Board Exams

Board Exams

Mathematics:Board Master Stroke (HSC-2019)

PUBLISH DATE 27th February 2019


Subject:- Mathematics

Author:-  Mrs.Deepashree Prasad Joshi

                 M.Sc, B.Ed


            Revision is important one day before the exam for Maths.

            The following points are to be remembered by students. It will help to score in Maths.

  • Collect your material:

Students should have notes those can be classified on the basis of the following points:

  1. Theorems and corollary
  2. Formulae
  3. Counter example in selective problems


  1. Theorems:

Write the theorems in exam in correct way as per textbook. Avoid different methods to prove the statement of the theorem which is not given in the textbook. Only logical correct methods will be credited by a suitable marking scheme.

If theorem is extended with an example, then write the solution of an example in detail. Do not mention it in short. Use that theorem to find out an answer.

Eg: in ‘A pair of straight line’ chapter, a theorem for an acute angle between the lines represented by ax2+2hxy+by2=0 is asked with an extension that ‘…. Hence find the condition for perpendicular lines.’ So, here only mentioning ‘a+b=0’ is not sufficient answer. m1m2=-1 as lines are perpendicular ... ... a= -b ...a+b=0

Topper cases may lose a mark if they do not proceed in detail.

In ‘trigonometric function’ chapter,

To prove cosine rule, use a geometrical method instead of using projection rule

(until it is asked)

In textbook, sine rule and cosine rules are proved, but student should know how to prove sine rule from cosine rule and vice-versa (which is not in textbook)

  • Applications of vectors to geometry are also important.
  • In integration, maximum part of proof depends on statement itself.
  • In definite integration, properties are important.


  1. Formulae

Apply formulae accurately to save manual calculations. In some questions, formulae should be modified.

Memories the formulae


Note: Click to Formulae to view in enlarged










Note: Click to Formulae to view in enlarged

  1. Counter examples

“every differentiable function is continuous but not conversely.” To prove this statement, you will use example |x|.


In new paper pattern, you are going to solve compulsory 30 questions and with options, there are 36 questions. Alternative questions are asked of the same topic. You can not skip any chapter.


No.of questions

Internal No. of options

Compulsory marks each

Total marks

Marks with options

Question No. from

Section A






Q.1 to 6

Section B






Q.7 to 14

Section C






Q.15 to 20

Section D






Q.21 to 30









Each M.C.Q. is of 1 mark. It depends upon your basic knowledge, understanding. It may include a little bit calculation (which does not waste time).

E.g. To find order of differential equation of all circles having radius r; (instead of doing manual calculations) you should know relation between order and arbitrary constants. “In general, the number of arbitrary constants of an ordinary D.E is given by the order of the highest derivative.”

Write down answer of M.C.Q. with an option and its answer. Do not skip any one of them. Miss-matching of option and answer will not carry a mark, though one of them is correct. Different answer for same M.C.Q. will not be counted correct.

It has no internal option.


Each question is of 2 marks. Two main steps will carry 2 marks. Formula can b acted as 1st step in some example’s students should note that one main step can be simplified into one or more sub-steps.

Give reasons o each new step.

e.g for simplification of logical statements, mention the logical equivalence properties.

It has 3 internal options.

Half of the weightage of question paper is in section-D only. H.O.T.s may be included in it.

4 main steps will be credited.

Following suggestions will be needful

  • In general solution of trigonometric equations, inclusion of m, n ∈ Z is necessary.
  • In integration, logically correct method carries marks.
  • For logic, write the conclusion after constructing truth/switching table.
  • Check the direction of current flow as per sign conversions.
  • For truth table use T, F & for switching table 1,0.                                    
  • For L.P.P., identity special case “infinite many solution” if it is present in example. Graph should be clean and clear. Feasible region and corner points should be shown clearly.
  • For continuity, L’Hospital rule should not be used in theory exam.
  • Continuity at the point, in range should be shown in respective methods.



