Strictly as per MATH AA SYLLABUS AHL Series
MODEL PAPER FOR FEB 2020 / MARCH 2020 TERM ASSESSMENT for DUBAI SCHOOLS Name of Candidate: __________________ Paper: 1 Duration: 2 hours
Subject: Mathematics Level: AA- HL Date:
INSTRUCTIONS TO CANDIDATES • • • • • • •
Do not open this examination paper until instructed to do so. You are not permitted access to any calculator for this paper. Section A: Answer all questions. Section B: Answer all questions. Unless otherwise stated in the question, all numerical answers must be given exactly or correct to three significant figures. A clean copy of the Mathematics HL formula booklet is required for this paper. The maximum mark for this examination paper is [105 marks].
Question No. Marks Obtained Out of
1
2
3
4
5
6
7
8
Total
11
9
10
9
8
17
22
19
106
Invigilator’s Signature: _______________________ Subject Teacher’s Signature: _______________________
Questions created by: prof. Iyer None of the questions are copied from any past paper or from any book or IB related website. Created strictly as per new Math AA curriculum first exam 2021 confining to the standards. Content © Prof.Iyer. For detailed mark schemes write to ibwithiyer@gmail.com Interested schools who wish to register for IB Assessment services write to office@ibwithiyer.com Prof Iyer works in an IB school as head of the department. He is one of the authors – of one of the higherlevel book, Examiner and Curriculum Manager of IB Math. Now developing a single- authored text book for the new curriculum of Math –both For AA and AI to be released in September 2020 .He supports. IB / A level / AP students all over the world .Besides teaching in school, he also guides students of many IB SCHOOLS in both IB and in TEST Prep exams- SAT/ ACT / AP s. Post IB , He teaches Calculus and statistics for Undergrad and Post grad programs of US and UK universities for the past 15 years He is the contributor of the MATHEMATICAL TIMES for the international section . He has been teaching IB , British and US curriculum Mathematics since 2005 . He is reachable at ibwithiyer@gmail.com
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*FRESHMEN
MODEL PAPER AA HL – TERM ASSESSMENTN FEB / MARCH 2020 FOR DUBAI SCHOOLS QUESTIONS COPYRIGHT© PROF.IYER IBWITHIYER@GMAIL.COM
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Question 1 If the nth term of an Arithmetic progression equals n and mth term of an the same progression equals m , a. Prove that common difference equals -1 b. Find (m+n) th term c. Find the sum of first(m+n) terms
11 marks
(4) (4) (3)
MODEL PAPER AA HL – TERM ASSESSMENTN FEB / MARCH 2020 FOR DUBAI SCHOOLS QUESTIONS COPYRIGHT© PROF.IYER IBWITHIYER@GMAIL.COM
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Question 2 If Tn+1 = 2(3n-1) and Tm-1 = 3(2m+1) are (n+1) th and (m-1) th term of 2 different geometric progressions for n≼ đ?&#x;? đ?’‚đ?’?đ?’… đ?’Ž ≼ đ?&#x;? a. Find the ratios of mth term and nth term b. Prove that when mth term equals nth term, đ??Ľđ??¨đ?? đ?&#x;‘ đ?&#x;? =
đ?’Žâˆ’đ?&#x;‘ đ?’?+đ?&#x;?
9 marks
(4)
(5)
MODEL PAPER AA HL – TERM ASSESSMENTN FEB / MARCH 2020 FOR DUBAI SCHOOLS QUESTIONS COPYRIGHTŠ PROF.IYER IBWITHIYER@GMAIL.COM
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Question 3 If đ?‘źđ?’? a. b. c.
đ?’Œ = ∑đ?’?đ?’Œ=đ?&#x;?(đ?&#x;?đ?’Œ − đ?&#x;‘ ) and đ?‘˝đ?’? = ∑đ?’?+đ?&#x;? đ?’Œ=đ?&#x;?(đ?&#x;? − đ?&#x;‘ ) Find the nth term of each U and V series Using (a) or other otherwise, find the first 3 terms of each series Find đ?‘źđ?’? đ?’‚đ?’?đ?’… đ?‘˝đ?’? đ?’Šđ?’? đ?’•đ?’†đ?’“đ?’Žđ?’” đ?’?đ?’‡ đ?’?
