Mathematics is perceived to be a scary subject by many students, but it is not difficult to score good marks if you practice enough and write the exam with a fresh mind .The state of your mind on the day of the exam matters significantly as you’re not writing out of memory but are actively solving sums during the paper. Don’t compromise on a fresh, active and boosted state of mind for studying a little more.
Here are some tips on revision and on writing the paper.
REVISION:
Read NCERT chapter summaries: A quick way to revise, going through them enables you to cover your entire syllabus in terms of definitions and formulae.
Pay attention to definitions and theorems.
Grade 11 syllabus:
Go through the summary of these chapters once: Sets, relations and functions, trigonometry, permutation and combinations, and conic sections (just the standard equations).
Except for permutations and combinations and conic sections, these chapters directly form a base for certain chapters in the grade 12 syllabus.
Permutations and combinations: required for questions on probability.
Conic sections: The formulae given here will help you draw the rough sketches for questions on finding areas using integration.
Relations and functions: Revise the definitions , graphs and utility of some common functions, such as the modulus function, the identity function and the greatest integer function. Practice how to prove a given relation is an equivalence relation, the given function is bijective or not or whether the given binary operation follows laws of closure, associativity or not as these are frequently asked in the examination.
Calculus: It forms the largest chunk of your paper, so revise all formulae, especially those for inverse trigonometric functions and logarithmic functions.
INTEGRATION AS LIMIT OF A SUM: Most of the students tend to ignore this topic. This is usually given in exams for 6 marks and is very scoring, provided the student is thorough with the procedure.
Vectors: You should be thorough with the basics such as the direction cosines, angle between vectors, etc, and their uses. They often help in checking small portions of big questions.
3-D geometry: There is a generic method for each type of question (such as finding the reflection, finding the normal, etc.). Go through these methods.
Don’t forget to practice MISCELLANEOUS EXERCISE given at the end of each chapter. Many questions are directly picked up from here in the Board examination. Practice at least 3 previous year question papers.
Be mentally prepared for a difficult question paper and don’t get carried away on seeing an easy or doable question paper. Silly mistakes become inevitable if you do that.
If you have the time, you can refer to NCERT Exemplar.
Don’t exhaust yourself on the day before the exam by solving too many questions or revising extensively, but keep in touch with the writing practice by solving one or two past papers during the days before the paper.
WRITING TIPS:
As far as possible, start your paper from 6 marks questions as they have quite heavy weightage and are usually very scoring. Moreover, they form a major part of the paper and you can relax a bit after completing that heavy part.
Also, Speed is extremely important, so you can start with the questions you are the most confident about. This will also boost your confidence.
Try attempting the paper section wise. The order of sections can vary (preferably from section D to section A).
Proving questions are a blessing in disguise, as you know what your final answer ought to be. Note down what is given to you (say, A is a symmetric matrix ⇒ AT = A) and what needs to be proved. This way, you know what information you can use, and where you have to head.
Always mention the units in questions on linear programming, the application of derivatives and the application of integration.
Integration:
Write the constant of integration while evaluating indefinite integrals.
For instance,
∫x²dx = x³/3 + C and not just x³/3
Try to state the property that you are using. Remember to change the limits of integration while using substitution in definite integrals.
Application of derivatives: Ensure that you have used both the first and second order condition, even if you find the answer with just the first derivative.
Application of integrals: Always draw a rough sketch (even if it isn’t to scale), as this carries marks.
Continuity and differentiability: Always show that Rolle’s Theorem and Lagrange’s mean value Theorem can be applied to the given function before proceeding with the question.
Linear programming:
Don’t forget to mention the scale.
Verify the coordinates of the corner points with the equations of the lines; do not simply read them off the graph to be on the safe side.
Determinants: As far as possible, evaluate the determinant (of the 3×3 matrix) only when you have reduced the matrix to a form that has two zeroes in a single row or column. Also, make sure that you use the symbol of determinant and not that of a matrix while evaluating the determinant. Same goes when you are solving a problem involving matrices.
Probability- While solving any problem, especially on Bayes’ theorem always define the events correctly and clearly mention the formula used. All this carries marks.
Differentiation: while evaluating second order derivative of a function in parametric form, don’t forget to multiply by dt/dx at the end.
For instance,
Find d²y/dx² when x= t² and y = t³ dx/dt= 2t , dy/dt= 3t² dy/dx= 3t/2 d²y/dx²= d/dt(dy/dx)*dt/dx = 3/2*1/2t=3/4t
CHECKING YOUR PAPER:
Leave at least fifteen minutes at the end of the paper to check your answers. Check the paper in the following order:
Verify if you’ve attempted all the questions.
Check the questions you feel (intuitively) you may have made a mistake in.
Check the answers that involve numerical calculation/ giving an unknown answer.
There is no need to check proofs unless you’ve checked everything else.
Here are some more verification hacks:
Integrals: Differentiate the answer (only if it can be done quickly) to check if you get the given function back.
Finding areas using integration: Certain answers can be verified using standard formulas, such as that for the area of a circle and the area of an ellipse.
Matrices: If, for a matrix A, you have calculated the inverse, verify that AA-1 = I.
Functions and Inverse: take an arbitrary value of x, find y and then cross check in the inverse function for g(y)=x , where g is the inverse function.
That's all for this article! Hope it helps you. Feel free to contact us in case of any suggestions or queries; we'd be happy to help!
Good luck and Happy Studying!
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