Maths is a subject which has a high scope in career opportunities for scoring good marks. In Maths, it will define the result of the student. Also, the importance of Maths is reflected in the question pattern of various board exams (CBSE, ICSE, State Boards) that have different levels.So, for understanding the pattern of exams, students should go for previous year’s questions. Students should search for Top 50 most important questions for board exams” and practice them to score well. By practicing Most important Maths questions for CBSE board then students can achieve balance and obtain high marks.
If students keep on practicing the maximum number of important questions, then their confidence and accuracy in doing questions will increase. With practice of Top 50 most important Maths questions for board exams, students can improve their level and score 90%+ in Mathematics in board exams.Here are some chapter-wise important topics, expected questions, and tips on how to do maximum questions based on exams.
This guide will help you prepare for 12th Board Maths exam and score high marks.
How Are These 50 Questions Selected?
Approximately 50 questions are prepared from previous years’ analysis. These questions are generally asked in examinations and carry high marks. These Top 50 Most important Maths questions for board exams are taken from different chapters and formulas with high weightage, which is quite important. Each question is designed from a different pattern of asking questions from different sections. These Top 50 Most important Maths questions for board exams test the concept and understanding of the student.
Students who are able to solve these Most important Maths questions for CBSE board can check their scoring potential. And they need to understand how to practice more. To get high scoring potential and build confidence, students should practice by finding important questions in one place so that they do not waste time searching for important questions everywhere.
Board Exam Maths Paper Pattern Overview
Mathematics board papers require both conceptual clarity and problem-solving skills to answer questions. As per that, there is a need to understand the pattern of paper designs.
Marks Distribution
The paper usually carries a total of 100 marks. The Maths paper is 100 marks, out of which 80 marks are for the theory paper and 20 marks are allotted for internal exams in schools, which are based on practical papers and 10 marks given on the practical paper itself.
There is an internal choice in the question paper, where students can choose one question for solving while solving from two choices of questions.
As per the marks, there are different types of question design in mathematics and repeatedly asking Top 50 most important Maths questions for board exams as per the weightage of chapters
- MCQ questions contain 1 mark.
- Short Answer Questions (2-3 marks): For these questions, step-wise explanations need to be included.
- Long Answer Questions (4-6 marks): In these questions, there is a need for detailed solutions to the problem.
By practicing these Top 50 most important Maths for board exams questions, students can able to manage their time and understanding of different types of questions.
- 1-1.5 minutes → for 1 mark question
- 4-6 minutes → for 2-3 marks question
- 10-12 minutes → for 4-6 marks question
With proper time management, students get to know how to solve questions on time and get some time for quick revision.
Must-Know Preparation Strategy Before Practicing These Questions
For solving questions after practicing, it’s important for the preparation of Mathematics board exam papers to have some quick revision.
- Revision of important formulas and making a small chart of these formulas for multiple revisions.
- Complete the 2nd chapter of NCERT. This will form a strong base.
- Practice of Top 50 most important Maths questions for board exams and also practice a number of questions from the sample papers.
In these examples, understand the concept: how to smartly solve questions through steps, presentation, and how diagrams are used in solving these questions.
Continuous practice of questions will help to avoid mistakes. Try to practice the maximum number of questions.
Chapter-wise Weightage (Class 10 & 12)
Different chapters have different marks as per weightage . There is a need to give importance to different chapters based on their weightage.
Class 10 important Maths questions as per Weightage of chapters.
- Real Numbers – 6 marks
- Polynomials – 6 marks
- Pair of Linear Equations in Two Variables – 8 marks
- Triangles – 9 marks
- Circles – 3 marks
- Trigonometry – 12 marks
- Mensuration – 10 marks
- Statistics & Probability – 10 marks
Class 12 important Maths Question as per Weightage of chapters
- Relation & Functions – 8 marks
- Inverse Trigonometric Functions – 4 marks
- Matrices & Determinants – 10 marks
- Calculus (Major Weightage: Differentiation & Integration) – 14 marks
- Vectors & 3D Geometry – 14 marks
- Linear Programming – 5 marks
- Probability – 5 marks
Every chapter has important topics from which many questions are frequently asked and also asked high scoring Maths questions for boards.
