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Most Challenging Class 10th Math Problems and Tips to Solve

Most Challenging Class 10th Math Problems and Tips to Solve

by PW Gulf
November 19, 2024
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Class 10th Math Problems: Math can feel difficult, especially for Class 10 students facing tough topics. As exams get closer, students often come across tricky problems that require not just calculations but also strong thinking and problem-solving skills. Complex algebra, challenging geometry, and other hard questions can seem scary at first. But with the right tips and strategies, solving these problems becomes easier. 

Here we’ve shared some of the hardest Class 10 math problems and simple ways to solve them. Whether you want to understand concepts better or do well in exams, these tips will help you succeed in Class 10 math.

Class 10 Maths Curriculum Overview

The Class 10 Maths syllabus typically includes the following key chapters:

  1. Real Numbers

  2. Polynomials

  3. Pair of Linear Equations in Two Variables

  4. Quadratic Equations

  5. Arithmetic Progressions

  6. Triangles

  7. Coordinate Geometry

  8. Statistics

  9. Probability

  10. Circles

  11. Areas Related to Circles

  12. Surface Areas and Volumes

  13. Statistics and Probability

Most Challenging Class 10th Math Problems

Class 10 mathematics is an important milestone in a student's education, especially in the Indian system. The syllabus introduces challenging topics like algebra, geometry, trigonometry, and statistics to build problem-solving skills.

Each chapter presents unique challenges and concepts that require a deep understanding and analytical thinking.

Real Numbers

One of the toughest questions in this chapter involves proving irrationality or finding HCF and LCM using prime factorization.

Example Question: Prove that 22​ is irrational.

Solution:
Assume 22​ is rational, which means it can be expressed as pqqp​, where pp and qq are coprime integers. Then:

Root 2​=qp​⟹2=q2p2​⟹p2=2q2

This implies that p2 is even, hence p must be even (since the square of an odd number is odd). Let p=2kp=2k:

(2k)2=2q2  ⟹  4k2=2q2  ⟹  q2=2k2

Thus, q is also even, contradicting our assumption that pp and qq are coprime. Therefore, 22​ is irrational.

Polynomials

Example Question: Find the zeros of the polynomial f(x)=x2−5x+6.

Solution:
To find the zeros, we set f(x)=0f(x)=0:

x2−5x+6=0

Factoring gives:

(x−2)(x−3)=0

Thus, the zeros are x=2 and x=3.

Pair of Linear Equations

Example Question: Solve the following equations:

  1. 3x+4y=103x+4y=10

  2. 5x−3y=−15x−3y=−1

Solution:

Using the elimination method:Multiply the first equation by 33:

9x+12y=30

Multiply the second equation by 44:

20x−12y=−4

Adding these equations:

29x=26  ⟹  x=2629

Substituting x back into one of the original equations to find y.

Quadratic Equations

Example Question: Solve for roots using the quadratic formula for x2+x−6=0.

Solution:Using the quadratic formula:

x=−b±b2−4ac2a

Here, a=1,b=1,c=−6a=1,b=1,c=−6:

Calculating:

b2−4ac=1+24=25

Thus,

x=−1±52x=2−1±5​

This gives us roots x=2 and x=−3.

Trigonometry

Trigonometry poses some of the hardest questions for Class 10 students.

Example Question: Find the height of a tower if the angle of elevation from a point on the ground is 30∘30∘, and the distance from that point to the base of the tower is 50m.50m.

Solution:

Using tangent function:

Let height be h:

tan⁡(30∘)=h50  ⟹  h=50tan⁡(30∘)

Since tan⁡(30∘)=13tan(30∘)=3​1​:Thus,

h=503≈28.87mh=3​50​≈28.87m

HOTS Questions for Class 10 Maths with Solutions PDF

HOTS questions are designed to enhance critical thinking and problem-solving skills among students.

Example HOTS Questions

  1. Prove that if two angles are complementary, then their cosines are equal:

Given angles A and B such that A + B = 90∘

Using trigonometric identities:
cos(A)=sin(B)
Hence proved.

Downloadable Resources

Students can access PDFs containing HOTS questions for further practice. For example, a comprehensive PDF can be found at PW Gulf website itself.

Most Difficult Maths Questions for Class 10 ICSE

ICSE students often encounter challenging problems that require a solid understanding of concepts.

Example Question:

Find the area of a triangle with vertices at coordinates (0,0), (4,0), (0,3).

Solution:

Using the formula for area based on coordinates:

Area=12∣x1(y2−y3)+x2(y3−y1)+x3(y1−y2)∣=12∣0(0−3)+4(3−0)+0(0−0)∣=12∣12∣=6m2​

Most Repeated Questions in Maths Class 10 PDF

Familiarity with frequently asked questions can significantly enhance exam preparedness.

Key Topics Covered

  • Real Numbers

  • Polynomials

  • Linear Equations

  • Quadratic Equations

  • Statistics

  • Trigonometry

Students should focus on solving these repeated questions to build confidence.

Hardest Questions of Maths Class 10 Trigonometry

Trigonometry remains one of the most challenging areas in Class 10 mathematics.

Example Question: Prove that:

1+tan2(A)=sec2(A)

Solution:Using Pythagorean identities:

Starting from left side,

1+tan2(A)=sec2(A)

This follows from

tan(A)=sin(A)cos(A)and sec(A)=1cos(A).Therefore proved

Tips to Solve Challenging Math Problems

Here is the required Tips to Solve Challenging Math Problems listed here:

  1. Understand Concepts Thoroughly: Ensure you grasp fundamental concepts before attempting complex problems.

  2. Practice Regularly: Regular practice helps reinforce learning and improve speed.

  3. Break Down Problems: Divide complex problems into smaller parts to simplify them.

  4. Use Visual Aids: Diagrams can help visualize problems better.

  5. Work on Previous Year Papers: Familiarize yourself with exam patterns and frequently asked questions.

Class 10 math includes many tough topics that need focus and regular practice to understand. By working on HOTS (Higher Order Thinking Skills) questions, learning tricky concepts in trigonometry and algebra, and solving important questions from past exams, students can improve their problem-solving skills. 

Using helpful resources like PDFs with tough questions and solutions can make exam preparation easier. With dedication and smart study habits, every student can handle even the hardest math problems successfully.

Most Challenging Class 10th Math Problems FAQs

Q1: What makes Class 10 math problems challenging?
Ans: Class 10 math problems can be tough because they involve advanced concepts like algebra, trigonometry, and geometry, requiring strong problem-solving and analytical skills.

Q2: How can I improve my problem-solving skills in Class 10 math?
Ans: You can improve by practicing regularly, understanding the concepts deeply, and solving HOTS (Higher Order Thinking Skills) questions and past exam papers.

Q3: Which are the hardest chapters in Class 10 math?
Ans: Trigonometry, algebra, and geometry are often considered the hardest because they include complex formulas and tricky problem-solving steps.

Q4: Are there any resources to help with tough math problems?
Ans: Yes, you can use PDFs with solved examples, online tutorials, and practice books focused on HOTS questions for better preparation.

Q5: What are some tips to solve tough Class 10 math problems?
Ans: Understand the concepts clearly, practice step-by-step solutions, use diagrams for visualization, and focus on frequently asked and repeated questions.

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