This document contains instructions and questions for a GCSE mathematics exam. It begins by providing spaces for students to write their name, center number, and candidate number. It then provides instructions for the exam, information about marking, and advice for students. The exam contains 14 multiple-choice questions testing a variety of math skills like data collection, calculations, problem solving, geometry, and more.
This document consists of 15 printed pages containing instructions and questions for a Secondary 4 Express Mathematics Preliminary Examination. It includes 9 multiple choice questions testing a range of math skills, such as evaluating expressions, solving equations, finding percentages and rates, working with graphs and charts, calculating speed and perimeter, and identifying equations of lines. The candidate is asked to show their working and answers directly on the question paper.
This document contains instructions for a mathematics preliminary examination for Secondary Four students at River Valley High School. It provides details such as the date of the exam, time allowed, instructions for completing the exam, mathematical formulas, and a list of 22 questions covering various math topics. Students are to show their working and answer all questions in the allotted time of 2 hours.
1) The document is a mark scheme for GCSE Mathematics (Linear) 1MA0 Higher (Calculator) Paper 2H exam from Summer 2012.
2) It provides notes on marking principles for examiners, such as marking all candidates equally, awarding marks for correct working shown, and following standard procedures around parts of questions and probability answers.
3) The mark scheme then provides detailed guidance on marking for each question, including expected methods, intermediate working, and final answers for full marks.
This document contains a mathematics exam for the Caribbean Examinations Council Secondary Education Certificate. The exam has two sections and contains 8 questions. Section I contains 5 compulsory questions testing algebra, geometry, and data analysis skills. Section II contains 2 optional questions on algebra and relations/functions, geometry and trigonometry, or statistics. The exam tests a range of mathematical concepts and requires both calculations and explanations. It aims to comprehensively assess students' general mathematics proficiency.
This document contains an 11-question mathematics exam for the Caribbean Examinations Council Secondary Education Certificate. The exam has two sections, with Section I containing 8 questions and Section II containing 3 questions. Candidates must answer all questions in Section I and any two questions from Section II. The exam covers topics such as algebra, geometry, trigonometry, and data analysis.
This document contains a 38-question mathematics assessment on circles for Form 3 students in Malaysia. The test covers topics like diameters, radii, chords, arcs, angles, and cyclic quadrilaterals. It includes both multiple choice and written response questions. The test is administered according to standardized instructions and is meant to evaluate students on several learning constructs related to understanding mathematical terms and concepts in English.
This document consists of 15 printed pages containing instructions and questions for a Secondary 4 Express Mathematics Preliminary Examination. It includes 9 multiple choice questions testing a range of math skills, such as evaluating expressions, solving equations, finding percentages and rates, working with graphs and charts, calculating speed and perimeter, and identifying equations of lines. The candidate is asked to show their working and answers directly on the question paper.
This document contains instructions for a mathematics preliminary examination for Secondary Four students at River Valley High School. It provides details such as the date of the exam, time allowed, instructions for completing the exam, mathematical formulas, and a list of 22 questions covering various math topics. Students are to show their working and answer all questions in the allotted time of 2 hours.
1) The document is a mark scheme for GCSE Mathematics (Linear) 1MA0 Higher (Calculator) Paper 2H exam from Summer 2012.
2) It provides notes on marking principles for examiners, such as marking all candidates equally, awarding marks for correct working shown, and following standard procedures around parts of questions and probability answers.
3) The mark scheme then provides detailed guidance on marking for each question, including expected methods, intermediate working, and final answers for full marks.
This document contains a mathematics exam for the Caribbean Examinations Council Secondary Education Certificate. The exam has two sections and contains 8 questions. Section I contains 5 compulsory questions testing algebra, geometry, and data analysis skills. Section II contains 2 optional questions on algebra and relations/functions, geometry and trigonometry, or statistics. The exam tests a range of mathematical concepts and requires both calculations and explanations. It aims to comprehensively assess students' general mathematics proficiency.
This document contains an 11-question mathematics exam for the Caribbean Examinations Council Secondary Education Certificate. The exam has two sections, with Section I containing 8 questions and Section II containing 3 questions. Candidates must answer all questions in Section I and any two questions from Section II. The exam covers topics such as algebra, geometry, trigonometry, and data analysis.
This document contains a 38-question mathematics assessment on circles for Form 3 students in Malaysia. The test covers topics like diameters, radii, chords, arcs, angles, and cyclic quadrilaterals. It includes both multiple choice and written response questions. The test is administered according to standardized instructions and is meant to evaluate students on several learning constructs related to understanding mathematical terms and concepts in English.
The document provides instructions and information for a practice GCSE mathematics exam. It includes details about the exam such as the time allowed, materials permitted, and total marks. It provides advice to students to read questions carefully, watch the time, and attempt all questions. It also includes commonly used formulas for the exam.
- The document is an exam for the Caribbean Examinations Council's Secondary Education Certificate in Mathematics.
- It contains two sections - students must answer all questions in Section I and two questions from Section II.
- Section I contains 8 questions testing a range of math skills like fractions, currency conversion, compound interest, simplifying expressions, and graphing.
- Section II contains 4 multi-part questions on algebra, functions, graphs, geometry, and trigonometry.
1) The document is an exam for mathematics taken in May/June 2007. It contains instructions for students and lists common formulas.
2) Section 1 contains 3 questions testing skills in calculations, ratios, fractions, and writing equations. Section 2 has 4 sub-questions evaluating algebraic manipulation, simplification of expressions, writing equations from word problems, and geometry constructions.
3) The exam tests a wide range of mathematics concepts and skills through multi-step word problems and diagrams requiring calculations, algebraic manipulations, geometric constructions, and use of formulas.
This document contains a practice paper for GCSE Mathematics with 27 multiple choice and worked problems. The problems cover a range of topics including number calculations, simplifying expressions, graphs, symmetry, fractions, factorizing, simultaneous equations, and trigonometry. Full worked solutions and marks allocations are provided. An analysis shows the paper assessed different areas of mathematics, with the highest proportion of marks (47%) assessing algebraic skills and techniques.
