10th Maths Public Exam Important Questions and Answers

Preparing for the Class 10 Mathematics public exam requires focusing on the most frequently asked questions from each chapter. Many questions in the board exam follow similar patterns every year, so practicing these important questions and understanding their solutions can help students score higher marks. When students clearly understand the concepts and practice step-by-step answers, it becomes easier to attempt long and short questions confidently in the exam.

Real Numbers Important Question and Answer

a^2-b^2=(a-b)(a+b)

a

b

aba + ba – b

One of the common questions in the Real Numbers chapter asks students to factorize expressions using algebraic identities. For example, students may be asked to factorize an expression like $x^2-25$ . Using the difference of squares identity, the expression can be written as $(x - 5) (x + 5)$ . Questions like this usually appear as short answer questions and can easily earn marks if the identity is remembered correctly.

Another type of question from this chapter asks students to find the HCF of two numbers using Euclid’s Division Algorithm. The solution requires repeatedly applying the algorithm until the remainder becomes zero, and the last divisor becomes the HCF.

Polynomials Important Question and Answer

In the Polynomials chapter, a frequently asked question is to find the zeros of a quadratic polynomial. For example, if the polynomial is $x^2 – 5x + 6$ , students must factorize it into $(x - 2) (x - 3)$ . From this, the zeros of the polynomial are 2 and 3. Understanding how to factorize quadratic expressions helps students solve such questions quickly.

Another common question asks students to verify the relationship between the zeros and coefficients of a polynomial. If the polynomial is $ax^2+bx+c$ , then the sum of the zeros equals $- b / a$ and the product of the zeros equals $c / a$ .

Pair of Linear Equations in Two Variables

\begin{cases}a_1x+b_1y+c_1=0\a_2x+b_2y+c_2=0\end{cases}

This chapter often includes questions where students must solve two equations using the elimination method or substitution method. For example, consider the equations $x + y = 7$ and $x - y = 1$ . Adding both equations gives $2 x = 8$ , which means $x = 4$ . Substituting this value into the first equation gives $4 + y = 7$ , so $y = 3$ .

Word problems based on ages, numbers, and money transactions are also common. Students should practice converting such situations into equations before solving them.

Quadratic Equations Important Question and Answer

x=−b±b2−4ac2ax=\frac{-b\pm\sqrt{b^2-4ac}}{2a}

a

b

c

-10-8-6-4-224681020406080100-2.002.00

A common question from the Quadratic Equations chapter is solving an equation using the quadratic formula. For example, if the equation is $x^2-7x+10=0$ , we first identify the values $a = 1$ , $b = - 7$ , and $c = 10$ . Substituting these into the quadratic formula gives the solutions $x = 5$ and $x = 2$ .

Students may also be asked to form a quadratic equation when the roots are given. This type of question checks whether students understand the relationship between roots and coefficients.

Arithmetic Progression Important Question and Answer

a_n=a+(n-1)d

Arithmetic Progression questions often ask students to find a specific term of the sequence. For example, if the first term $a = 3$ and the common difference $d = 2$ , the tenth term can be found using the formula $a_n=a+(n-1)d$ . Substituting the values gives $a_{10}=3+(9×2)=21$ . Another common problem type asks students to determine which term of the sequence equals a given number. These questions test students’ ability to apply the formula correctly.

Triangles Important Question and Answer

a^2+b^2=c^2

a

b

\sqrt{a^2 + b^2} \approx 21.21

a2+b2=c2≈225.00+225.00=450.00a^2 + b^2 = c^2 \approx 225.00 + 225.00 = 450.00

abc

In the Triangles chapter, students are often asked to solve problems using the Pythagorean theorem. For example, if a right-angled triangle has sides of length 3 cm and 4 cm, the hypotenuse can be calculated using the formula. Substituting the values gives $c^2=3^2+4^2=9+16=25$ , so $c = 5$ . Students should also practice questions related to similar triangles and proportional sides, as these are frequently included in the exam.

Trigonometry Important Question and Answer

sin⁡2θ+cos⁡2θ=1\sin^2\theta+\cos^2\theta=1

θ\theta

cos⁡2θ≈0.671\sin^2\theta \approx 0.329,\;\cos^2\theta \approx 0.671

sin⁡2θ+cos⁡2θ≈1\sin^2\theta + \cos^2\theta \approx 1

θ = 35°|cos θ| = 0.819|sin θ| = 0.574cos² θsin² θ0.671 + 0.329 = 1

Trigonometry questions often involve simplifying expressions using identities. For instance, if students are asked to simplify $sin⁡2θ+cos⁡2θ\sin^2\theta+\cos^2\theta$ , the value is always equal to 1 according to the fundamental trigonometric identity. Another important question type involves finding trigonometric ratios for standard angles such as 30°, 45°, and 60°. Memorizing these values is essential for solving exam questions quickly.

Statistics Important Question and Answer

\bar{x}=\frac{\sum f_ix_i}{\sum f_i} Statistics questions commonly ask students to find the mean of grouped data. Students must create a table including class intervals, frequency, and midpoints before applying the mean formula. Careful calculation is important in this chapter because small mistakes in arithmetic can affect the final answer. Practicing several problems helps students become faster and more accurate.

Probability Important Question and Answer

P(E)=\frac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}} Probability questions are usually straightforward. For example, when a die is thrown, the probability of getting an even number can be calculated by counting the favourable outcomes. The even numbers on a die are 2, 4, and 6, so there are three favourable outcomes out of six total outcomes. Therefore, the probability is $3/6$ , which simplifies to $1/2$ . Students should practice similar examples involving coins, cards, and dice to understand probability concepts clearly.

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Final Preparation Tips for the Public Exam

Students aiming to score high marks in the Class 10 Mathematics public exam should focus on understanding formulas, practicing important questions from every chapter, and revising regularly. Solving previous year question papers helps students become familiar with the exam pattern. Writing clear steps, checking calculations carefully, and managing time effectively during the exam will greatly increase the chances of scoring 80 to 90 marks or even higher.