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POLICY GUIDELINES FOR MATHEMATICS PAPERPaper Pattern and Distribution of MarksMathematics HSSC-IIThe question paper is organized into following three sections, namely: "Section A, B & C": Questions posed may be text based or derived/unseen but in similar pretext and difficulty level as per the lessons taught in the course. Distribution of the questions with respect to cognitive domain within each section shall roughly be around 30 percent Knowledge (K), 50 percent Understanding (U) and 20 percent Application (A).The Questions in these subjects should be designed in such a manner that no pet-definitions are asked or required from the candidates to be reproduced. Moreover the questions should be appropriately designed whilst keeping in consideration the time for thought-process (particularly in U and A Cognitive Domain questions) and the length of the subsequent text to be produced by the candidates. SECTION — AThis section consists of question number one with 20 compulsory structured part questions - Multiple Choice Questions (MCQs) of one mark each. These MCQs should preferably be designed in such a way that they cover the whole course taught. These MCQs should objectively test the understanding of the concepts of the candidates in these subjects.SECTION — BThis section consists of question number two (02) with preferably 16 part questions – Short Response Questions (SRQs) of four (04) marks each. The candidates are required to attempt (respond to) any Twelve (12) SRQs for a maximum total of 48 marks in this section.SECTION — CThis section consists of Six (06) Extended Response Question (ERQs) of 8 marks each. Candidates are required to attempt (respond to) any Four (04) of these ERQs as per their choice and convenience for a maximum of 32 marks. These questions may comprise of two or more part questions each if deemed necessary by paper setter in order to balance out the distribution various concepts and knowledge areas from different Cognitive Domains taught in course. Annexure for Policy Guidelines for Paper SettingDefinitions and DisclaimerPolicy guidelines for paper setting vide Notification No.6-8/FBISE/RES/CC/918 dated 27 August 2019 have been conveyed for general information. Definitions of some terminologies and disclaimers are given in this annexure.DefinitionsCognitive DomainsCognitive domain refers to development of mental skill and acquisition of knowledge. In the questions papers developed by Federal Board of Intermediate & Secondary Education, Islamabad from hereon will be intended to test the following cognitive domains of the candidates:Knowledge:Approximately 30% Question in each sectionUnderstanding:Approximately 50% Question in each sectionApplication:Approximately 20% Question in each sectionKnowledge (K)Knowledge refers to the ability of the candidates to recall the learned or memorized information or data.ExamplesA child reciting the alphabets of EnglishMemorization and reproducing the dates and other facts etc. e.g. Pakistan came into being on 27th Night of Ramadan-ul-Mubarak. Related Verbs (Command Words)Arrange, define, duplicate, label, list, memorize, name, order, recognize, relate, recall, repeat, reproduce, state etc.Understanding (U)Understand (also called Comprehension) refers to ability of the candidates to comprehend (a set of) information and/or situation and provide his/her response to it accordingly.ExamplesPerforming analyses and illustrating the observationsComprehending the concepts of Social, Natural and Physical Sciencese.g.Discuss different types of noise and their impact on human health briefly. Related Verbs (Command Words)Classify, describe, discuss, explain, express, identify, indicate, locate, recognize, report, restate, review, select, translate, rephrase, differentiate, compare etc.Application (A)Application refers to the ability to use learned material in new and concrete situation to solve problems and/or to design a schedule or task.ExamplesPerforming analyses and illustrating the