An isometric drawing shows an object in 3D with all three axes inclined equally at 120 degrees. Key features include:
- All three dimensions are shown in a single view
- Dimensions can be measured directly from the drawing
- Common examples include isometric views of geometric shapes, objects, assemblies and sectioned components
- Construction involves maintaining equal angles between the three axes and using an isometric scale to reduce dimensions
This document provides a summary of a 2 hour mathematics enrichment session on lines and planes in 3-dimensions. It includes 10 problems involving calculating angles between lines and planes using trigonometric ratios. The problems include diagrams of prisms, pyramids and cuboids with given measurements. The document concludes with answers to the 10 problems.
Here are the key steps to solve quadratic equations:
1. Factorize the quadratic expression if possible. This allows using the zero product property.
2. Use the quadratic formula if factorizing is not possible:
x = (-b ± √(b^2 - 4ac)) / 2a
3. Solve for the roots. The roots are the values of x that make the quadratic equation equal to 0.
4. Check your solutions in the original equation to verify they are correct roots.
5. Determine the nature of the roots:
- If the discriminant (b^2 - 4ac) is greater than 0, there are two real distinct roots.
- If the discriminant
This course provides a working knowledge of college-level algebra and its applications. Emphasis is on solving linear and quadratic equations, word problems, and polynomial, rational and radical equations and applications.
Students perform operations on real numbers and polynomials, and simplify algebraic, rational, and radical expressions. Arithmetic and geometric sequences are examined, and linear equations and inequalities are discussed.
Students learn to graph linear, quadratic, absolute value, and piecewise-defined functions, and solve and graph exponential and logarithmic equations.
Other topics include solving applications using linear systems, and evaluating and finding partial sums of a series.
Includes 10 hours of 1-on-1 live, on demand instructional support from SMARTHINKING.
Introductory Algebra is a not-for-credit course which prepares students to successfully complete College Algebra.
1) The document provides the Idaho content standards for 4th grade mathematics. It outlines 8 goals covering number and operation, computation, and estimation.
2) For each goal there are multiple objectives that specify skills students should master by 4th grade. The objectives are coded by cognitive level and whether a calculator can be used.
3) Shaded objectives are taught but not assessed on the Idaho Student Achievement Test (ISAT). The document provides details on content limits and formats for assessing each objective.
The document provides an overview of a mathematics enrichment course for additional mathematics teachers in central Malaysia in 2009. It identifies common weaknesses and mistakes among student groups in various math topics like functions, quadratic equations, coordinate geometry, and circular measures. For each topic, it outlines the specific mistakes and provides recommendations for teachers to rectify weaknesses and remind students of important steps and formulas.
Circles and tangents with geometry expressionsTarun Gehlot
This document presents 13 examples exploring properties of circles and their tangents using a geometry expressions software. The examples are grouped into sections on circle common tangents, arbelos figures (circles squeezed between other circles), and circles and triangles. The examples demonstrate various geometric relationships that can be expressed algebraically using the software, such as the intersection points of common tangents, ratios of trapezium areas defined by common tangents, and the radii of nested circles.
1. The document provides instructions for a GCSE mathematics exam, including information about the structure, time allowed, materials permitted and formulas.
2. It instructs students to write their name, center number and candidate number in the boxes at the top of the page.
3. Students are advised to read questions carefully, try to answer every question, check answers at the end and use the time guide for each question.
The document is a mark scheme for GCSE Mathematics (2MB01) Higher 5MB2H (Non-Calculator) Paper 01 exam from March 2012. It provides notes on marking principles and guidance for examiners on how to apply the mark scheme and award marks for questions 1 through 9 on the exam. The summary includes key details about the document type and content while being concise in 3 sentences or less.
Mark Scheme (Results) June 2012 GCSE Mathematics (2MB01) Higher Paper 5MB3H_01 (Calculator) provides guidance for examiners on marking the GCSE Mathematics exam from June 2012. It includes notes on general marking principles, how to award marks for various parts of questions, and specific guidance for marking some sample questions from the exam. The document is published by Pearson Education and provides information to ensure accurate and consistent marking of the GCSE exam.
The document is a mark scheme for a GCSE mathematics exam. It provides guidance to examiners on how to mark students' responses, including what constitutes correct working and answers for different parts of questions. The document also provides background information on the exam board and qualifications.
4 4 revision session 16th april coordinate geometry structured revision for C...claire meadows-smith
The Community Maths School is offering a structure revision programme to prepare students for the Core 1 exam on May 19th. The programme will include 6 revision sessions from March 24th to April 28th covering topics like translations of graphs, simultaneous equations, inequalities, and coordinate geometry. Additional exam practice sessions will be held on May 5th and May 12th. Resources and past papers will be available on the Exam Solutions website and Mathscard app.
The document provides the mark scheme for the March 2012 GCSE Mathematics (2MB01) Higher 5MB2H (Non-Calculator) Paper 01 exam. It outlines the general principles for marking the exam, including how to award full marks if deserved and how to follow through marks from previous steps. The document also provides subject-specific guidance for marking questions involving areas like probability, linear equations, and multi-step calculations.
This document provides instructions and information for a practice GCSE Mathematics exam. It specifies that the exam is 1 hour and 45 minutes long and covers various topics in mathematics. It provides the materials allowed, instructions on completing the exam, information about marking and time allocation, and advice to students. The exam contains 18 questions testing skills in algebra, graphs, geometry, statistics, and problem solving. It is out of a total of 80 marks.
This document provides instructions and information for a practice GCSE mathematics exam. It outlines what materials are allowed, how to answer questions, how marks are allocated, and advice for taking the test. The exam contains 20 multiple-choice and written-response questions testing a range of math skills, including algebra, geometry, statistics, and transformations. It is 80 marks total and lasts 1 hour and 30 minutes.
This document provides a mark scheme for GCSE Mathematics (Linear) 1MA0 Higher (Calculator) Paper 2H from March 2013. It outlines the general principles that examiners should follow when marking, such as awarding all marks that are deserved and following through correct working. It also provides specific guidance on marking certain types of questions involving areas like probability, linear equations, and multi-step calculations. The document aims to ensure examiners apply marks consistently across all candidates.
