Mathematics for Class 8 under the Single National Curriculum (SNC) 2022 is published by the Punjab Curriculum and Textbook Board (PCTB). It replaces the older PTB edition and organises 13 units across five domains, Numbers and Operations, Algebra, Measurement, Geometry, and Statistics and Probability, spread over 241 pages.
For Class 8 Science group students moving to the new national curriculum, this book brings a slightly different structure and a few new topics, like Probability and Transformations, compared to the old syllabus. The chapter notes and important questions on this page make it easier to revise each domain before the annual exam.
Book Overview
| Class | 8 |
| Subject | Mathematics |
| Curriculum | Single National Curriculum (SNC) 2022 |
| Board | Punjab Curriculum and Textbook Board (PCTB) |
| Authors | Dr. Shafiq-ur-Rehman, Muhammad Ishfaq Baig, Muhammad Akhtar Shirani, Madiha Mehmood |
| Edition | Experimental Edition 2023-24 |
| Total Chapters | 13 (across 5 domains, plus Answers, Glossary and Symbols) |
| Total Pages | 241 |
| Format | PDF (Free Download) |
Chapter List
Chapter 1: Real Numbers (Domain 1: Numbers and Operations)
This unit revisits the real number system built from natural numbers, whole numbers, integers, and rational and irrational numbers. It establishes core properties like the commutative, associative, and distributive laws for addition and multiplication, and introduces absolute value as a way to describe a number’s distance from zero regardless of sign. These properties form the algebraic groundwork used throughout the rest of the book.
Important Questions:
- What is the commutative property of multiplication? For any two real numbers a and b, a·b = b·a, e.g. 13×7 = 7×13.
- What is an irrational number? A number that cannot be expressed as a ratio of two integers, such as √3.
- Find the absolute value of -8. |-8| = 8, since absolute value is always non-negative.
- State the distributive property. a(b+c) = a·b + a·c, e.g. 2(3+4) = 2×3+2×4 = 14.
Chapter 2: Estimation and Approximation
This unit teaches how to round numbers to a required degree of accuracy and identify significant figures in a value. It also covers rounding negative integers, which follows a slightly different method than positive numbers, and shows how estimation gives quick, workable answers in situations where an exact value isn’t necessary.
Important Questions:
- What is a significant figure? A digit that contributes to the precision of a number, including all non-zero digits and certain zeros.
- Round -234576 to 3 significant figures. -235000 (3 s.f.), rounding based on the digit after the third significant figure.
- Why is estimation useful in daily life? It gives a quick, reasonably accurate answer without needing an exact calculation, such as estimating a shopping bill.
- How does rounding a negative integer differ from a positive one? The same significant-figure rule applies, but the sign is kept in mind so the rounded value stays on the correct side of zero.
Chapter 3: Square Roots and Cube Roots
This unit explains how to find square roots using prime factorization and the long division method, and extends the same logic to cube roots and perfect cubes. Word problems, like finding the side of a cube-shaped box from its volume, show how these calculations apply outside the textbook.
Important Questions:
- Find the cube root of 216 using prime factorization. 216 = 2³×3³, so the cube root is 2×3 = 6.
- Is 1100 a perfect cube? No, since no integer cubed equals 1100.
- Find the cube of 0.4. 0.4³ = 0.064.
- What method is used to find square roots of large numbers? The long division method, along with prime factorization for perfect squares.
Chapter 4: Sets
This unit reviews set notation, types of sets, and the core operations: union, intersection, complement, and difference. Venn diagrams are used heavily to demonstrate De Morgan’s Laws and to simplify combined operations on three sets at once, giving students a visual way to check their algebraic answers.
Important Questions:
- State De Morgan’s Law for union. (A∪B)’ = A’∩B’.
- What is a Venn diagram used for? It visually represents sets and the relationships, union, intersection, between them using overlapping circles.
- If A∩B = ∅, what are A and B called? Disjoint sets, since they share no common elements.
- How is (A∩B)∪C found using a Venn diagram? Shade the region common to A and B, then combine it with all of C.