10 marks (3) (3) (4)
‘
MODEL PAPER AA HL – TERM ASSESSMENTN FEB / MARCH 2020 FOR DUBAI SCHOOLS QUESTIONS COPYRIGHTŠ PROF.IYER IBWITHIYER@GMAIL.COM
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Question 4
9 marks
𝒏
𝐼𝑓 ∑ 𝐥𝐨𝐠 𝒙𝒊 = 𝑺 𝒊=𝟏
a. Find the nth term of S b. Find x in terms of n if S = 1
∑𝒏𝒊=𝟏(𝒍𝒐𝒈𝒙)𝒊 = 𝑻 find T in terms of n
(1) (4) for x >10
(4)
MODEL PAPER AA HL – TERM ASSESSMENTN FEB / MARCH 2020 FOR DUBAI SCHOOLS QUESTIONS COPYRIGHT© PROF.IYER IBWITHIYER@GMAIL.COM
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Question 5 Given log (x+2) – log (x-1)-1 = y a. Find the range of x values for which y exist b. Given y = 0, find the values of x c. If log is replaced by natural logarithm (ln) Find the value of x
8 marks (2) (4) (2)
MODEL PAPER AA HL – TERM ASSESSMENTN FEB / MARCH 2020 FOR DUBAI SCHOOLS QUESTIONS COPYRIGHT© PROF.IYER IBWITHIYER@GMAIL.COM
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Question 6
17 marks đ?&#x;? đ?’™
Given f(x) = a. Using First principles, find the derivative of f(x) b. Find the equation of tangent using the result of (a) at x= 1 c. If equation of normal at x =-1 cuts at x=a and y =b, Find a and b d. Find the second derivative and hence find the nth derivative of f(x)
Question 7
22 marks
If f(x) = (x -2), g(x) = 2
a. b. c. d.
(3) (3) (4) (7)
đ?’™+đ?&#x;? đ?’™đ?&#x;? −đ?&#x;“đ?’™âˆ’đ?&#x;”
and h(x) = f(x).g(x)
Find domain of f(x) Find the range of x values for which g(x) < 0 Find all possible asymptotes of h(x) Does asymptotes of h(x) intersect each other ? Investigate đ?&#x2018;¨
đ?&#x2018;Š
e. Resolve g(x) in the form of + đ?&#x2019;&#x2122;â&#x2C6;&#x2019;đ?&#x;&#x201D; đ?&#x2019;&#x2122;+đ?&#x;? f. Use binomial theorem to expand upto x3 terms using the result of (e )
(2) (3) (5) (3) (4) (5)
Question 8
If f(x) = 2 sin (2x -1) -1 a. Find the amplitude and periodicity of f(x) b. Transform f(x) to g(x) where g(x)= sin x describing all transformations in detail c. Write [f( x + ½ ) + 1 ] in terms of tan x using identities d. Solve for x if
[ đ??&#x;( đ??ą + ½ )+ đ?&#x;? ] đ?&#x203A;&#x2018; đ?? ( â&#x2C6;&#x2019;đ?&#x2019;&#x2122;) đ?&#x;?
đ?&#x;? đ?&#x;?
= for đ?&#x;&#x17D; â&#x2030;¤ đ?&#x2019;&#x2122; â&#x2030;¤ đ?&#x;?đ??&#x2026;
e. Sketch f(x) and g(x) on same graph
19 marks (2) (5) (4) (4) (4)
MODEL PAPER AA HL â&#x20AC;&#x201C; TERM ASSESSMENTN FEB / MARCH 2020 FOR DUBAI SCHOOLS QUESTIONS COPYRIGHTŠ PROF.IYER IBWITHIYER@GMAIL.COM
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For any feedback/ criticisms please write to prof. Iyer at ibwithiyer@gmail.com Prof Iyer Mumbai India Resource and support - / World Groups /Schools / IBI Network / Class Networks / IB Japan Cohort / IB DUBAI /IB Singapore Content copyright of the Question paper © prof. Iyer / 2020
MODEL PAPER AA HL – TERM ASSESSMENTN FEB / MARCH 2020 FOR DUBAI SCHOOLS QUESTIONS COPYRIGHT© PROF.IYER IBWITHIYER@GMAIL.COM
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