observationsComprehending the concepts of Social, Natural and Physical Sciencese.g. Illustrate the similes and metaphors given in the poem Daffodils.Related Verbs (Command Words)Apply, choose, demonstrate, dramatize, employ, illustrate, interpret, operate, practice, schedule, sketch, solve, use, write etc.Sections of PaperThere are three or four (03 or 04) sections in each question paper:Section-A Contains Multiple Choice Questions (MCQs). All questions are compulsory without any external or internal choice. Usually comprises of 20% of total marks of the (theory if applicable) paper.Section BContains Short Response Questions (SRQ). Candidates may have external choice up to 33%. In addition to that internal choice may also be offered based upon model, content and/or nature of the subject. This section may contain approximately 50% of total marks in some of subjects of the (theory if applicable) paper. Section CThis section usually contains Extended Response Questions (ERQ). Candidates may have external choice in the questions. In addition to that internal choice may also be offered based upon model, content and/or nature of the subject. For ERQs it may contain approximately 30% of total marks in some subjects of the (theory if applicable) paper.ChoiceSometimes the candidates are required to attempt a certain number of questions from a given pool or group of questions, it is commonly known as choice in questions.There are two types of choices External Choice Whenever the candidates are required to solve (respond to) a certain number of questions from a given pool it is called external choice. This choice may be around 33% in a section. e.g.1.Answer any six parts in about 30-40 words each. (Out of eight questions)2.Attempt any eight questions from the following.(Out of eleven questions)Internal Choice Whenever the candidates have to solve (respond to) a question mandatorily but they have an option within the question it is called internal choice.DisclaimersThe cognitive levels and categories written in sample model paper are for explanation purpose only. In the actual question papers administered during examination shall not contain description of these cognitive domains.Association of the cognitive domains is solely based on subject expert’s judgment and may be subject to errors and/or omissions.In the class rooms and during teaching the candidates (students) need to be taught about the time management in accordance with allocation of marks to the questions. Federal Board HSSC-II ExaminationMathematics Model Question PaperVersion Number SECTION – A Time allowed: 25 minutes Marks: 20Note:Section-A is compulsory. All parts of this section are to be answered on the separately provided OMR Answer Sheet which should be completed in the first 25 minutes and handed over to the Centre Superintendent. Do not use lead pencil.Q.1 Choose the correct answer i.e. A / B / C / D by filling the relevant bubble for each question on the OMR Answer Sheet according to the instructions given there. Each part carries one mark. 1.Let fx=2x+4 and hx=3x2+4. If g(x) be a function such that fx≤g(x)≤h(x) for x∈[-1, 1] then limx→0 gx is:A.2B.3C.4D.52.If domain of fx=4-x2 is [-2, 2], then which of the following represents a graph of fx?A.CircleB.Semi-circle C.SquareD.Hyperbola 3.Which of the following represents f-12, if fx=2tanx ?A.π4 B.7π20 C.π2D.3π4 4.If fx=cosx, x∈π2, π then what results f'3π4?A.32B.12C.-32D.-125.In which of the following intervals, a function fx=2x2-8x+1 increases?A.(-∞, 2]B.(-∞, 0]C.[0, ∞)D.(2, ∞)6.For a function fx=sinsinx what evaluates f'(0)?A.1B.0C.–1 D.does not exist7.Which of the options represent f(x), if f'x=ex+sinx+1 and f0=2?A.fx=ex+cosx+xB.fx=ex-cosx+x+2C.fx=xex-1-cosx+x+3D.fx=ex+cosx8.What evaluates 0π4 etanxcos2xdx? A.e – 1B.eC.π4D.0Page 1 of 29.The graph of fx=axgtdt is shown in the figure. For what value of x does f(x) has its maximum value?A.aB.bC.cD.dadbc10.Which of the following lines passes through (–7, 7), (–7, –7) and (–7, 0)?A.x=-7B.y=-7 C.x+y=-7D.y=-x+7 11.Let y=1x what is the number of x–intercepts and y–intercepts? A.No interceptsB.Two x–interceptsC.Two y–interceptsD.One x and one y–intercept12.At what angle lines 3y=2x+5 and 3x+2y=8 cut each other?A.