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Class 7 Mathematics NCERT Exemplar Solutions
Chapter 1: Integers
This chapter extends the concept of integers introduced in Class 6. Students learn to perform all four arithmetic operations on positive and negative integers—addition, subtraction, multiplication, and division. Key properties such as the commutative, associative, and distributive laws are explored. For example: $(-4) + (+3) = -1$ and $(-2) \times (-3) = +6$. The NCERT Exemplar problems reinforce how integers behave under various operations and real-life contexts like profit-loss, temperature changes, and elevations.
Chapter 2: Fractions & Decimals
Learn how to compare, simplify, and operate on fractions and decimals. Understand addition, subtraction, multiplication, and division of fractions such as $\frac{3}{4} + \frac{1}{8} = \frac{7}{8}$, and decimals like $1.25 \times 0.4 = 0.50$. The chapter also explains conversion between fractions and decimals, equivalent fractions, and real-life applications involving measurements, money, and distances. These Exemplar Solutions include step-by-step explanations for each operation, making complex calculations simple.
Chapter 3: Data Handling
This chapter introduces students to data collection, organization, and representation. Learn to use bar graphs, double bar graphs, pie charts, and mean, median, and mode to analyze data sets. Example: The mean of numbers $5, 10, 15$ is $\frac{5 + 10 + 15}{3} = 10$. Data handling builds analytical and logical reasoning, helping students interpret information in real-world contexts such as surveys and statistics.
Chapter 4: Simple Equations
Learn to form and solve linear equations in one variable. Understand how equality is maintained while performing operations on both sides of an equation. Example: Solve $2x + 5 = 15$ to get $x = 5$. Students practice translating word problems into algebraic equations and solving them systematically. This chapter lays the groundwork for algebraic problem-solving in higher classes.
Chapter 5: Lines & Angles
Explore different types of lines and angles such as complementary, supplementary, adjacent, and vertically opposite angles. Learn important relationships like: if two lines intersect, opposite angles are equal. Understand how the sum of angles on a straight line is $180^\circ$ and around a point is $360^\circ$. The Exemplar Solutions include geometry-based reasoning questions that strengthen conceptual understanding and logical proofs.
Chapter 6: Triangles
Study the classification of triangles based on sides and angles—equilateral, isosceles, scalene, acute, right, and obtuse. Understand the properties of congruence through criteria such as SAS, ASA, and SSS. Learn the sum of the angles of a triangle is $180^\circ$. Example: If two angles of a triangle are $50^\circ$ and $60^\circ$, the third angle is $70^\circ$. This chapter builds reasoning and geometric accuracy.
Chapter 7: Comparing Quantities
Learn how to compare quantities using ratios, proportions, percentages, and simple interest. Understand formulas like percentage = $\frac{\text{part}}{\text{whole}} \times 100$ and simple interest $SI = \frac{P \times R \times T}{100}$. Apply these concepts to real-life contexts such as discounts, profit-loss, and banking. NCERT Exemplar questions help students master ratio-based reasoning and financial arithmetic.
Chapter 8: Rational Numbers
Discover rational numbers and their properties on the number line. A rational number is expressed as $\frac{p}{q}$, where $q \neq 0$. Learn about equivalent rational numbers, addition and multiplication rules, and their representation between integers. Example: $\frac{1}{2} + \frac{1}{3} = \frac{5}{6}$. The Exemplar exercises focus on simplifying rational expressions and identifying the smallest or greatest rational number between two given numbers.
Chapter 9: Perimeter & Area
This chapter teaches how to calculate perimeter and area of various plane figures like rectangles, squares, triangles, parallelograms, and circles. Learn formulas such as perimeter of rectangle $= 2(l + b)$, area of triangle $= \frac{1}{2} \times \text{base} \times \text{height}$, and area of circle $= \pi r^2$. Students solve practical problems involving measurement of land, walls, and boundaries using Exemplar questions for accuracy and speed.
Chapter 10: Algebraic Expressions
Get introduced to algebraic expressions like $2x + 3y - 5$. Learn how to add, subtract, and simplify expressions using like and unlike terms. Understand basic identities such as $(a + b)^2 = a^2 + 2ab + b^2$. The Exemplar exercises include step-by-step simplifications and problem-solving techniques to strengthen algebraic manipulation.
Chapter 11: Exponents & Powers
Understand the laws of exponents and apply them in calculations involving large and small numbers. Key rules include $a^m \times a^n = a^{m+n}$ and $(a^m)^n = a^{mn}$. Learn how to represent very large numbers using scientific notation. Example: $6.022 \times 10^{23}$ represents Avogadro’s number. The Exemplar Solutions simplify exponent rules through numerous practice problems.
Chapter 12: Practical Geometry, Symmetry & Visualising Solid Shapes
Master the construction of geometric figures such as triangles, parallel lines, and perpendicular bisectors using a compass and ruler. Study symmetry and identify lines of symmetry in shapes like rectangles, squares, and circles. Develop spatial visualization of 3D objects like cubes, cuboids, cylinders, cones, and spheres through nets and isometric drawings. This chapter enhances both visualization and drawing skills essential for geometry.