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ALL Past Questions TOPIC WISE For The Last 10-12 years

Topic : Statistics - Moving Averages

The average number, in lakhs, of working days lost in strikes during each year of the period 1981–90 was:

Marks [5]

1981	1982	1983	1984	1985	1986	1987	1988	1989	1990
1.5	1.8	1.9	2.2	2.6	3.7	2.2	6.4	3.6	5.4

Calculate the three yearly moving averages and draw the moving averages graph.

Choice in 2005

The number of Traffic offences committed in a certain city over a period of 3 years is given as below:

Marks [10]

Years	Jan-Mar	Apr-Jun	Jul-Sep	Oct-Dec
1980	74	56	48	69
1981	83	52	49	81
1982	94	60	48	79

Calculate four monthly moving averages and illustrate these and original figures on one graph.

Comment briefly on a local politician's claim that traffic offences were on the increase.

Choice in 1999

Calculate 5-yearly moving averages for the following data of the number of commercial and industrial failures in a country from 1982 to 1997:

Marks [7]

Years	No. of Failures	Year	No. of Failures
1982	23	1990	9
1983	26	1991	13
1984	28	1992	11
1985	32	1993	14
1986	20	1994	12
1987	12	1995	9
1988	12	1996	3
1989	10	1997	1

Display the actual and trend values on the same graph using the same axes for both.

Choice in 1998

Equation of Parabola Proving L.H.S. = R.H.S. Measures of Dispersion Solution of Inverse Trigonometric Equations Equation of Ellipse

Topics Covered
1.	Determinants	32..	Lines of Regression
2.	Matrices	33.	Simple Definition
3.	Condition for a 2nd degree equation to represent a pair of Straight lines	34.	Conditional Probability
4.	Angle between the pair of Straight Lines	35.	P (A È B) = P (A) + P (B) – P (A Ç B)
5.	Equation of Angle Bisector	36.	Odds in favour and odds against an event
6.	Finding equation of Straight Lines separately from the given equation of a pair of Straight Lines	37.	Combined Problem of Addition & Multiplication Theorem of Probability
7.	Equation of a Line passing through the point of intersection of two given lines, satisfying ertain conditions	38.	P (at least one of them occurs) = 1-P (none of them occurs)
8.	Equation of a pair of lines parallel to the given equation of pair of Straight Lines	39.	Modulus and Amplitude of Complex Numbers
9.	PS = e PM	40.	Basic Properties of Complex Numbers
10.	The vertex and focus of the Parabola	41.	Maximum and minimum values of \|z\|
11.	Equation of Parabola	42.	Square root of Complex Numbers
12.	Parabola – Locus	43.	Cube root of unity
13.	Eccentricity of the Ellipse	44.	De Moivre's Theorem
14.	Equation of Ellipse	45.	Locus of Complex Numbers – Straight Line
15.	Hyperbola	46.	Locus of Complex Numbers – Circle
16.	Solution of Inverse Trigonometric Equations	47.	Geometry of Complex Numbers
17.	Proving L.H.S. = R.H.S.	48.	Differential Equations in which the variables are separable
18.	Domain and Range	49.	Differential Equations
19.	Differential Calculus – Simple Differentiation	50.	Linear Differential Equations
20.	Applications of Differential Calculus; Mean Value Theorem	51.	Plane
21.	Maxima and Minima	52.	Sphere
22.	Integral Calculus - Simple and Definite Integration	53.	Scalar (dot) product of two Vectors
23.	Area and volume	54.	Cross product of two Vectors
24.	Measures of Dispersion	55.	Triple Products
25.	Karl Pearsons Coefficient	56.	Index Numbers
26.	Spearman's Coefficient of Rank Correlation	57.	Statistics – Moving Averages
27.	Kendall's Rank Correlation	58.	Annuities
28.	Discount	59.	Application of Calculus in commerce and Economics
29.	Bills of Exchange	60.	Baye's Theorem
30.	Depreciation	61.	Binomial Distribution
31.	Average due date

Advantages
1.	Topicwise presentation of all past questions allows topicwise revision. Past questions are the most important questions you must solve first.
2.	Frequency analysis shows types of past questions with marks, year reference and whether choice or compulsory, short or long.
3.	Eliminates questions on topics not part of a forthcoming Board Exam.
4.	Adds model questions for new topics in a forthcoming Board Exam.
5.	Data is presented from the most recent to earlier years, covering 10-12 years.
6.	Perfect for making strategy and for the prioritization of study objectives.

