CBSE Class 10 Maths Competency Based Questions 2024 PDF

Real Numbers : This chapter deals with the concept of real numbers, including rational and irrational numbers. Students will explore the fundamental properties of real numbers, focusing on how to represent them on the number line. They will also learn about the Euclidean algorithm, which helps find the greatest common divisor (GCD) of two numbers. This chapter forms the basis for understanding the number system and its properties in detail. Students will also be introduced to the fundamental theorem of arithmetic and its application in the factorization of numbers.

Polynomials: In this chapter, students learn about polynomials, which are expressions involving variables and coefficients, connected by addition, subtraction, and multiplication. The chapter covers the definition and classification of polynomials based on the degree (linear, quadratic, cubic, etc.). Students will also learn about the relationship between the roots and coefficients of a polynomial using Vieta’s formulas. Factorization of polynomials and solving polynomial equations are key aspects of this chapter, which help students understand how to break down complex expressions into simpler factors.

Pair of Linear Equations in Two Variables: This chapter introduces students to solving systems of linear equations. The main methods discussed include substitution, elimination, and graphical methods. Students will learn how to find the value of two variables that satisfy both equations simultaneously. This chapter also involves solving word problems related to linear equations and understanding the geometric interpretation of a system of equations, where the solution represents the point of intersection of two lines.

Quadratic Equations: In this chapter, students are introduced to quadratic equations, which are polynomial equations of degree 2. Students will learn various methods to solve these equations, including factorization, completing the square, and using the quadratic formula. The chapter also covers the discriminant, which helps determine the nature of the roots (real, equal, or complex) of a quadratic equation.

Arithmetic Progressions: This chapter covers sequences and series, focusing on arithmetic progressions (AP). An arithmetic progression is a sequence of numbers in which the difference between consecutive terms is constant. Students will learn how to find the nth term of an AP, the sum of the first n terms, and solve problems involving real-life situations where AP applies, such as in finance (loan repayments) and daily life (bus schedules, etc.).

Triangles: In this chapter, students study the properties of triangles, including congruence and similarity. They will learn about the different types of triangles based on sides and angles and the theorems related to them. The chapter includes important results like the Pythagorean theorem and properties of similar triangles. Students will also learn about angle bisectors, medians, and altitudes, as well as the criteria for congruence and similarity of triangles (SSS, SAS, ASA, and RHS).

Coordinate Geometry: This chapter introduces the Cartesian plane, where students learn how to plot points and interpret coordinates. The distance formula, which calculates the distance between two points in a plane, and the section formula, which helps in dividing a line segment into a given ratio, are crucial topics. Students will learn how to calculate the area of a triangle when its vertices are given by their coordinates. The chapter also covers the basic concept of straight lines and the equation of a line.

Introduction to Trigonometry: This chapter focuses on the basic trigonometric ratios: sine, cosine, and tangent. Students will learn how to use these ratios in right-angled triangles to find unknown sides or angles. The relationships between the sides and angles of right triangles are explored in detail, helping students understand how to apply trigonometric ratios to solve problems. This chapter lays the groundwork for further exploration into trigonometry and its applications in geometry.

Some Applications of Trigonometry: This chapter extends the concepts learned in the previous chapter by applying trigonometry to real-world problems. Students will use trigonometric ratios to solve problems involving heights and distances, such as finding the height of a building or the distance between two points. These applications require the use of angles of elevation and depression, further enhancing students' understanding of trigonometry’s practical use.

Circles: The chapter on circles focuses on various properties of circles, such as the relationship between the radius, chord, and the center. Key concepts include tangents, secants, and arcs. Students will learn about theorems related to the angles formed by a tangent and a chord, and the relationship between the angle subtended by a chord at the center and at any point on the remaining part of the circle. This chapter also covers the properties of cyclic quadrilaterals.

Areas Related to Circles: In this chapter, students will calculate the area of sectors and segments of circles. They will learn to find the areas of combinations of plane figures involving parts of circles, including sectors, segments, and areas between two concentric circles (rings). Formulas for the area of a sector and segment are introduced and used to solve real-life problems.

Surface Areas and Volumes: This chapter explain three-dimensional geometry and focuses on the calculation of surface areas and volumes of various solids, such as cubes, cuboids, spheres, cylinders, and cones. Students will learn the formulas to calculate the surface area and volume of these shapes and apply them to solve practical problems involving everyday objects.

Statistics: In the statistics chapter, students will learn how to organize and interpret data. This includes representing data in the form of tables, bar graphs, histograms, and frequency polygons. Students will also be introduced to measures of central tendency: mean, median, and mode. The chapter will guide students on how to calculate these measures and understand their significance in data analysis.

Probability: Probability is the study of how likely an event is to happen. In this chapter, you will learn how to calculate the probability of different events and understand concepts like complementary events. This is useful for solving problems related to chances and likelihood in everyday situations.