π6B.π4C.0D.π213.Which of the following options does not satisfy 4x-3y<2?A.1, 1B.0, 0C.(3, 0)D.(-2, 1)14.Through which graph, inequation 2x+3y>4 states its solution set?A.straight line B.half planeC.parabolaD.triangle15.What is the equation of the axis of a parabola y2-2y+8x-23=0?A.y = –1B.x = 3C.y = 1D.x = –316.If (5, –2), (5, 4) are the vertices of an ellipse, then centre of the ellipse is: A.(0, 0) B.(5, 3)C.(5, 1)D.(5, 0) 17.Which shape is the graph of 4x2+y2-8x+4y-9=0?A.CircleB.EllipseC.ParabolaD.Hyperbola18.For what value of ∝, vectors 4i+3j-3k and ∝i+3k have the same magnitude? A.±5 B.5C.25D.–5 19.The covertices of hyperbola x2 – 4y2 = 16 are:A.(±4, 0)B.(0, ±4)C.(±2, 0)D.(0, ±2)20.What is the projection of i-k along j+k?A.12B.-12C.-12D.-1____________________Page 2 of 2Federal Board HSSC-II Examination Mathematics Model Question PaperTime allowed: 2.35 hours Total Marks: 80Note: Sections ‘B’ and ‘C’ comprise pages 1-2 and questions therein are to be answered on the separately provided Answer Book. Use supplementary answer sheet i.e., sheet B if required. Write your answers neatly and legibly.SECTION – B (Marks 48)Q.2Attempt any TWELVE parts. All parts carry equal marks. (12 4 = 48)i.If fx=x+1 and gx=1x2 , x≠0 then find (a)fog(x)(b)gof(x)(c)fof(x)(d)gog(x)ii.Evaluate iii.Find dydx if y=x+1x32-1x12-1 , x≠1iv.Find dydx if x=a(cost+t sint) and y=a(sint- tcost).v.Find y4 if y=cos3xvi.Use differentials to approximate the value of (33)15. vii.Evaluate lnxx2dxviii.A ball is moving in a straight line with acceleration a=2t+8 (a)Find velocity of the ball if v=12m/Sec when t=0(b)Find distance covered by the ball if s=0 when t=0ix.Graph the solution region of the following system of linear inequalities by shading: x.Show that the points A (0, 0), B (2, 1), C (3, 3) and D (1, 2) are the vertices of a rhombus. xi.Find equations of two parallel lines, perpendicular to 2x-y+3=0 such that the product of x and y–intercepts is 3. xii.If the lines 3y=4x-5 and 3y=-4x-13 are diameters of a circle and the point (-5, 0) is also on that circle. Find the equation of this circle. xiii.Write the equation of parabola with focus (–2, –7) that opens to the right and contains the point (6, –1). Page 1 of 2 Turn Over xiv.Find the length of the chord cut off from the line 2x+3y=13 by the circle x2+y2=26.xv.Find the volume of the parallelepiped for which the given vectors are the three edges: u=i-4j-k , v=i-j-2k and w=2i-3j+k xvi.Find the angle between the vectors: u=3i+j-k and v=2i-j+k . SECTION – C (Marks 32)Note:Attempt any FOUR questions. All questions carry equal marks.(4 8 = 32)Q.3Letfx=x-12x+1 ifif x<3x≥3(i)Sketch the graph of the function about x = 3(ii)Find (iii)Find (iv)Is f(x) continuous at x = 3?Q.4Consider the function fx=sinx+122cos2x, where x∈(0, 2π)(i)Find f'(x)(ii)Find f''(x)(iii)Find possible extreme values of f(x)(iv)Find the values of x∈(0, 2π) where f(x) has maximum and minimum values.Q.5For 0π2cosx1+sinx(2+sinx)dx(i)Transform the given definite integral into 01du1+u(2+u)(ii)Resolve 11+u(2+u) into partial fractions(iii)Evaluate the integral 0π2cosx1+sinx(2+sinx)dxQ.6The diagram shows the line l passing through A-1, 1, B5, 5. Given that C(4, 1). Find: (i)Slope of line l(ii)Equation of line l(iii)Area of ?ABC(iv)The length of BC giving your answer correct to two decimal places.ylBxCAQ.7Each unit of food item X costs Rs. 25 and contains 2 units of protein and 4 units of iron while each unit of food item Y costs Rs. 30 and contains 3 units of protein and 2 units of iron. Each animal must receive at least 12 units of protein and 16 units of iron each day. How many units of each food item should be fed to each animal at the smallest possible cost? Q.8Find the centre, foci, eccentricity, vertices and equations of directices of the conic x2-y2+8x-2y-10=0* * * * *Page 2 of 2 ................
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