Chapter 5: Ratio, Rate and Proportion
This unit covers ratios, rates, and both direct and inverse proportion, building up to compound proportion problems that combine two or more simple ratios into one. Tables and graphs are used to show how one quantity changes as another changes, which is useful for real-life planning and budgeting problems.
Important Questions:
- What is compound proportion? The relationship formed when two or more simple proportions are combined into a single problem.
- If y is inversely proportional to x, what happens to y when x doubles? y is halved, since the product xy stays constant in inverse proportion.
- If x=1 gives y=80 and x=2 gives y=40, find y when x=4. y = 20, following the inverse relationship xy = 80.
- What is the difference between ratio and rate? A ratio compares two quantities of the same kind, while a rate compares two quantities of different kinds, such as speed in km/hour.
Chapter 6: Percentage and Financial Arithmetic
This unit applies percentage calculations to real financial situations: profit and loss, discount, tax, and simple and compound interest. Clear formulas for loss percentage and discount percentage are given alongside worked examples based on everyday buying, selling, and borrowing scenarios.
Important Questions:
- What is the formula for loss percentage? Loss % = (Loss ÷ Cost Price) × 100.
- What is percentage discount? Percentage Discount = (Discount ÷ Market Price) × 100.
- A shopkeeper marks an item Rs. 1000 and gives a 10% discount. Find the selling price. Discount = Rs. 100, so the selling price is Rs. 900.
- What is markup in banking terms? The extra amount a bank charges above the principal when lending money.
Chapter 7: Number Sequence and Patterns (Domain 2: Algebra)
This unit introduces arithmetic and geometric sequences and shows how to find the general term of each using a formula. Students practise spotting the pattern in a sequence, calculating the common difference or common ratio, and using it to predict later terms without listing every number.
Important Questions:
- Find the 5th term of the geometric sequence 1, 2, 4, 8, … Using aₙ = a₁r^(n-1): a₅ = 1×2⁴ = 16.
- What is a geometric sequence? A sequence where each term is found by multiplying the previous term by a constant ratio r.
- Find the common ratio of 3, 9, 27, 81. r = 9/3 = 3.
- What is the general term formula for a geometric sequence? aₙ = a₁r^(n-1), where a₁ is the first term and r is the common ratio.
Chapter 8: Expansion and Factorization
This unit covers the laws of exponents and uses them to expand algebraic expressions like (2x+3y)² and simplify expressions with powers. Multiple factorization methods, common factors, grouping, and trinomial factorization, are practised so students can reverse an expansion back into its original factors.
Important Questions:
- Simplify (2⁴)³ using laws of exponents. (2⁴)³ = 2^(4×3) = 2¹² = 4096.
- Expand (2x+3y)(2x+3y). (2x+3y)² = 4x²+12xy+9y².
- Simplify a⁴ × a⁹. a⁴×a⁹ = a¹³, adding the exponents.
- Simplify 9⁸ ÷ 9³. 9⁸÷9³ = 9⁵, subtracting the exponents.
Chapter 9: Linear Equations and Inequalities
This unit teaches how to solve linear equations and inequalities in one variable, including cases where multiplying or dividing by a negative number reverses the inequality sign. Graphical representation of inequalities on a number line is also covered, giving a visual check for the solution set.
Important Questions:
- Solve 2x – 5 > 1. 2x > 6, so x > 3.
- Solve -3x ≤ 6 for x. Dividing by -3 reverses the inequality: x ≥ -2.
- What happens to an inequality when both sides are multiplied by a negative number? The inequality sign reverses direction.
- Solve the linear equation 2x – 5 = 1 for x. 2x = 6, so x = 3.
Chapter 10: Mensuration (Domain 3: Measurement)
This unit calculates the surface area and volume of 3D shapes such as cylinders, cones, spheres, and composite figures, along with the arc length and area of a circle’s sector. Concepts like secant lines and points inside or outside a circle are also introduced as groundwork for the geometry unit that follows.
Important Questions:
- What is the formula for the arc length of a sector? Arc length = (θ/360°) × circumference of the circle.
- What is a secant line? A straight line that intersects a circle at two points.
- What is a pyramid? A 3D shape with a flat polygon base and triangular sides that converge at a single top point, called the apex.