This document provides the final mark scheme for Edexcel's Core Mathematics C1 exam from January 2012. It lists the questions, schemes for awarding marks, and total marks for each question. The six mark questions cover topics like algebra, inequalities, coordinate geometry, and calculus. The longer questions involve multi-step problems applying these concepts, including sketching curves, finding equations of tangents and normals, and solving word problems involving formulas.
The document provides instructions and information for a practice GCSE mathematics exam. It includes details about the exam such as the time allowed, materials permitted, and total marks. It provides advice to students to read questions carefully, watch the time, and attempt all questions. It also includes commonly used formulas for the exam.
- The document is an exam for the Caribbean Examinations Council's Secondary Education Certificate in Mathematics.
- It contains two sections - students must answer all questions in Section I and two questions from Section II.
- Section I contains 8 questions testing a range of math skills like fractions, currency conversion, compound interest, simplifying expressions, and graphing.
- Section II contains 4 multi-part questions on algebra, functions, graphs, geometry, and trigonometry.
1) The document is an exam for mathematics taken in May/June 2007. It contains instructions for students and lists common formulas.
2) Section 1 contains 3 questions testing skills in calculations, ratios, fractions, and writing equations. Section 2 has 4 sub-questions evaluating algebraic manipulation, simplification of expressions, writing equations from word problems, and geometry constructions.
3) The exam tests a wide range of mathematics concepts and skills through multi-step word problems and diagrams requiring calculations, algebraic manipulations, geometric constructions, and use of formulas.
This document contains a practice paper for GCSE Mathematics with 27 multiple choice and worked problems. The problems cover a range of topics including number calculations, simplifying expressions, graphs, symmetry, fractions, factorizing, simultaneous equations, and trigonometry. Full worked solutions and marks allocations are provided. An analysis shows the paper assessed different areas of mathematics, with the highest proportion of marks (47%) assessing algebraic skills and techniques.
An isometric drawing shows an object in 3D with all three axes inclined equally at 120 degrees. Key features include:
- All three dimensions are shown in a single view
- Dimensions can be measured directly from the drawing
- Common examples include isometric views of geometric shapes, objects, assemblies and sectioned components
- Construction involves maintaining equal angles between the three axes and using an isometric scale to reduce dimensions
This document provides a summary of a 2 hour mathematics enrichment session on lines and planes in 3-dimensions. It includes 10 problems involving calculating angles between lines and planes using trigonometric ratios. The problems include diagrams of prisms, pyramids and cuboids with given measurements. The document concludes with answers to the 10 problems.
Here are the key steps to solve quadratic equations:
1. Factorize the quadratic expression if possible. This allows using the zero product property.
2. Use the quadratic formula if factorizing is not possible:
x = (-b ± √(b^2 - 4ac)) / 2a
3. Solve for the roots. The roots are the values of x that make the quadratic equation equal to 0.
4. Check your solutions in the original equation to verify they are correct roots.
5. Determine the nature of the roots:
- If the discriminant (b^2 - 4ac) is greater than 0, there are two real distinct roots.
- If the discriminant
This course provides a working knowledge of college-level algebra and its applications. Emphasis is on solving linear and quadratic equations, word problems, and polynomial, rational and radical equations and applications.
Students perform operations on real numbers and polynomials, and simplify algebraic, rational, and radical expressions. Arithmetic and geometric sequences are examined, and linear equations and inequalities are discussed.
Students learn to graph linear, quadratic, absolute value, and piecewise-defined functions, and solve and graph exponential and logarithmic equations.
Other topics include solving applications using linear systems, and evaluating and finding partial sums of a series.
Includes 10 hours of 1-on-1 live, on demand instructional support from SMARTHINKING.
Introductory Algebra is a not-for-credit course which prepares students to successfully complete College Algebra.
1) The document provides the Idaho content standards for 4th grade mathematics. It outlines 8 goals covering number and operation, computation, and estimation.
2) For each goal there are multiple objectives that specify skills students should master by 4th grade. The objectives are coded by cognitive level and whether a calculator can be used.
3) Shaded objectives are taught but not assessed on the Idaho Student Achievement Test (ISAT). The document provides details on content limits and formats for assessing each objective.
The document provides an overview of a mathematics enrichment course for additional mathematics teachers in central Malaysia in 2009. It identifies common weaknesses and mistakes among student groups in various math topics like functions, quadratic equations, coordinate geometry, and circular measures. For each topic, it outlines the specific mistakes and provides recommendations for teachers to rectify weaknesses and remind students of important steps and formulas.
Circles and tangents with geometry expressionsTarun Gehlot
This document presents 13 examples exploring properties of circles and their tangents using a geometry expressions software. The examples are grouped into sections on circle common tangents, arbelos figures (circles squeezed between other circles), and circles and triangles. The examples demonstrate various geometric relationships that can be expressed algebraically using the software, such as the intersection points of common tangents, ratios of trapezium areas defined by common tangents, and the radii of nested circles.
1. The document provides instructions for a GCSE mathematics exam, including information about the structure, time allowed, materials permitted and formulas.
2. It instructs students to write their name, center number and candidate number in the boxes at the top of the page.
3. Students are advised to read questions carefully, try to answer every question, check answers at the end and use the time guide for each question.
The document is a mark scheme for GCSE Mathematics (2MB01) Higher 5MB2H (Non-Calculator) Paper 01 exam from March 2012. It provides notes on marking principles and guidance for examiners on how to apply the mark scheme and award marks for questions 1 through 9 on the exam. The summary includes key details about the document type and content while being concise in 3 sentences or less.
Mark Scheme (Results) June 2012 GCSE Mathematics (2MB01) Higher Paper 5MB3H_01 (Calculator) provides guidance for examiners on marking the GCSE Mathematics exam from June 2012. It includes notes on general marking principles, how to award marks for various parts of questions, and specific guidance for marking some sample questions from the exam. The document is published by Pearson Education and provides information to ensure accurate and consistent marking of the GCSE exam.
The document is a mark scheme for a GCSE mathematics exam. It provides guidance to examiners on how to mark students' responses, including what constitutes correct working and answers for different parts of questions. The document also provides background information on the exam board and qualifications.