  Its applications

1. Matrix     

Solve linear equations:- method of inversion method of reduction

2. Logic 

Switching circuits

3.  Sine, Cosine, projection rule

Area of triangle

 4. Vectors: S.T.P  

Geometrical applications to vectors & volume of the tetrahedron, Parellopiped

5. L.P.P

Problems related to diet transportation/ investment/ advertising firm

6. Differentiations 

1)Tangent, Normal

2)Rate measure

3)Mean value Theorems 

4)Maxima, minima


7. Definite integrations

Area under the curve

8. Differential Equation

Growth, decay, Newton’s law.


At last , Note that-

-Write new section on new page

-Do not mix answers of different sections

-solutions written by pencil, though it is correct, it will not be checked.

-Marks are given to each correct step Be ready with basic concepts , formulae for the questions which are application based or the questions out of textbook.

-Avoid silly mistakes & remind the following points-

  • Cos-1x ≠1/cosx, (cosx)-1=1/cosx
  • Cosx=(cosx)n but Cosx2≠cosx2
  • ∫f(x).g(x) ≠∫f(x) dx. ∫g(x)dx
  • Cos (x+y) ≠ cosx+cosy
  • √x+y ≠   √x+ √y
  • Growth & Decay rate of x w.r.t is dx/dt
  •  Growth :dx/dt = kx , k>0
  • Decay :dx/dt = -kx , k>0

Time - Management

Following table shows sufficient time for per question


Marks for each question

No.of questions

Time per question

Approximate time




2 min





3 min





6/7 min





9/10 min







Try to keep at least 5 min for checking

The Writer Mrs.Deepashree Prasad Joshi M.Sc, B.Ed

  • Abasaheb Graware College -10 years.
  • Worked as paper setter at Maharashtra state level exams- 4 years
  • Worked as paper setter for C-Dac.
  • Worked in project related to dictionary for maths held by C-Dac
  • Delivered lectures on Mathematics, new paper pattern at M.E.S Waghire Junior College , Saswad & at Deshpande College Baramati
  • Worked for project of audio of 11th maths content held by I.C.T  
  • Delivered a lecture on new paper pattern for HSC students at Yashwantrao Chavan Natyagruha, arranged by

Maths Tips for last minute preparation of Board Exam

Every student aims for a bright career by scoring well in board examination. With the board exam already started, there is a sudden nervousness in the atmosphere. The pressure to perform well and excel in the exam is forever lurking on the student’s head.

  1. First and foremost, important is to be positive
  2. Students should take care of their health. Eat light and hygienic home cooked food and take enough that is 5-6 hours’ sleep
  3. It is also essential to meditate for half an hour and exercise for equal time to keep calm and fit
  4. Manage your time while studying and writing the paper wisely
  5. Revise the chapters which carry maximum weightage and those of which you are confident
  6. Study atleast the basic concepts and theory questions well of all chapters as all chapters are compulsory
  7. Do not try to study new concepts or problems at the eleventh hour as you may lose confidence
  8. Study illustrative problems and summary well of each topic
  9. Write down the important formulae and theory questions till you can remember
  10. Learn steps and methods and solve every problem stepwise and methodically
  11. Discuss/Explain your answers to others to understand if you are wrong
  12. You know your strength and weakness the best – Plan your entire study schedule and solving of the paper around your strong and weak points
  13. Be aware of the new exam pattern as you must attempt 30 questions of various difficulty levels
  14.  Remember while attempting MCQ’s write the answer along with its option key
  15. Read your question paper slowly and carefully and start solving questions that you find easier and confident about its correctness
  16. Don’t leave aside a single topic from the textbook, don’t read solved problems but try to solve them individually
  17. Don’t leave any question un-attempted. Write any steps you know though you cannot solve the problem completely
  18. Keep the last 10 minutes in the exam to read your answers and make corrections if necessary
  19. While doing all this don’t over stress yourself
  20. Keep targets, keep realistic approach and achievable milestones
  21. Reduce the use of social media, replace this time with exercise to keep fit

Wish you all the best and great success in the examination!

Mrs. Rekha Deshpande

M.Sc., M.Phil, D.H.E

Former Member of Board of Studies

 Co-ordinater of board textbook for Mathematics

Retired after 37 of service in Garware College


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