems similar to what may appear on the exam. The exam will have two parts, one allowing a calculator and one not.
1 of 11UMGC College Algebra MATH 107 6980 - Fall 2020 – Instruct.docxteresehearn
1 of 11
UMGC College Algebra MATH 107 6980 - Fall 2020 – Instructor: Timothy J. Elsner
Page 1 of 11
MATH 107 FINAL EXAMINATION - Nov 15, 2020 - Due Tue Nov 17 11:59 pm
This is an open-book exam. You may refer to your text and other course materials as you work on the exam, and you may
use a calculator. You must complete the exam individually. Neither collaboration nor consultation with others is allowed.
MAKE CERTAIN YOUR SUBMITTAL IS CLEARLY READABLE. FOR THE SHORT ANSWER SECTIONS make sure your ANSWER IS CIRCLED
There are 30 problems. Problems #1–12 are Multiple Choice.
Problems #13–21 are Short Answer. (Work not required to be shown)
Problems #22–30 are Short Answer with work required to be shown. Also read:
Mathematics in Montessori
MULTIPLE CHOICE
1. Determine the domain and range of the piecewise function. 1._______
A. Domain [ -5, 5]; Range [- 6, 6]
B. Domain [- 4, 5]; Range [- 6, 6]
C. Domain [- 6, 5]; Range [- 4, 6]
D. Domain [- 6, 6]; Range [- 4, 5]
2. Solve: x = √−8x + 9 and check your solution(s) 2.________
A. x = - 9
B. x = 1
C. x = {-9, 1}
D. No
Solution
2 of 11
3. Determine the x interval(s) on which the function is increasing. 3.__________
A. (−4, 0] and [4, ∞)
B. [0, 4]
C. (−∞, 3) ∪ [−1, 5 ]
D. (−∞, −4] and [0, 4 ]
4. Determine whether the graph of Y = | x | - 3 is symmetric with respect 4. _________
to the origin, the x-axis, or the y-axis.
A. symmetric with respect to the x-axis only
B. symmetric with respect to the y-axis only
C. symmetric with respect to the origin only
D. not symmetric with respect to the x-axis, not symmetric with respect to the y-axis,
and not symmetric with respect to the origin
5. Find the solution to the inequality : | 6 – x | + 3 < 8 5. ___________
A. (????, ∞)
B. (???? , ???????? )
C. (−∞, ????) ∪ (????????, ∞)
D. (−1, −????????)
3 of 11
6. Which of the following represents the graph of −3x + 5y = 15 ? __________
A. B.
C. D.
7. Write a slope-intercept equation for a line perpendicular to the line −3x + 5y = 15
which passes through the point (6, – 5).
A. y = − ????
???? ???? + ????
B. y = ????
???? ???? − ????????
C. y = − ????
???? ???? + ????
D. y = ????
???? ???? − ????????
4 of 11
8. Choose what type of graph is below ? 8.___________
A. It is not a function.
B. It is a function and it is one-to-one.
C. It is a function but it is not one-to-one.
D. It is not a function and it is not one-to-one.
9. Express as a single logarithm: log (2x + 1) + log 2x - 4 log x 9.__________
A. log ( 4x+1
4x )
B. log ( 2x(2x+1)
4x )
C. log ( 4x2 - 2x)
D. log ( 2???? (2???? + 1)
????4 )
10. Which of the functions correspond to the graph? 10.__________
A. f(x) = e x
B. f(x) = e x – 1
C. f(x) = log(x)
D. f(x) = log(x) – 1
5 of 11
11. Suppose that for a function f(x), that it has exactly 1 zero (or 1 X-intercept)
Which of the following statements MUST true? (only one answer is correct) 11. _________
A. f(x) is linear and has a positive slope.
B.
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Mathematics Mid Year Form 4 Paper 2 2010
1. _________________________________________________________ Mathematics Form 4
Instructions : This question paper consist of two sections. Section A and Section B.
Answer all questions in Section A and four questions in Section B. The diagrams in the
questions provided are not drawn to scale unless stated. The marks allocated for each
question and sub-part of a question are shown in brackets. You may use a non-
programmable scientific calculator.
Section A
[52 marks]
1. The following Venn diagram shows sets K, L and M such that the universal set
ξ = K ∪ L ∪ M . On the diagram, shade the set
(a) K ∩ L'
(b) K ∪ L ∩ M ' [3 marks]
L M L M
K K
Answer :
(a) (b)
2. The Venn diagrams below shows the sets P, Q and R such that the universal set,
ξ = P ∪ Q ∪ R . Shade the region indicated.