4 4 revision session 16th april coordinate geometry structured revision for C...claire meadows-smith
The Community Maths School is offering a structure revision programme to prepare students for the Core 1 exam on May 19th. The programme will include 6 revision sessions from March 24th to April 28th covering topics like translations of graphs, simultaneous equations, inequalities, and coordinate geometry. Additional exam practice sessions will be held on May 5th and May 12th. Resources and past papers will be available on the Exam Solutions website and Mathscard app.
The document provides the mark scheme for the March 2012 GCSE Mathematics (2MB01) Higher 5MB2H (Non-Calculator) Paper 01 exam. It outlines the general principles for marking the exam, including how to award full marks if deserved and how to follow through marks from previous steps. The document also provides subject-specific guidance for marking questions involving areas like probability, linear equations, and multi-step calculations.
This document provides instructions and information for a practice GCSE Mathematics exam. It specifies that the exam is 1 hour and 45 minutes long and covers various topics in mathematics. It provides the materials allowed, instructions on completing the exam, information about marking and time allocation, and advice to students. The exam contains 18 questions testing skills in algebra, graphs, geometry, statistics, and problem solving. It is out of a total of 80 marks.
This document provides instructions and information for a practice GCSE mathematics exam. It outlines what materials are allowed, how to answer questions, how marks are allocated, and advice for taking the test. The exam contains 20 multiple-choice and written-response questions testing a range of math skills, including algebra, geometry, statistics, and transformations. It is 80 marks total and lasts 1 hour and 30 minutes.
This document provides a mark scheme for GCSE Mathematics (Linear) 1MA0 Higher (Calculator) Paper 2H from March 2013. It outlines the general principles that examiners should follow when marking, such as awarding all marks that are deserved and following through correct working. It also provides specific guidance on marking certain types of questions involving areas like probability, linear equations, and multi-step calculations. The document aims to ensure examiners apply marks consistently across all candidates.
This document provides the final mark scheme for Edexcel's Core Mathematics C1 exam from January 2012. It lists the questions, schemes for awarding marks, and total marks for each question. The six mark questions cover topics like algebra, inequalities, coordinate geometry, and calculus. The longer questions involve multi-step problems applying these concepts, including sketching curves, finding equations of tangents and normals, and solving word problems involving formulas.
The document provides instructions for a mathematics exam. It instructs students to fill out their personal information, use black or blue ink, answer all questions in the spaces provided, and show their working. It notes the total marks for the paper is 60 and which questions require clear written communication. The document advises students to read questions carefully, keep track of time, try to answer every question, and check their work. It also includes a blank formulae page.
The document provides a mark scheme for a GCSE mathematics exam. It outlines the general marking guidance which instructs examiners to mark candidates positively and award full marks for deserved answers. It also notes specific codes used within the mark scheme to indicate different types of marks. The bulk of the document consists of a question-by-question breakdown of 15 exam questions, providing the expected answers, marks allocated, and detailed guidance on awarding marks for work shown.
This document contains a mark scheme for a GCSE mathematics exam. It provides guidance for examiners on how to apply marks for different parts of student responses. Some key points include:
1) Examiners must mark all students equally and reward students for what they show they can do rather than penalize for omissions.
2) Full marks should be awarded if the answer matches the mark scheme.
3) Working should be considered, even if the final answer is incorrect, to award method marks where appropriate.
4) Follow through marks can be awarded if subsequent working is based on a previous correct response.
5) Marks cannot be awarded for one part of a question in another part
The document is a mark scheme for GCSE Mathematics (2MB01) Foundation 5MB2F (Non-Calculator) Paper 01 exam from March 2012. It provides notes on marking principles and guidance for how to apply marks for specific types of questions and responses. It also includes worked examples showing the breakdown of method and accuracy marks for sample multi-step questions.
This document provides the mark scheme and answers for the Edexcel Decision Mathematics D1 exam from January 2013. It lists the questions, marks allocated, and model answers or marking points for each part. The exam consisted of multiple-choice, short answer, and multi-step word problems involving topics like linear programming, networks, and critical path analysis. The highest number of marks available for a single question was 8 marks for question 3. In total, the exam was worth 76 marks.
1. This document contains a math exam with 31 questions testing various math skills like algebra, geometry, statistics, and problem solving.
2. The exam is broken into questions with points allocated for each part. An assessment sheet is provided to track points earned for each question.
3. The questions range in difficulty from basic operations to multi-step word problems. Various math concepts are covered, including fractions, ratios, graphs, equations, probability, and more.
Mark schemes provide principles for awarding marks on exam questions. This document contains:
1) Notes on general marking principles such as awarding all marks, following through errors, and ignoring subsequent work.
2) Examples of mark schemes for GCSE math questions, including breakdowns of method marks and accuracy marks for steps in solutions.
3) Guidance on codes used in mark schemes and policies for partial answers, probability notation, and more.
1. Indices involve rules for exponents like xa+b = xaxb and (xa)b = xab. Solving exponential equations uses these rules.
2. Graph transformations include translations, stretches, reflections, and asymptotes. Translations replace x with (x-a) and y with (y-b).
3. Sequences are functions with successive terms defined by a rule. Geometric sequences multiply successive terms by a constant ratio while arithmetic sequences add a constant.
3 revision session for core 1 translations of graphs, simultaneous equation...claire meadows-smith
The Community Maths School has structured a revision programme to prepare students for the Core 1 exam. The programme is based on the AQA AS exam but is suitable for most boards. Over six revision sessions in March and April, the school will provide hints, exam solutions, and practice questions on topics like translations of graphs, simultaneous equations, and inequalities. Additional exam practice sessions will be held in May to help students for the Core 1 exam on May 19th.
1. This document appears to be an exam paper for the Edexcel GCSE Methods in Mathematics exam. It provides instructions for students on how to complete the exam.
2. The exam consists of multiple choice and free response questions covering topics like operations with fractions, probability, geometry, and algebra. It is 1 hour and 45 minutes long.
3. Students are provided a formula sheet but are instructed not to write on it. Calculators are not permitted. Questions are worth varying point values adding up to a total of 100 points.
This document appears to be the cover page and instructions for a GCSE mathematics exam. It provides information such as the exam date and time allotted, materials allowed, instructions for candidates, and a formulae page. Candidates are instructed to show all work, not spend too long on any single question, and attempt all 23 questions, writing their answers in the provided spaces. The formulae page lists various mathematical formulas that may be useful for the exam but on which candidates are not allowed to write.
