Most Challenging Class 10th Math Problems and Tips to Solve

Mathematics can be daunting for students, but with the right approach and practice, students can score well in the subject. Students preparing for the class 10 board exams often encounter difficulties and seek solutions to master the subject. In this blog, we have included the 10 Most Challenging Class 10th Math Problems which students commonly face and will share tips and strategies to solve these complex problems. In this blog, we have covered some major problems faced by the students during the preparation and the preparation strategy they can follow.

Most Challenging Class 10th Math Problems:

The difficulty level of the problems may vary depending on the student’s understanding and learning style. Still, there are some specific problems that students face difficulty while solving. Below, we have listed some of these maths problems with tips to solve them:

1. Proofs involving Trigonometric Identities:

Challenges:

Solving trigonometry-related problems requires an in-depth understanding of trigonometry concepts, trigonometric identities, and algebraic manipulations.

Tips to solve problems related to trigonometry:

• The most important thing that students should remember while solving the trigonometric problems is to memorise the fundamental identities for sin²θ + cos²θ = 1, tan²θ + 1 = sec²θ & cot²θ + 1 = cosec²θ. Knowing the identities will help you a lot while solving the problems.
• Another important tip is simplifying the expressions using different algebraic techniques like factoring, expanding, and combining terms.
• Another important tip that students should keep in mind is that, if necessary, you can convert all trigonometric functions given in the question to sines and cosines, as solving them is way simpler.

Example: Prove that cos²A + sin²A = 1.

Proof: Let us take a right-angled triangle ABC, having a right angle at B, we have:

AB² + BC² = AC²  –(1)

Dividing the eq (1)by AC², we get

AB²/AC² + BC²/AC² = AC²/AC²

i.e. (AB/AC)² + (BC/AC)² = (AC/AC)²

(cos A)² + (sin A)² = 1

i.e. cos² A + sin² A = 1

Also Read: Real-Life Applications of Trigonometry

2. Word problems involving quadratic equations:

Challenges:

Sometimes, it may be difficult for students to solve and decode real-world problems into quadratic equations.

Tips to solve word problems related to quadratic equations:

• The simpler trick to solve these types of word problems is to identify and convert them into a quadratic equation.
• Understand the question and solve the problem using the quadratic equation.
• The most important tip that every student should keep in mind is to cross-check the answer and the steps they used to solve the problem.

Example: A rectangular garden has an area of 120 square meters. If its length is 5 meters more than its width, find the dimensions of the garden.

Solutions: Let us assume that the width of the garden is x, then the length will be (x + 5)

We know that the area of a rectangular garden is:

area = length * width

120 = (x + 5) * x

120 = x² + 5x

x² + 5x – 120 = 0

Solving the above equation using factorisation:

(x + 15x)(x – 8x) = 0

x = -15 or 8

Since, the width of the garden cannot be negative, therefore width (x) = 8 meters

Length = (x + 5) = (8 + 5) = 13 meters

3. Geometry problems (Circles, Triangles and Quadrilaterals):

Challenges:

Proving theorems and solving problems related to geometrical shapes may be difficult sometimes as they involve complex logical reasoning.

Tips to solve problems related to Geometry:

• Understand the problem, visualise and draw a clear diagram to make the problem easy to solve.
• There are so many theorems and properties that students are advised to apply the geometric properties and theorems related to the question.
• Students can solve the problems using indirect proof if they face difficulty with direct proofs.

Example: Prove that the angle in a semicircle is a right angle.

Proof: Let us understand by the figure:

In the above figure, AOB is a straight line passing through the centre O.

Therefore, angle subtended by arc AB at O is ∠AOB = 180°

According to the theorem, the angle subtended by an arc at the centre is doubled the angle subtended by it on any point on the remaining part of the circle.

∠AOB = 2∠APB

∠AOB/2 = ∠APB

180°/2 = ∠APB

∠APB = 90°

Hence proved

4. Mensuration problems involving 3D shapes:

Challenges:

It may be difficult for the students to calculate the surface area and volume of different complex shapes can be challenging.

Tips to solve problems related to mensuration:

• In mensuration problems related to 3D it is important to imagine and try to draw a rough diagram of the shapes and its components.
• Applying the appropriate formulas related to the surface, area and volume is important.
• To solve the question in easy steps, students can also divide the complex shapes into simpler ones and use tricks to solve them.

Example: Find the total surface area of a cone with radius 5 cm and height 12 cm.

Solution:

Surface area of a cone = πr(r + l)

where r is the radius and l is the slant height.

Slant height (l) = √(r² + h²)

l = √(5² + 12²) = 13 cm

Surface area = π * 5 * (5 + 13) = 282.74 cm²

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5. Statistics and Probability:

Challenges:

Understanding concepts like mean, median, mode, and probability can be difficult. Sometimes, students face difficulty while solving problems involving data interpretation.

Tips to solve problems related to statistics and probability:

• Understand the concepts of statistics and probability theoretically and experimentally. You can use tables or graphs to represent the data.
• Students are advised to get familiar with mean, median and mode concepts and formulas.
• Use the correct formulas to calculate the required statistics, and practice solving problems related to permutations and combinations.

6. Algebraic Expressions and Identities:

Challenges:

Simplifying expressions with exponents, radicals, and factoring can sometimes be complex for the students.

Tips to solve problems related to algebraic expressions and identities:

• It is important to remember that whenever you are solving any questions, breaking down expressions into simpler factors helps get a solution easily and make the complex solution easy.
• Practice factorising expressions using various techniques and properties.
• Memorise important algebraic identities and apply them wisely in different equations.

Example: Simplify the expression (2x²y³)^4 / (4x³y)^2.

Solution:

= (16x^8y^12) / (16x^6y^2)

= x^(8-6) * y^(12-2)

= x²y¹⁰

7. Equations and Inequalities:

Challenges:

Solving multiple equations simultaneously can be confusing for the students due to the complex nature of the questions.

Tips to solve problems:

• Choose an appropriate method to determine whether the equation can be solved through elimination or substitution.
• Once you have decided the method (substitution or elimination), apply the method to solve for one variable.
• Practice more and more problems to get familiar with the pattern and formulas.

8. Coordinate Geometry:

Challenges:

Visualising & applying formulas can sometimes be difficult for the students. Coordinate geometry problems involve finding equations for lines, circles, and other geometric figures.

Tips to solve problems related to coordinate geometry:

• Understand the concepts of distance, slope and midpoint and apply the formulas accordingly.
• Visualise the problem by plotting the given points.
• Verify your results by substituting the coordinates into the equation.

9. Exponents & Surds:

Challenges:

Understanding and applying the rules of exponents and radicals involving simplification and rationalisation can be challenging.

Tips to solve problems related to exponents and surds:

• Break down the number under the radical into its prime factors.
• Identify perfect squares that can be removed from the radical.
• If necessary, eliminate radicals from the denominator.

10. Ratio and proportion problems:

Challenges:

Identifying and solving proportions involving direct and inverse variation can be tricky for the students sometimes.

Tips to solve problems related to ratio and proportion:

• Express the relationship between the quantities as a proportion.
• Solve the proportion for the desired value.
• Practice more problems related to ratio and proportion.

The above are some problems that students face while preparing for the Class 10 exams. These are some general problems, there might be some other problems too that as a student you can face during the preparation, if there is so you can drop your problems in the comment box and we will try to solve and help you out in this.

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