(a) P'∪Q
(b) P ∩ Q ∩ R ' [3 marks]
Answer :
(a)
P Q
R (b)
P Q
R
3
suesha_2010___________________________________________________________________________________
2. _________________________________________________________ Mathematics Form 4
3. Solve the quadratic equation m 2 − 10 = m(1 − 2m) . [ 4 marks]
Answer :
5n 2 + 3
4. Solve the equation = 2. [4
8n
marks]
Answer :
5. The diagram shows a composite solid formed by the combination of a cylindrical
solid with a base diameter of 10 cm and a height of 21 cm and a cone that has a slant
height of 13 cm. Calculate the volume, in cm3, of the combined solid.
[5 marks]
13 cm
21 cm
10 cm
Answer :
4
suesha_2010___________________________________________________________________________________
3. _________________________________________________________ Mathematics Form 4
6. (a) Determine whether the following statement is true or false.
“ 52 = 25 or 16 = 4.”
(b) Complete the following statement by using the quantifier “all” or “some” to make
it a false statement.
“ __________ triangles are isosceles triangles.”
(c) Make a general conclusion by induction for the sequence of numbers 17, 21, 33,
53, … which follows the following number pattern.
17 = 4(0)2 + 17
21 = 4(1)2 + 17
33 = 4(2)2 + 17
53 = 4(3)2 + 17
[5 marks]
Answer :
(a) ………………………….…………..
(b) ………………………………..…….
(c) ………………………………………
7. (a) Determine whether each of the following sentences are statements or non-
statement.
(i) x + 7 x
(ii) 2 x 2 + 5 x 2 = 7 x 2
(b) Write two implications based on the following sentence.
x 3 < 0 if and only if x < 0
(c) Complete the premise in the following argument.
x
Premise 1 : If is a proper fraction, then x < y .
y
Premise 2 : ……………………………………………
Conclusion : x < y.
[5 marks]
Answer :
(a) (i) ……………………………………..
(ii) …………………………………….
(b) Implication 1 : ……………………………………………………………..
Implication 2 : ……………………………………………………………..
5
suesha_2010___________________________________________________________________________________
4. _________________________________________________________ Mathematics Form 4
(c) …………………………………………………………………………………..
8. In the dagram, O is the origin. The straight line RT is parallel to the x-axis and the
straight line PQ and RS are parallel. The equation of RS is x + 2 y = 12 .
y
R T
P
x
S
Q (6, -6)
(a) State the equation of RT.
(b) Find the equation of PQ and hence, state its x-intercept. [5 marks]
Answer :
(a)
(b)
T
14 cm P
9. 60°
O S
Q 7 cm
6
suesha_2010___________________________________________________________________________________
5. _________________________________________________________ Mathematics Form 4
In the diagram, TS and PQ are arcs of two different circle which have the same centre
O. OQS is a straight line.
22
It is given that ∠ QOP=60º and ∠ SOT=90º. Using π = , calculate
7
(a) the perimeter, in cm, of the sector OTS,
(b) the area, in cm2, of the shaded region.
[6 marks]
Answer :
(a)
(b)
10. (a) Expand ( 4 x − 1)( x + 5 ) .
(b) Factorise 4 x 2 − 1 .
(c) Solve the equation 2( 3 − x 2 ) = 4 x . [6
marks]
Answer :
(a)
(b)
(c)
7
suesha_2010___________________________________________________________________________________
6. _________________________________________________________ Mathematics Form 4
11. (a) Complete the following statement using ‘all’ or ‘some’ to construct a true
statement.
………………………… prime numbers are odd numbers.
(b) Change the truth value of the following statement by using the word ‘not’.
An empty set is a subset of any set.
(c) Write two implications based on the following sentence.
( x − 5)( x + 3) = 0 if and only if x = 5 or x = −3
(d) 3=1+1+1
6=2+2+2
9=3+3+3
Based on the above information, form a general conclusion for the sequence 3, 6,
9, ...
[6 marks]
Answer :
(a) ……………………………………………….
(b) ……………………………………………….
(c) Implication 1 : …………………………………………………..
Implication 2 : …………………………………………………..
(d) ………………………………..
Section B
[48 marks]
12. The data in the diagram shows the length, in mm, of 36 leaves plucked from a tree
in a garden.
