Mathematics (71) Paper & Study Tips

Greetings, friends. Of course, now you know what is here before you. Mathematics simplified by mathematicians (not me, my expert teachers). On a general basis, it is observed that comparatively, students feel Geometry is more difficult than Algebra. And some feel that entire Mathematics is difficult. These may or may not be true, but yet today, I am gonna clear all the delusions regarding Mathematics; let’s go for it.

NOTE: In the tips given below, all the matter can be divided into two groups. All that is given in italic (slant) font is specially for the students who aspire to score 39 or 40 and want no mark to be deducted by the moderators. Other matter in normal font is for everyone.


  1. Study every chapter section-wise. Study each concept of each chapter in-depth such that you won’t find it difficult to answer any question. Don’t move on the next concept/chapter unless you have made the previous one PERFECT. In short, in-depth analysis of each and every topic should be done. If any problem arises while studying, consult a teacher/mentor.
  2. Do not copy solutions from guides. Use guides only to know the method.
  3. Learn all formulae by heart thoroughly. The best way to memorize formulae is to write the formulae 20 times (on/before the day the exercise related to it starts). And keep on revising all the learnt formulae every week by writing one time each (fix a day of the week for this). Also make a formula list like below (you can use this, but check it before)     Algebra Formulae  Geometry Formulae
  4. Don’t ignore the solved examples given in the textbooks because each of the question papers will contain at least 2 solved examples. Also solve the exercise questions atleast 3 times throughout the year. Expertise the questions in the exercises given because they form at least 70% of the question paper, that is about 28 marks in each paper.
  5. Do not leave anything for option to study (it is OK if you not attempt extras in exam, rather I will say never attempt extras) because you may think extra questions may cover that part. But, imagine if the other question(s) are also tough, then?
  6. For remembering the trigonometry formulae of ratios, remember OSHACHOTA (ओशाछोटा) i.e. (Opposite,Sin,Hypotenuse…..Adjacent,Cos,Hypotenuse…..Opposite, Tan,Adjacent). Now how to crack the trick – Take first group OSH…. Remove the center letter which tells us the ratio name… Here it is sin… So, sin=O/H i.e opposite divided by hypotenuse. Also remeber the partners – Sin-Cosec, Cos-Sec, Tan-Cot…. for the partner of each ratio just make the fraction invertendo (ulta… upar ka niche, niche ka upar).
  7. For remembering the Mean, Median, Mode formula; consider NEMO fish and 3 goats. Remember the line Nemo aur tin meme…. Divide Nemo into Ne(Mean) and mo(Mode). Similarly Meme into Me(Mean) and Me(Median). So you get Mean-Mode = 3(Mean-Median). Just keep in mind that on both sides Mean comes first.
  8. Even, for some sums in Geometry, you need to know some properties of Algebra like Invertendo, Componendo, Dividendo, etc.
  9. Many-a-times it is noticed that incircles are not properly constructed. At one side is comes in or out. So, there is a trick for constructing accurate angle bisectors. In the first step, when drawing arcs on the angle rays, take more distance and then in the second step, take lesser distance.
  10. Go through the following images to know the correct way of writing certain things (how it is accepted in boards). Also some confusions are cleared in the following images.CaptureConfusion 1Confusion 2
  11. HOTS questions given behind are always asked (one/two in each paper). So do them thoroughly. And just don’t worry, even if the name is HOTS, actually in reality they are very cool. However, what’s in the name?


The common presentation tips regarding all the subjects are available on GENERAL PRESENTATION TIPS post. Following are featured especially for Science and Technology Paper . To understand these in a better way, refer Algebra (71) March 2017 Solution and Geometry (71) March 2017 Solution