(1) The document is the front cover and instructions for a mathematics preliminary examination. It provides instructions such as writing one's name and index number, answering all questions, showing working, and bundling all work together at the end.
(2) The examination contains 14 pages with 80 total marks across multiple choice and written answer questions involving topics like algebra, trigonometry, calculus, statistics, and geometry.
(3) Several mathematical formulas are provided for reference, including formulas for compound interest, mensuration, trigonometry, and statistics. Candidates are advised to use these formulas where appropriate.
This document provides instructions and information for a GCSE mathematics exam, including the exam paper reference number, candidate details to fill in, materials allowed, instructions to candidates, information about marking, and a formulae page. It specifies that the exam is 2 hours long and contains 23 questions covering a range of mathematics topics. Candidates are advised to show their working, work steadily, and attempt all questions.
This document contains instructions and questions for a mathematics exam. It provides information about the exam such as the date, time allowed, materials permitted, and instructions for completing and submitting the exam. The exam contains 7 multi-part questions testing a variety of mathematics concepts including algebra, geometry, trigonometry, statistics, and matrix operations.
This document is the cover page for a mathematics preliminary examination. It provides instructions for candidates taking the exam, including writing their identification information, answering all questions, showing necessary work, using calculators appropriately, and specifying the degree of accuracy for answers. It also lists several mathematical formulas that may be useful for the exam, such as formulas for compound interest, mensuration, trigonometry, and statistics. The total number of marks for the exam is 80.
This document is a mathematics exam for Secondary 4 students consisting of 10 questions testing various math concepts. It provides instructions for students on how to answer the questions, lists relevant mathematical formulas, and presents the questions which cover topics like matrices, trigonometry, financial math, algebra, geometry, and statistics. The exam is 100 marks total and students are given 150 minutes to complete it.
This document is the first paper of the Secondary 4 Express / 5 Normal Mathematics Preliminary Examination from 2009. It consists of 16 printed pages and has 10 questions. The questions cover a range of mathematics topics including calculations, simultaneous equations, rates of change, sets and probabilities. Students are instructed to show their working, use calculators appropriately, and express their answers to a given degree of accuracy. They must answer all questions and ensure their work is securely fastened together at the end. The total number of marks for the paper is 80.
1. The document is a mathematics exam for Secondary 4 students consisting of 23 questions testing topics like algebra, trigonometry, geometry, and statistics.
2. The exam is 80 marks and students are instructed to show working, use a calculator, and answer in the spaces provided on the question paper.
3. The questions cover topics such as solving equations, factorizing expressions, finding probabilities, sketching graphs, proving geometric statements, and interpreting data from tables and graphs.
(1) The document is an examination paper for Secondary 4/5 students in mathematics. It consists of 13 printed pages containing 11 questions testing various math concepts.
(2) Instructions are provided for candidates, including writing their name, working clearly, using calculators where appropriate, and expressing some answers to a given degree of accuracy or in terms of pi.
(3) The exam covers topics like algebra, trigonometry, geometry, calculus, statistics, and financial mathematics. Questions involve factorizing expressions, solving equations, using circle properties, graphing functions, and probability.
This document contains instructions and questions for a mathematics preliminary examination. It consists of 7 questions testing skills in algebra, trigonometry, geometry, statistics, and problem solving. Students are instructed to show their working, use formulas provided, and give answers to a specified degree of accuracy. A total of 100 marks are available across the exam.
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.
The document is the question paper for a Secondary 4 mathematics examination consisting of 11 questions testing topics including algebra, geometry, trigonometry, statistics, and sequences and series. The exam has a maximum score of 100 marks and covers areas such as simplifying expressions, solving equations, calculating lengths, areas, volumes, probabilities, and interpreting graphs. Candidates are instructed to show working, use calculators appropriately, and express answers to a given degree of accuracy.
This document is the cover page and instructions for a 1 hour 45 minute GCSE Mathematics exam. It provides information such as the materials allowed, instructions for completing the exam, exam structure, and advice for students. The exam consists of 27 multiple choice and free response questions testing a variety of math skills, including algebra, geometry, statistics, and trigonometry. Students are advised to read questions carefully, watch the time, attempt all questions, and check their work. Calculators are not permitted.
This document discusses finding the areas of various shapes including squares, rectangles, parallelograms, triangles, trapezoids, kites, and rhombuses. It provides the area formulas for each shape: the area of a square is the length of its side squared; the area of a rectangle is base times height; the area of a parallelogram is base times height; the area of a triangle is one-half base times height; the area of a trapezoid is one-half the height times the sum of the bases; the area of a kite and rhombus is one-half the product of the diagonals times the height. Examples are provided for finding the areas of different
This document provides instructions for a test. It begins by instructing students not to open the question paper until instructed by the invigilator. It then provides the following information:
1) The test contains 90 questions worth 4 marks each, with 1 mark deducted for incorrect answers.
2) Instructions are provided for correctly filling out the answer sheet, including using a pencil to shade bubbles, marking the answer for each question, and verifying information.
3) A sample question is provided from the mathematics section to demonstrate the multiple choice format.
The document provides instructions for sketching a sinusoidal graph in 3 steps: 1) Identify the key characteristics of the sinusoidal function, including median line, amplitude, period, and start point. 2) Draw the median line and mark the start, end, maximum, and minimum points. 3) Join the points with a smooth curve. It then gives an example sinusoidal function to sketch.
The document is a preliminary examination paper for Secondary 4/5 students in Jurongville Secondary School. It consists of 22 questions on elementary mathematics covering topics like mensuration, algebra, trigonometry, statistics, and coordinate geometry. The paper is 80 marks and students are instructed to show working for questions where necessary. They are provided with relevant formulas and given 2 hours to complete the exam.
This document provides an agenda and notes for a math class that is reviewing quadratic functions and equations. It includes warm-up problems to solve quadratic equations algebraically and graphically, identifies an upcoming test on sections 10.1-10.3, and provides class work where students must show the steps to graph quadratic functions using a table of values.