- What is the formula for the area of a sector? Area of a sector = (θ/360°) × πr².
Chapter 11: Congruency, Similarity, Triangles & Transformation (Domain 4: Geometry)
This unit compares congruent and similar triangles, then moves into geometric transformations, translation, rotation, reflection, and enlargement. Students learn to find a scale factor between two similar shapes and to describe how a shape changes under each type of transformation, including negative scale factors that both resize and invert a shape.
Important Questions:
- What is enlargement in transformation? A transformation that resizes a shape by a given scale factor from a fixed centre of enlargement.
- How do you find the scale factor between two similar shapes? Divide a length in the image by the corresponding length in the original shape.
- What is the centre of enlargement? The fixed point from which all points of a shape are enlarged or reduced by a scale factor.
- What happens to a shape enlarged by a scale factor of -2? The shape is enlarged to twice its size and inverted (rotated 180°) about the centre of enlargement.
Chapter 12: Information Handling (Domain 5: Statistics and Probability)
This unit walks through organising raw data into frequency tables, histograms, and cumulative frequency curves, then calculating the mean, median, and mode of a data set. It also introduces dispersion, using range and variance to describe how spread out or consistent a set of values is.
Important Questions:
- What does dispersion describe? How spread out a set of data values is.
- What does range measure? Range is calculated using only the two extreme, highest and lowest, values in a data set.
- Why is variance used? Variance compares the consistency of two data sets; a smaller variance means more consistent data.
- What is the formula for variance by the definition method? S² = Σ(x-x̄)²/n, where x̄ is the mean.
Chapter 13: Probability
This unit introduces basic probability using sample space and events, then builds up to the addition law for mutually exclusive events and the multiplication law for independent events. Problems based on drawing coloured balls from a bag or tossing coins and dice are used to make the formulas concrete.
Important Questions:
- What is the addition law of probability for mutually exclusive events? P(A∪B) = P(A) + P(B).
- What is the multiplication law of probability for independent events? P(A∩B) = P(A) × P(B).
- If two events are mutually exclusive, what is P(A∩B)? P(A∩B) = 0, since they cannot occur together.
- In a bag with 20 red balls out of 100 total, find P(red). P(red) = 20/100 = 0.2.
Reference Material: Answers, Glossary and Symbols
The book closes with an Answers section giving solutions to the review exercises from each unit, a Glossary defining key mathematical terms like absolute value and additive identity, and a table of Symbols and Notations used throughout the book, such as ∪ for union and ∩ for intersection.
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⬇ Download PDFWho Should Read This
This book is for Class 8 students studying Mathematics under the Single National Curriculum 2022. Students in Science group schools following the new PCTB syllabus should use this textbook. It is also useful for students preparing for board exams under the new national curriculum and those transitioning from the old PTB edition.
Applicable Boards
This textbook is published by Punjab Curriculum and Textbook Board (PCTB) based on Single National Curriculum 2022. It is being implemented in Punjab Board affiliated schools. Federal Board and other provincial boards implementing SNC may also find this textbook useful.
FAQs
What is the difference between this SNC book and the old PTB Math 8 book?
The old PTB book followed the previous curriculum with 14 chapters. This new SNC 2022 book is organized into 5 domains and 13 units, includes new topics like Probability and Transformations, and is more aligned with the national standard.
Is this book for Science group students?
Yes, this Mathematics 8 SNC 2022 textbook is for Class 8 students in Science group schools following the new Single National Curriculum.
Does this book include Probability?
Yes, Domain 5 covers Statistics and Probability, including basic probability concepts, sample space, events, and theoretical and experimental probability.
Is Geometry included in this book?
Yes, Domain 4 covers Geometry, including congruency and similarity of triangles, construction, and transformations like translation, rotation, reflection, and enlargement.
Is this the latest edition?
Yes, this is the 2023-24 Experimental Edition based on Single National Curriculum 2022, published by Punjab Curriculum and Textbook Board.
Does this page include solved exercises?
This page summarizes each unit’s key concepts and important questions for quick revision. The full worked examples, exercises, and answer key are inside the downloadable PDF.