Top 50 Most Important Questions (Chapter-Wise Segmentation)
Class 10 – 25 Most Important Maths questions for CBSE board.(Divide like this)
Algebra (8 Questions)
Polynomials based on zeroes & coefficients
Q.1: Find the value of “p” from the polynomial x² + 3x + p, if one of the zeroes of the polynomial is 2.
Q.2: Does the polynomial a⁴ + 4a² + 5 have real zeroes?
Q.3: Find a quadratic polynomial whose zeroes are reciprocals of the zeroes of the polynomial f(x) = ax² + bx + c, a ≠ 0, c ≠ 0.
Quadratic equation application
Q.1: Find the roots of quadratic equations by factorisation:
(i) √2 x² + 7x + 5√2 = 0
Q.2: By the method of completion of squares show that the equation 4×2+3x+5=0 has no real roots.
Q.3. The coach of a cricket team buys 7 bats and 6 balls for Rs.3800. Later, she buys 3 bats and 5 balls for Rs.1750. Find the cost of each bat and each ball.
AP word problems
Q.1: Prove that am+n + am−n = 2am.
Q.2: If the following terms form an AP, find the common difference and write the next 3 terms:
3, 3 + √2, 3 + 2√2, 3 + 3√2, …
Geometry (7 Questions)
Similar triangles
Q.1: If the areas of two similar triangles are equal, prove that they are congruent.
Q.2: In an equilateral ΔABC, D is a point on side BC such that BD = (1/3) BC. Prove that 9(AD)2 = 7(AB)2.
Q.3: If the areas of two similar triangles are equal, prove that they are congruent.
Circle theorems
Q.1: In the given figure, AP, AQ and BC are tangents to the circle. If AB = 5 cm, AC = 6 cm and BC = 4 cm then the length of AP is
(A) 15 cm (B) 10 cm (C) 9 cm (D) 7.5 cm
Q.2: From an external point P, tangents PA and PB are drawn to a circle with centre 0. If ∠PAB = 50°, then find ∠AOB.
Constructions
Q.1: Draw a circle of radius 3 cm. Take two points P and Q on one of its extended diameters, each at a distance of 7 cm from its centre. Draw tangents to the circle from these two points P and Q.
Q.2: Draw a triangle ABC with side BC = 7 cm, ∠B = 45° and ∆A = 105°. Then construct a triangle whose sides are 3-5 times the corresponding sides of ∆ABC. (2011D)
Trigonometry (4 Questions)
Heights & distances
Q.1: Two poles of equal heights are standing opposite each other on either side of the road, which is 80 m wide. From a point between them on the road, the angles of elevation of the top of the poles are 60° and 30°, respectively. Find the height of the poles and the distances of the point from the poles.
Q.2: From the top of a 7 m high building, the angle of elevation of the top of a cable tower is 60° and the angle of depression of its foot is 45°. Determine the height of the tower.
Trigonometric identities
Q.1: Evaluate 2 tan² 45° + cos² 30° – sin² 60°.
Q.2: If sec θ + tan θ = 7, find sec θ – tan θ.
Mensuration (4 Questions)
Surface area & volume of combinations
Q1: A solid toy is in the form of a hemisphere surmounted by a right circular cone. The height of the cone is 2 cm, and the diameter of the base is 4 cm. Determine the volume of the toy. If a right circular cylinder circumscribes the toy, find the difference between the volumes of the cylinder and the toy. (Take π = 3.14)
Q2: A cone of height 24 cm and radius of base 6 cm is made up of modelling clay. A child reshapes it in the form of a sphere. Find the radius of the sphere.
Real-life case based questions
Q1. A circus tent consists of a cylindrical base surmounted by a conical roof. The radius of the cylinder is 10 m. The height of the tent is 60 m and that of the cone is 20 m. Find the volume of the tent and the area of the canvas used for making it.
Q.3: If the tangent to the curve y = x³ + ax + b at (1, –6) is parallel to the line x – y + 5 = 0, find the values of a and b.
Q.4: The radius of a sphere is estimated as 9 cm with an error of 0.03 cm. Calculate the approximate error in measuring its volume.