Solutions To All Past Questions

Topic : Statistics - Moving Averages

Question

Solution

Formulae/Concepts Used

Tips

The table given below shows the daily attendance in thousands at a certain exhibition over a period of two weeks.
Week I	Week II
52	55
48	47
64	61
68	65
52	58
70	75
72	81
Calculate 7 day moving Averages and illustrate these original information on the same graph using the same scales.
[7] Sevtion B Choice in 2001

Week	Allevidancein hundreds	Seven daymoving total	Seven daymoving average
Week1
Sunday	52
Monday	48
Tuesday	64
Wednesday	68	426	60.86
Thursday	52	429	61.29
Friday	70	428	61.14
Saturday	72	425	60.71
Week 2
Sunday	55	422	60.29
Monday	47	428	61.14
Tuesday	61	433	61.86
Wednesday	65	424	60.57
Thursday	58
Friday	75
Saturday	81

(1) The Moving Averages smooth out the cyclical movements in given time series the moving Averages are plotted against the corresponding years 1, 2, 3, 4 ......... and the successive points.
(2) If the values for the years 1, 2, 3, 4, ......... are a, b, c, d ......... then the formula for calculating 3-yearly, 4-yearly, 5-yearly ........ moving averages as
4-yearly as etc.

Make sure that - (i) The calculations are correct. (ii) Moving total and moving average are calculated properly. (iii) Graphs are plotted carefully.

Advantages Solutions To All Past Questions
•	They Allow Self Check.
•	They Guide As To How And How Much To Write In The Board Exam.
•	Learn Backwards From Answers.
•	Learn How To Answer In A Board Exam.
•	Tips And Formulae To Memorize.
•	Last Minute Help: Gain Marks Even While You Sit And Read In Bed!

Revision Notes
•	Revision Notes On What Has Already Come In The Last 10-12 Years Are Helpful Throughout The Year, Just Before Examinations, Or Even The Night Before Exam. They Provide A Quick Synopsis Of Solutions And Tips On Each Topic.

Conic Section – Parabola

Questions

Solutions

Formulae

Guidelines/Tips

Find the equation of the parabola whose vertex and focus lie on the y-axis at distances b and b' respectively from the origin.

[4]
Section A
Choice In 1997

We know that – for the parabola of the form (i.e. Axis of parabola is y-axis)
(x - a)2 = 4a (y-b) --------------- (1)
Vertex = (a, b)
Focus = (a, b + a)
In the question, it is given that vertex and focus lie on the y-axis at distances b and b' respectively i.e.

Parabola is of the form (1)
i.e. (x -a)2 = 4a (y-b) --------------------- (1) with
Vertex = (a, b); Focus = (a, b + a)
Thus,
Vertex = (a, b) = (0, b)                                    (Given)
Focus = (a, b + a) = (0, b')                               (Given)
Comparing the coordinates of vertex and focus, we have
a = 0, b = b      --------------- (i)
b + a = b'         --------------- (ii)
From (i) & (ii)
 b + a = b'
or a = (b' – b) --------------- (iii)
Substituting the values of a, b and a in (1), we have the required equation of parabola as (x – 0)2 = 4(b' –b) (y–b)
   x2 = 4(b' –b) (y–b)

Since, vertex and focus of parabola lie on
Y-axis. Hence, axis of parabola is Y-axis.

For the parabola of the form (i.e. Axis of parabola is Y-axis)
(x – a)2 = 4a (y – b) ------------ (1)
Vertex = (a, b)
Focus = (a, b + a)

i	Remember that – the axis of parabola is the axis on which vertex and focus li
ii	Carefully substitute the values.
iii	Follow Method 1 or Method 2, whichever you find easy.
iv	Do not forget to represent the information through figures.
v	For case: b>b'



Tick:How Do You Find This Topic?

Advantages
•	No Need To Make Separate Extensive Revision Notes.
•	Especially Excellent For Last Minute Revision.
•	Use Your Short-Term Memory To Boost Results By Reviewing These Notes The Night Before Exam, When Your Mind Is The Keenest!

Prioritize Using Smart Study Plan Interpretation
•	On Topic 11: Equation of Parabola, there have been four past questions in the last 13 years.
•	They came in the years 2007, 2006, 2005 and 1997.
•	Whether they were Compulsory or Choice questions is indicated by C or NC.
•	For example, the 2007 question was worth three marks and was Compulsory.
•	Suggested time to attempt all these 4 questions on your own is 30 minutes.

Frequency Analysis And Planning Chart

Advantages
•	Find Out Which Past Questions Were Difficult For You By Filling Out Each Circle According To How Difficult You Found A Question.
•	Study According To Your Personal Strengths.
•	Save Time By Planning Better.
•	Revise These Questions For A Second Time To Maximize Marks.
•	Have A Thorough Knowledge Of What Has Already Come In The Last 13 Years On Each Topic.

Remember

Going Over Past Questions Gives You More Confidence. Solutions To Every Past Question As Per Board Guidelines Ensure You Gain Every Possible Mark.

These Are The Most Important Hours You Will Spend Towards Preparation Of Your Board Exam.

Extras
•	How To Work Smart: 10 Keys To Success By Dr Sunita Gandhi.
•	Nutritional Guidelines By Dr Amitabh Pandit, A Well Known Naturopath.
•	Cd–Includes Ten Keys Of Dr Gandhi As Explained By The Students Of City Montessori School (Cms), Lucknow, Up And Testimonies of Students Who Have Used The Sure Success Series.

Please Note
•	Questions And Topics Not Relevant To A Future Board Exam Are Not Included.
•	New Model Questions Are Added Whenever A New Topic Has Been Included By The Council For A Forthcoming Board Exam.

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