8
suesha_2010___________________________________________________________________________________
7. _________________________________________________________ Mathematics Form 4
20 40 44 63 56 34 75 68 28
52 38 32 31 33 78 59 41 15
42 65 43 43 35 30 46 48 54
24 58 43 39 41 49 45 33 47
(a) Based on the data above and using a class interval of 10, complete the table given
below.
Length (mm) Frequency Cumulative Frequency Upper Boundary
0–9 0
10 – 19
20 – 29
30 – 39
40 – 49
50 – 59
60 – 69
70 - 79
[4 marks]
(b) Based on the table in (a),
(i) state the modal class,
(ii) calculate the estimated mean of the lengths of the leaves. [4 marks]
(c) For this part of the question, use the graph paper.
By using a scale of 2 cm to 10 mm on the horizontal axis and 2 cm to 5 leaves on
the vertical axis, draw an ogive for the data.
[4 marks]
Answer :
(b) (i) ………………………..
(ii)
13. (a) (i) State whether the following statements is true or false.
(a) 4 × 3 = 15 − 3
9
suesha_2010___________________________________________________________________________________
8. _________________________________________________________ Mathematics Form 4
(b) 64 = 4
(c) 4 × 3 = 15 − 3 and 64 = 4
(d) 4 × 3 = 15 − 3 or 64 = 4
(ii) Write down two implications from the sentence given below.
“ x 3 = 64 if and only if x = 4 ”
(iii) Complete the premise in the following argument.
Premise 1 : All acute angles are less than 90º.
Premise 2 : ……………………………………….
Conclusion : x is less than 90º. [8 marks]
p+6
(b) Solve the equation p 2 = . [4 marks]
2
Answer :
(a) (i) (a)………………………………..
(b) ……………………………….
(c) ………………………………
(d) ………………………………
(ii) Implication 1 : …………………………………………………..
Implication 2 : …………………………………………………..
(iii) ……….………………………………………………
(b)
14. (a) The Venn diagram shows the sets E, F and G such that the universal set,
ξ = E ∪ F ∪ G . On the diagram, shade
(i) E ∩ G (ii) ( E ′ ∪ F ) ∩ G
G G
F F
E 10 E
suesha_2010___________________________________________________________________________________
9. _________________________________________________________ Mathematics Form 4
[3 marks]
(b) y
On the Cartesian plane, PQRS is a
trapezium. PQ is parallel to RS.
P(6, 10)
S Q
(6, 10)
R(13, 2)
x
O
Find
(i) the equation of the straight line PQ,
(ii) the y-intercept of the straight line PQ [6
marks]
(c) Solve the equation 3n 2 + 14n − 5 = 0 . [3 marks]
Answer :
(b) (i)
(ii)
(c)
15. The data in the box below shows the marks obtained by a group of 40 pupils in a
Mathematics test.
51 50 54 61 56 47 54 62
60 53 57 46 52 60 74 49
64 63 42 55 70 66 57 69
45 56 62 59 58 63 64 51
11
suesha_2010___________________________________________________________________________________
10. _________________________________________________________ Mathematics Form 4
58 68 72 67 65 61 43 65
a. Using the data in the box above and a class interval of 5 marks, complete the
table below.
Marks Midpoint Frequency
36 - 40 38 0
41 - 45
[4 marks]
b. By using a scale of 2 cm to 5 marks on the x-axis and 2 cm to 1 pupil on the y-
axis, draw a frequency polygon for the data. [4 marks]
c. From your frequency polygon in (b),
(i) calculate the mean marks for the group of pupils,
(ii) state one information which relates the marks and the number of
pupils.
……………………………………………………………………………….
[4 marks]
16. The data in the diagram below shows the number of SMS received per day by a group
of students.
11 7 14 13 8 12 11
9 16 11 16 17 15 6
13 12 18 22 11 10 13
6 21 5 12 22 19 20
12 15 16 12 9 13 6
13 10 12 5 12 14 11
a. Using the data in the diagram above and a class interval of 5, complete the table
below.
12
suesha_2010___________________________________________________________________________________
11. _________________________________________________________ Mathematics Form 4
Number of Frequency Midpoint Upper
SMS received boundary
5-7 6 6 7.5
8 - 10
11 - 13
14 - 16
17 - 19
20 - 22
[4 marks]
b. Based on table above, calculate the estimated mean of the SMS received per day.
[3 marks]
c. By using a scale of 2 cm to 3 units on the x-axis and 2 cm to 2 units on the
y-axis, draw a histogram for the data. [4
marks]
d. State the modal class for the data above. [1 marks]
……………………………………….
13
suesha_2010___________________________________________________________________________________