This document provides instruction and examples for calculating distance between points on a coordinate plane and working with absolute value. It defines absolute value as the distance between two numbers and shows how to solve equations involving absolute value. Sample problems are provided to practice finding distances between points, evaluating absolute values, and solving absolute value equations. Students are asked to work through examples with a partner and complete related homework problems.
The document provides information about the format and content of the GCE O-Level Mathematics examination. It consists of two papers, each lasting 2 hours. Paper 1 tests fundamental skills and concepts through 25 short answer questions. Paper 2 tests higher-order thinking through 10-11 longer questions. Calculators and geometrical instruments are allowed. Answers should be given to three decimal places, unless otherwise specified. Various mathematical formulae are provided.
The document lists topics that could be assessed on the last of three papers, including: algebra, sequences, equations, graph transformations, functions, geometry concepts like area, volume, scale factors and shapes, trigonometry, vectors, and data/probability topics such as averages, graphs, and diagrams. Key mathematical areas covered are numbers, algebra, geometry, trigonometry, vectors, and statistics.
This document lists potential topics that could be assessed on the last foundation paper, including algebra, geometry, trigonometry, statistics, and probability concepts. Some examples are LCM and HCF, BIDMAS, exchange rates, coordinates and midpoints, volume and surface area, angles, arcs and sectors using trigonometry, speed-time graphs, averages, Venn diagrams, and two-way tables.
This document provides an acronym "A ripe forest" to help with persuasive writing techniques. It lists persuasive writing elements such as anecdotes, repetition, imperatives, pronouns, exaggeration, facts, opinions, rhetorical questions, emotive language, statistics, and triples. It notes you wouldn't use all of these but should choose the most appropriate for the task and remember purpose, audience, language, and layout.
This document provides a list of structural elements that may be present in a writing sample, including changes in time, place, sentence structure, focus, setting, and order. It identifies patterns, dialogue, flashbacks, sentence length, introductions, climaxes, conclusions, contrasts, and other techniques that reveal how a text is organized and what occurs within it.
This document provides an outline for a GCSE revision session taking place in June 2017. The session includes 6 activities to help students understand exam topics and develop effective revision strategies. Students will analyze exam extracts, consolidate language skills, review persuasive writing techniques, choose individual writing activities, discuss exam strategies, and create a personal revision plan. Useful revision tips and websites are also provided to support students in their preparation for the upcoming GCSE exams.
1. The document provides revision notes and ideas for various science topics organized into different units including fitness and health, human health and diet, staying healthy, the nervous system, drugs, staying in balance, controlling plant growth, and variation and inheritance.
2. Each topic within the units outlines key information to revise and provides one or two revision ideas such as making flashcards, designing experiments or diagrams, producing posters or leaflets, or developing question and answer activities.
3. Some common themes across the topics include the human body systems, health and disease, genetics, plant science, chemicals and their reactions, and polymers. The information and revision suggestions are aimed at different grade levels from E to A.
The document advertises "GradeBooster" classes that aim to improve exam grades through one-day or two-day master classes costing £180 and £300 respectively. The classes will take place at Kesgrave Community Centre on May 30th and 31st and in Bury St. Edmunds on June 1st and 2nd. Additional "Maths drop-in" sessions costing £20 per session or £30 for all three will be held on various Wednesdays and Mondays in May and June to provide extra math help for the GradeBooster classes.
This document contains a series of 21 math questions with explanations and worked examples. The questions cover topics like time, distance, rate, money, graphs, conversions between units, straight line graphs, and coordinate geometry. For each question, the number of marks available is provided. This appears to be a practice exam or set of worksheet problems for a math course.
The document provides examiners' reports and mark schemes for 21 math exam questions:
1) Question 1 involved subtracting times on a travel graph. Most students successfully subtracted the times, though some struggled with converting minutes to hours.
2) Questions 2-7 covered topics like travel graphs, percentages, sponsorship amounts, and staged charging structures. Most students answered parts of these questions correctly, though some made errors in calculations or failed to show their work.
3) Questions 8-21 covered a range of math topics from currency conversions to graphing lines. Many students struggled with interpreting scales accurately and converting between units consistently. Common errors included incorrect values, plotting points inaccurately, and failing to show steps in solutions
This document contains 22 math questions with explanations and worked examples related to topics like pie charts, percentages, ratios, time, money, operations, geometry, and measurement. The questions range from 1 to 7 marks and cover skills such as interpreting data in tables and charts, calculating percentages, solving word problems involving rates and time, using scales on maps, and calculating bearings and distances on diagrams.
This document contains examiners' reports on 22 math exam questions:
- Many students had difficulty drawing accurate pie charts and calculating percentages, angles, and sectors. Use of protractors was inconsistent.
- Bearings, scale drawings, and conversions between units also posed challenges. Accuracy was an issue.
- Multi-step word problems involving rates, proportions, or staged charging structures caused errors, as students struggled with understanding the concepts.
- Familiar topics like addition, subtraction, multiplication were generally answered correctly, but negatives signs and order of operations led to mistakes.
- Pythagoras' theorem, trigonometry including bearings were attempted, but understanding was sometimes lacking, leading to inaccurate responses.
This document contains a 14 question math exam with questions covering various topics including trigonometry, algebra, geometry, and calculus. The exam has a total of 58 marks. Each question is broken down into parts and shows the working and/or final answers. Marking schemes are provided showing the number of marks allocated to each part.
This document summarizes examiners' reports on questions from a math exam. Key points include:
- For question 2, many students found the correct length using Pythagoras' theorem but some made mistakes in algebra. Others started correctly with trigonometry but could not continue.
- Question 5 caused issues as some students subtracted rather than added when using Pythagoras' theorem, losing accuracy.
- Question 6 stumped many students who did not recognize it as a trigonometry problem. Few managed the full correct solution.
- Question 8 was generally answered poorly with many not understanding how to factorize or change the subject of a formula.
- Question 10 saw the preferred method of finding side lengths
This document provides a list of useful websites for spelling, grammar, language devices, general writing practice, and revision techniques. Key resources include sites run by Aylsham High School, OCR, and Kent Schools that offer guides to spelling, punctuation, grammar, sentence starters, and vocabulary. YouTube channels like Mr. Bruff provide videos explaining AQA exam question structures. Other sites provide quizzes on ambitious vocabulary, as well as general writing packs and mind mapping tools to support creative revision practices.