  1. Make boxes around main answers in all questions. For e.g. boxes around Mean= 40, m(arc ABC)=30º, etc..
  2. Write final answer in words for every question. In that, double underline the value which was asked.
  3. Don’t allow (make) any mistakes as far as possible. If any mistake, just put a straight cut, don’t scribble or overwrite.
  4. In every question, write the correct question and sub-question number. If the sub-question/question number is wrong, no marks are credited for that particular sub-question/question. So, after completing the paper, this is first thing you have to check.
  5. Diagrams – For Geometry, in Q.1 and Q.2, draw diagram wherever there is construction or extra labels, and in Q.3 to Q.5, draw diagram for every possible question. Draw correct diagrams with correct labels for trigonometry word-problems (Ref. Q.4 in solution link). Explanatory diagrams required for some word problems of Mensuration. For Algebra, draw diagrams in Chapter 2 and 3 based word problems consisting of geometrical figures, direction, etc.
  6. Algebra Chp. 5 – While finding Mean/Median/Mode… Write the symbolization for letters as given in textbook … For example, L=lower limit of Median/modal class= ….. etc.
  7. Whenever possible, write the method name by which you are solving a particular sum if there are many ways; like factorization, etc. In Quadratic, Assumed in Mean, etc.
  8. When asked to draw frequency polygon/curve, draw the table showing the points to be plotters, regardless of whether to be drawn using histogram or not. (Comment to know how to do that). When drawing pie-diagram, take radius 5 cm. Then start the first line by joining centre to right side (3 O’ clock) and then go anti-clockwise direction.
  9. In playing cards probability sums, when asked about the suites name them in the answer (Hearts, Spades, Club, Diamond). Same goes for face cards (King, Queen, Jack). In these sums, the statement ‘there are 52 cards in one deck of playing cards’ is compulsory before writing n(S). Also, wherever applicable and possible, write the denotation statements like ‘Let Heads be denoted by H and Tails by T’ etc. Well, that’s not compulsory for coins, die questions ; but it’s compulsory for girls-boys / men-women committee formation questions.
  10. For Geometry, if time permits, write full theorem statements instead of theorem name wherever possible and applicable. E.g. Tangent is perpendicular to radius at the point of contact.
  11. For  Geometric Construction, draw a analytical figure and write an analysis also. Also, write a final statement that ‘(given figure) with (given conditions) construction’. (except for 1 mark questions)
  12. When writing theorem proofs, first write the theorem statement given in the textbook. Then Given, Diagram ,To Prove, Construction (if required), Proof and again finally write (statement) is proved.
  13. Preferably, keep your aim to make the paper more spacious, clean and ultimately more presentable. One way to do that is leaving a line between specific steps. Another is to  leave two lines between sub-questions. And many more…
  14. If you taking graph supplement, don’t forget the write the correct question and sub-question nos. on each of the graph pages you are using.
  15. When drawing graph for linear equations, write the units (1,2,3…) on the negative side of the axes ; i.e below the X-axis and left side of the X-axis. Whenever plotting the points, plot each point individually, put a small circle around it and write its coordinates. Do this for all points, (Chp. 3 and Chp. 6-F. Polygon/curve)… Even the intersection point…Do it in a similar way, but put double-circle in place of one. When drawing the graph for solving linear equations, write the final answer statement on the graph also (in a corner). (If this point is confusing you, tell me. I will show a example image). When solving in graphical method, to find the point co-ordinates, write y in terms to x and not vice versa. i.e. if given equation is x+y-1=0 then always write as y=1-x and consider x value and substitute. If you write as x=1+y and consider y value first, it will not be wrong and points will be correct; but this is the wrong way. The reason behind this is that X-axis is independent axis and Y-axis is dependent axis.
  16. A complete NO NO NO to solving extra questions, because you have to do a lot more things in each sub-question so you may not finish the paper in time. So, in Mathematics, make the best choice possible and write that so perfectly that no one would be able to cut marks in it – This is what the moderators have told me (that’s more appreciated). Exception is for weaker students. Weaker students should try as many extra answers as possible
  17. You can write a solution set for linear equations also if the variables are x and y because then the answer is a point where x and y represent the respective co-ordinates. This solution the set is written as solution set = {(x,y)}. Just write the correct numbers in place of x and y and don’t ever forget both brackets.
  18. Avoid negative sign as much as possible. It is very hazardous because often in a hurry we forget to write it next step and the remaining entire sum goes wrong. Similarly, take care while changing signs while changing the sides.
  19. Be precise, accurate, confident, scientific and impressive in what you are writing. Again, you should expose your deep knowledge and interest in the topic so that you make a mark on the examiner.


  1. Chetana Publications – STD. X Mathematics I Algebra Master Key
  2. Chetana Publications – STD. X Mathematics II Geometry Master Key


Time management

Remember to make the time management suitable according to your needs. Also, be prepared to adjust the time management during examinations depending on the questions asked. Slight changes can de done, but remember to give the same time for checking. Suggesting to do checking before presentation.

Well, I think that’s enough about Mathematics. Any doubts regarding the subject about paper presentation/board rules (not about studying, your teacher will explain it better), please comment. Bye.

# Only for Educational Purposes.


14 thoughts on “Mathematics (71) Paper & Study Tips

  1. In maths or other 40 marks paper, after completion of paper, if I have a confidence that from a normal checker (not moderators) I will get 40 marks , but from moderators they could have a change of getting my score till 32 to 35 then should I purposely deduct 1 mark so I will get maximum 39 and my papers will not be checked by moderators also. This method is told to us by the checkers of our school to atleast get 39 which is way better than 32 or 35. My question is could I use this technique or is this legit? Plz answer and thank you in advance 😃


  2. No, don’t do this. Be confident. You and your school teachers are correct, there is always a risk. But they won’t reduce the marks to 35 and all. They usually reduce it to maximum 37/38 only. But don’t reduce your mark yourself. This is not diplomatic, it is cowardice. You know yourself then why to worry? Just follow my (teachers’) tips, then even moderator won’t reduce those marks 🤣


  3. Yes they may cut it to make your marks 39, because they generally want one topper only. But this is in the last option, first they check for the minor mistakes if any. (I have proofs for this, so don’t believe other talks)


  4. Hii, I just wanted to ask, have u drawn the borders and fig. with black pen? If not then which pencil have you used. And thank you very much for all the tips and shortcuts… Helps a lot.


  5. Most welcome. Regarding borders, I have used pencil only. I usually prefer Apsara pencils. But the main trick here is not the brand. Use a long point sharpener and sharpen the pencil to the max. Then press the point with very little force on the desk, so that it becomes only little blunt. Now you can apply pressure a little and draw the lines. (Actually telling the trick in words is difficult, but tried my best)


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