Statistics & Probability (2 Questions)
Mean, median, mode
Q.1: A student scored the following marks in 6 subjects:
30, 19, 25, 30, 27, 30
Find his modal score.
Simple probability
Q.1. If P(E) = 0.05, what is the probability of ‘not E’?
Class 12 – 25 Most Important Maths questions for CBSE board.
Calculus (10 Questions)
Differentiation + Application (tangent, normal)
Q1. The radius of the circle is increasing at the rate of
0.7cm/sec. What is the rate of increase of its circumference?
Q2. Find the maximum and minimum values of function
f(x) = sin 2x + 5.
Q.3: If the tangent to the curve y = x³ + ax + b at (1, –6) is parallel to the line x – y + 5 = 0, find the values of a and b.
Q.4: The radius of a sphere is estimated as 9 cm with an error of 0.03 cm. Calculate the approximate error in measuring its volume.
f(x) = sin 2x + 5.
Maxima & minima
Q.1: For the function \(f(x)=\sin 2x\), \(0<x<\pi\), find the stationary points and state whether they are maxima or minima.
Q.2: The function \(y = a\log x + bx^2 + x\) has extreme values at \(x = 1\) and \(x = 2\). Find the values of \(a\) and \(b\).
Integration + Area under curve
Q.1: Determine the antiderivative F of f(x) = 4x³ – 6, given F(0) = 3.
Q.2: Evaluate the integral (cos 2x + 2 sin 2x) / cos 2x.
Q.3: Find the area bounded by y² = 9x, x = 2, x = 4, and x-axis (first quadrant).
Q.4: Find the area bounded by the parabola y² = 4ax, the latus rectum, and the x-axis.
Differential equations
Q.1: Solve \( dy/dx = y \tan x \) with \( y(0)=1 \).
Answer (short): \( y = \sec x \).
Q.2: Curve passes through (1, π/4) with slope \( dy/dx = y/x – \cos(2y/x) \).
Answer (short): \( y = (\pi/4)\,x \).
Algebra (6 Questions)
Matrices (properties + solutions)
Q.1: For a 3×3 matrix with \( a_{ij} = |i – j|/2 \), write the element \( a_{23} \).
Answer (short): \( a_{23} = |2 – 3|/2 = 1/2 \).
Q.2: If \( A^2 = A \), find \( 7A – (I + A)^3 \).
Answer (short): \( 7A – (I + A)^3 = -I \).
Determinants (Cramer’s rule)
Q.1: If
\( A=\begin{bmatrix}1 & 2\\3 & -1\end{bmatrix} \) and
\( B=\begin{bmatrix}1 & 3\\-1 & 1\end{bmatrix} \), find A + B and AB.
Q.2: Find the line through A(1,3) and B(0,0) using determinants and find k if D(k,0) makes area of ΔABD = 3 sq units.
- Vectors & 3D (5 Questions)
- Dot/cross product
- Equation of line & plane
- Angle & distance
Vectors & 3D (5 Questions)
Q.1: Find a vector in the direction of \( \vec{v} = 2\hat{i} – 3\hat{j} + 6\hat{k} \) with magnitude 21.
Q.2: Find a vector of magnitude \( 5\sqrt{2} \) making angles \( \pi/4 \) with X-axis, \( \pi/2 \) with Y-axis and acute with Z-axis.
Q3. Find the angle between X-axis and the vector î + ĵ + k̂.
Dot/cross product
Q.1.Suppose a = -2i + 3j + 5k and b = i + 2j + 3k are two vectors, then find the value of the dot product of these two vectors.
Q2. Write the direction cosines of the vector -2î + ĵ – 5k̂.
Equation of line & plane
Q.1.If a line makes angles 90°, 135°, 45° with the x, y and z-axes respectively, find its direction cosines?
Find an equation of the plane containing the line of intersection of (x+2y+3z-4=0) and (2x+y-z+5=0) and perpendicular to (5x+3y+6z+8=0).
Angle & distance
Q.1. If a line makes angles 90°, 60° and θ with X, Y and Z-axis respectively, where θ is an acute angle, then find θ.