Check the exam details and come prepared with the necessary equipment. Listen carefully to the instructions and time each question to move on if you exceed the allotted time. Read questions multiple times and highlight key words. Consider your reading approach and read the entire text. Plan for essay questions and stick to the outline while writing for the intended purpose and audience. Use techniques you've practiced and revision guides for advice.
The document provides various revision tips for students preparing for exams. It recommends creating a revision plan and sticking to a schedule that increases revision time as exams approach. Students should start revising early instead of cramming last minute. Taking regular breaks is also suggested to avoid burnout. The tips include organizing notes by subject, using memory techniques like mnemonics and flashcards, getting tested by others, and practicing past essays and short plans under timed conditions.
This document contains 18 math questions with varying levels of difficulty related to topics like Pythagoras' theorem, percentages, proportions, geometry, and financial calculations. The questions provide worked examples, diagrams, and multi-step word problems for students to practice solving. Scores are provided after each question indicating the total marks available for getting the problem correct.
The examiner's report discusses common mistakes students made on several math exam questions involving Pythagoras' theorem and trigonometry. For questions about right triangles, many students doubled instead of squaring lengths, added lengths instead of squaring and adding them, or subtracted squares. On questions involving finding perimeters or diameters of shapes, some students incorrectly found areas instead. The report provides insight into where additional instruction is needed, such as understanding differences between areas and perimeters, and properly applying trigonometric functions and formulas.
2. GCSE Mathematics 1MA0
Formulae: Higher Tier
You must not write on this formulae page.
Anything you write on this formulae page will gain NO credit.
1
Volume of prism = area of cross section × length Area of trapezium = (a + b)h
2
a
cross
section h
lengt
h b
4 3 1 2
Volume of sphere = ʌU Volume of cone = ʌU h
3 3
Surface area of sphere = 4ʌU 2 Curved surface area of cone = ʌUO
r
l h
r
In any triangle ABC The Quadratic Equation
The solutions of ax2 + bx + c = 0
C
where D 0, are given by
b a −b ± (b 2 − 4ac)
x=
2a
A c B
a b c
Sine Rule = =
sin A sin B sin C
Cosine Rule a2 = b2 + c 2 – 2bc cos A
1
Area of triangle = ab sin C
2
2
*P40645A0228*
3. Answer ALL questions.
Write your answers in the spaces provided.
You must write down all stages in your working.
You must NOT use a calculator.
1 Sam wants to find out the types of film people like best.
He is going to ask whether they like comedy films or action films or science fiction films
or musicals best.
(a) Design a suitable table for a data collection sheet he could use to collect this
information.
(2)
Sam collects his data by asking 10 students in his class at school.
This might not be a good way to find out the types of film people like best.
(b) Give one reason why.
. . . . . . . . . . ............................................................................................. . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . ............................................................................................. . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(1)
(Total for Question 1 is 3 marks)
3
*P40645A0328* Turn over
4. 2 The diagram shows a patio in the shape of a rectangle.
Diagram NOT
3m accurately drawn
3.6 m
The patio is 3.6 m long and 3 m wide.
Matthew is going to cover the patio with paving slabs.
Each paving slab is a square of side 60 cm.
Matthew buys 32 of the paving slabs.
(a) Does Matthew buy enough paving slabs to cover the patio?
You must show all your working.
. . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . .
(3)
The paving slabs cost £8.63 each.
(b) Work out the total cost of the 32 paving slabs.
£ . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . .
(3)
(Total for Question 2 is 6 marks)
4
*P40645A0428*
5. *3 Bill uses his van to deliver parcels.
For each parcel Bill delivers there is a fixed charge plus £1.00 for each mile.
You can use the graph to find the total cost of having a parcel delivered by Bill.
80
70
60
50
Cost (£) 40
30
20
10
0
0 5 10 15 20 25 30 35 40 45 50
Distance (miles)
(a) How much is the fixed charge?
£ . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . .
(1)
Ed uses a van to deliver parcels.
For each parcel Ed delivers it costs £1.50 for each mile.
There is no fixed charge.
(b) Compare the cost of having a parcel delivered by Bill with the cost of having a parcel
delivered by Ed.
(3)
(Total for Question 3 is 4 marks)
5
*P40645A0528* Turn over
6. 4 Here are the speeds, in miles per hour, of 16 cars.
31 52 43 49 36 35 33 29
54 43 44 46 42 39 55 48
Draw an ordered stem and leaf diagram for these speeds.
(Total for Question 4 is 3 marks)
6
*P40645A0628*
7. 5
Medicine
You can work out the amount of medicine, c mO, to give to a child by using the formula
ma
c=
150
m is the age of the child, in months.
a is an adult dose, in mO
A child is 30 months old.
An adult’s dose is 40 mO.
Work out the amount of medicine you can give to the child.
................................. . . . . . . . . . . . . . mO
(Total for Question 5 is 2 marks)
7
*P40645A0728* Turn over
8. 6 Here are the ingredients needed to make 12 shortcakes.
Shortcakes
Makes 12 shortcakes
50 g of sugar
200 g of butter
200 g of flour
10 mO of milk
Liz makes some shortcakes.
She uses 25 mO of milk.
(a) How many shortcakes does Liz make?
. . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . .
(2)
Robert has 500 g of sugar
1000 g of butter
1000 g of flour
500 mO of milk
(b) Work out the greatest number of shortcakes Robert can make.
. . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . .
(2)
(Total for Question 6 is 4 marks)
8
*P40645A0828*
9. 7 Buses to Acton leave a bus station every 24 minutes.
Buses to Barton leave the same bus station every 20 minutes.
A bus to Acton and a bus to Barton both leave the bus station at 9 00 am.
When will a bus to Acton and a bus to Barton next leave the bus station at the same time?
. . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . .
(Total for Question 7 is 3 marks)
8 (a) Expand 3(2y – 5)
. . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . .
(1)
(b) Factorise completely 8x2 + 4xy
. . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . .
(2)
(c) Make h the subject of the formula
gh
t =
10
h = . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . .
(2)
(Total for Question 8 is 5 marks)
9
*P40645A0928* Turn over
11. *10 Railtickets and Cheaptrains are two websites selling train tickets.
Each of the websites adds a credit card charge and a booking fee to the ticket price.
Railtickets Cheaptrains
Credit card charge: 2.25% of ticket price Credit card charge: 1.5% of ticket price
Booking fee: 80 pence Booking fee: £1.90
Nadia wants to buy a train ticket.
The ticket price is £60 on each website.
Nadia will pay by credit card.
Will it be cheaper for Nadia to buy the train ticket from Railtickets or from Cheaptrains?
(Total for Question 10 is 4 marks)
11
*P40645A01128* Turn over
12. 11
2x
3x – 15
Diagram NOT
accurately drawn
2x 2x + 24
The diagram shows a parallelogram.
The sizes of the angles, in degrees, are
2x
3x – 15
2x
2x + 24
Work out the value of x.
x = . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . .
(Total for Question 11 is 3 marks)
12
*P40645A01228*
13. 12 Jane has a carton of orange juice.
The carton is in the shape of a cuboid.
Diagram NOT
accurately drawn
20 cm
10 cm
6 cm
The depth of the orange juice in the carton is 8 cm.
Jane closes the carton.
Then she turns the carton over so that it stands on the shaded face.
Work out the depth, in cm, of the orange juice now.
.............................................. cm
(Total for Question 12 is 3 marks)
13
*P40645A01328* Turn over
14. 13
Diagram NOT
accurately drawn
x
The diagram shows a regular hexagon and a regular octagon.
Calculate the size of the angle marked x.
You must show all your working.
°
..............................................
(Total for Question 13 is 4 marks)
14
*P40645A01428*
15. 14 The diagram shows the position of a lighthouse L and a harbour H.
N
N
L
H
The scale of the diagram is 1 cm represents 5 km.
(a) Work out the real distance between L and H.
.............................................. km
(1)
(b) Measure the bearing of H from L.
°
..............................................
(1)
A boat B is 20 km from H on a bearing of 040°
(c) On the diagram, mark the position of boat B with a cross (×).
Label it B.
(2)
(Total for Question 14 is 4 marks)
15
*P40645A01528* Turn over
16. 15 Harry grows tomatoes.
This year he put his tomato plants into two groups, group A and group B.
Harry gave fertiliser to the tomato plants in group A.
He did not give fertiliser to the tomato plants in group B.
Harry weighed 60 tomatoes from group A.
The cumulative frequency graph shows some information about these weights.
60
50
40
Cumulative
frequency
30
20
10
0
140 150 160 170 180 190
Weight (g)
(a) Use the graph to find an estimate for the median weight.
.............................................. g
(1)
16
*P40645A01628*
18. 16 (a) Simplify (m–2)5
. . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . .
(1)
(b) Factorise x2 + 3x – 10
..........................................................................
(2)
(Total for Question 16 is 3 marks)
17 (a) Write down the value of 100
. . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . .
(1)
(b) Write 6.7 × 10–5 as an ordinary number.
..........................................................................
(1)
(c) Work out the value of (3 × 107) × (9 × 106)
Give your answer in standard form.
..........................................................................
(2)
(Total for Question 17 is 4 marks)
18
*P40645A01828*
19. 18
y
7
6
C
5
4
3
2
A B
1
O 1 2 3 4 5 6 7 8 x
Triangle ABC is drawn on a centimetre grid.
A is the point (2, 2).
B is the point (6, 2).
C is the point (5, 5).
1
Triangle PQR is an enlargement of triangle ABC with scale factor and centre (0, 0).
2
Work out the area of triangle PQR.
.............................................. cm2
(Total for Question 18 is 3 marks)
19
*P40645A01928* Turn over
20. 19 Wendy goes to a fun fair.
She has one go at Hoopla.
She has one go on the Coconut shy.
The probability that she wins at Hoopla is 0.4
The probability that she wins on the Coconut shy is 0.3
(a) Complete the probability tree diagram.
Hoopla Coconut shy
Wendy
0.3 wins
Wendy
0.4 wins
.............. Wendy does
not win
Wendy
..............
wins
.............. Wendy does
not win
.............. Wendy does
not win
(2)
(b) Work out the probability that Wendy wins at Hoopla and also wins on the
Coconut shy.
..............................................
(2)
(Total for Question 19 is 4 marks)
20
*P40645A02028*
22. *21
D
O C
Diagram NOT
accurately drawn
50°
A B
B, C and D are points on the circumference of a circle, centre O.
AB and AD are tangents to the circle.
Angle DAB = 50°
Work out the size of angle BCD.
Give a reason for each stage in your working.
(Total for Question 21 is 4 marks)
22
*P40645A02228*
23. 22 The table gives some information about the speeds, in km/h, of 100 cars.
Speed (s km/h) Frequency
60 s - 65 15
65 s - 70 25
70 s - 80 36
80 s - 100 24
(a) On the grid, draw a histogram for the information in the table.
60 70 80 90 100
Speed (s km/h)
(3)
(b) Work out an estimate for the number of cars with a speed of more than 85 km/h.
..............................................
(2)
(Total for Question 22 is 5 marks)
23
*P40645A02328* Turn over
25. 25 The diagram shows a solid metal cylinder.
Diagram NOT
accurately drawn
9x
2x
The cylinder has base radius 2x and height 9x.
The cylinder is melted down and made into a sphere of radius U.
Find an expression for U in terms of x.
. . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . .
(Total for Question 25 is 3 marks)
25
*P40645A02528* Turn over
26. 26 The graph of y = f(x) is shown on each of the grids.
(a) On this grid, sketch the graph of y = f(x – 3)
y
6
5
4
3
2
1
–5 –4 –3 –2 –1 O 1 2 3 4 5 6 7 x
–1
–2
–3
–4
(2)
26
*P40645A02628*
27. (b) On this grid, sketch the graph of y = 2f(x)
y
8
7
6
5
4
3
2
1
–5 –4 –3 –2 –1 O 1 2 3 4 5 6 7 x
–1
–2
–3
(2)
(Total for Question 26 is 4 marks)
TOTAL FOR PAPER IS 100 MARKS
27
*P40645A02728*