Q.2. If a line makes angles 90°, 135°, 45° with the x, y and z axes respectively, find its direction cosines.
Probability (2 Questions)
- Bayes theorem
- Conditional probability
Bayes theorem
Q.1. In a neighbourhood, 90% of children were falling sick due to flu and 10% due to measles and no other disease. The probability of observing rashes for measles is 0.95 and for flu is 0.08. If a child develops rashes, find the child’s probability of having the flu.
Q2.. If A, B and C have chances of being selected as a manager at a private firm it is in the ratio 4:1:2. The chances for them to introduce changes in marketing strategies are 0.3, 0.8 and 0.5, respectively. If a change has taken place, find the probability that it is due to the selection of B.
Conditional probability
Q.1. Given that the events A and B are such that P(A) = 1/2, P (A ∪ B) = 3/5, and P(B) = p. Find p if they are
(i) mutually exclusive
(ii) independent
Q2: 5 cards are drawn successively from a well-shuffled pack of 52 cards with replacement. Determine the probability that (i) all the five cards should be spades? (ii) only 3 cards should be spades? (iii) None of the cards is a spade?
Linear Programming (2 Questions)
Graph-based optimal solution
Q1: Solve the following LPP graphically:
Maximise Z = 2x + 3y, subject to x + y ≤ 4, x ≥ 0, y ≥ 0
Q2: A manufacturing company makes two types of television sets; one is black and white and the other is colour. The company has resources to make at most 300 sets a week. It takes Rs 1800 to make a black and white set and Rs 2700 to make a coloured set. The company can spend not more than Rs 648000 a week to make television sets. If it makes a profit of Rs 510 per black and white set and Rs 675 per coloured set, how many sets of each type should be produced so that the company has a maximum profit? Formulate this problem as a LPP given that the objective is to maximise the profit.
Smart Solving Tips for Scoring Full Marks
There is a need for a proper strategy for scoring the highest marks in Mathematics.
Marking Strategy: It’s important to practice Top 50 most important Maths questions for board exams and practice these questions with proper steps then students can score high marks in maths.
Mention the formula before solving a question to help with the answer.
Use diagrams to gain conceptual clarity in understanding. This can help wherever there is a demand for it in a question.
Write the solution of the question with a proper box to the answer.
With these strategies, students can improve their representation of solutions.
Common Mistakes That Reduce Marks
The student must avoid the mistakes which students often make in Mathematics questions. There is a need to have good strategies for the exam.
Skipping Steps: (i) Avoid skipping the steps while solving questions and use the proper method.
(ii) Practice the maximum number of questions from practice books to avoid calculation mistakes and speed up the calculation method.
(iii) Students should avoid making mistakes when explaining units, as this can lead to losing marks if a question is asked in a form that they are not able to interpret correctly.
(iv) Use rough diagrams as required, which will help to avoid mistakes. After writing the right answer, students sometimes don’t get full marks, so use proper diagrams as per the demand of the question.
Read the question properly, and then start doing it.
One-Day Before Exam Strategy
- Revise the short chart of formulas with examples to make sure which formula can be applied for which type of questions
- Don’ t go for the start of a new topic.
- Practice 10-15 Most important Maths questions for CBSE board.
- Don’t scroll phone too much for building distraction
Keep calm and stable have proper sleep of 7 hrs to give brain to work actively in exam
With this by one again make quick revision of Top 50 most important Maths questions for board exams and recall the steps of solution and mistake needed to avoid a proper accurate solution given of questions.keep your confidence level high.
Final Motivation+ Bonus Tips
You have prepared enough by practicing Top 50 most important Maths questions for board exams. Your confidence level will rise through practice. The more questions you solve, the more accurately and quickly you will be able to answer questions. So, here is the proper advice for exam day:
(i) Avoid exam stress and don’t take tension.
(ii) Make a time management plan for each type of question to be done in exams.
(iii) Do a quick revision of formulas and concept theorems.
(iv) In the exam hall, make sure every question is attempted and tried to be solved, even after understanding.
These Top 50 most important Maths questions for board exams are going to be very helpful in solving the maximum number of questions accurately and getting marks above 90% in Maths, which can significantly boost your overall result very much.
