Mathematics for Class 8 (English Medium) is the official textbook published by the Punjab Textbook Board (PTB), covering 10 chapters across 133 pages. It is part of the official Class 8 syllabus, taking students from sets and real numbers through financial arithmetic, algebra, geometry, and statistics in English.
For Class 8 students studying in English medium, this book builds the algebra and geometry foundation needed for Class 9 and board exams ahead. The chapter summaries and important questions on this page make revision faster, whether you are checking a formula or reviewing a full topic before a test.
Book Overview
| Class | 8 |
| Subject | Mathematics |
| Medium | English Medium |
| Board | Punjab Textbook Board (PTB) |
| Total Chapters | 10 |
| Total Pages | 133 |
| Format | PDF (Free Download) |
Chapter List
Chapter 1: Operations on Sets
This chapter reviews sets and their standard notations for natural numbers (N), whole numbers (W), integers (Z), primes (P), and rational numbers (Q), then covers subsets, proper and improper subsets, and the power set of a set with 2ⁿ elements. It verifies the commutative and associative laws of union and intersection, the distributive laws, and De Morgan’s laws, and uses Venn diagrams to demonstrate operations on three overlapping sets.
Important Questions:
- What is a proper subset? A set A is a proper subset of B if every element of A is in B but at least one element of B is not in A, written A ⊂ B.
- How many subsets does a set with n elements have? 2ⁿ subsets, including the empty set and the set itself.
- State De Morgan’s Law for two sets. (A ∪ B)’ = A’ ∩ B’ and (A ∩ B)’ = A’ ∪ B’.
- Write the power set of B = {3, 6, 9}. P(B) = {∅, {3}, {6}, {9}, {3,6}, {3,9}, {6,9}, {3,6,9}}.
Chapter 2: Real Numbers
This chapter defines irrational numbers as those that cannot be written as p/q, and the set of real numbers R as the union of rational numbers Q and irrational numbers Q’. It explains terminating and non-terminating decimal fractions, teaches finding squares and square roots by prime factorization and the division method, and covers cubes and cube roots along with the properties of cubes of positive, negative, even, and odd numbers.
Important Questions:
- What is an irrational number? A number that cannot be written in the form p/q where p, q are integers and q≠0, such as √2 or √5.
- How is the set of real numbers defined? R = Q ∪ Q’, the union of the set of rational numbers and the set of irrational numbers.
- Find the cube root of 125. 125 = 5×5×5 = 5³, so the cube root of 125 is 5.
- What kind of decimal is produced by an irrational number? A non-terminating, non-repeating decimal.
Chapter 3: Number Systems
This chapter explains the base of a number system and covers four number systems in detail: the binary system (base 2) used inside computers, the base-5 system, the octal system (base 8), and the familiar decimal system (base 10). It teaches how to convert numbers from the decimal system into binary, base-5, and octal systems using successive division, and how to convert numbers from these systems back into decimal using expanded place-value notation.
Important Questions:
- What is the base of a number system? The number of digits used in that system; for example, the binary system has base 2 and the decimal system has base 10.
- Why is the binary system important? Because computers store and process information using binary numbers, making it essential in modern computing.
- Convert (1101)₂ into decimal. 1×2³+1×2²+0×2¹+1×2⁰ = 8+4+0+1 = 13.
- What method is used to convert a decimal number into another base? The method of successive division by the base of the target system.
Chapter 4: Financial Arithmetic
This chapter covers compound proportion, including direct and inverse proportion, partnership, and inheritance problems, then introduces banking through the four types of accounts (PLS savings, current deposit, PLS term deposit, and foreign currency accounts) and negotiable instruments like cheques, demand drafts, and pay orders. It explains percentage-based profit, loss, and discount calculations, life and vehicle insurance, and how to compute income tax using Pakistan’s taxable income slabs.
Important Questions:
- What is the difference between direct and inverse proportion? In direct proportion, increasing one quantity increases the other; in inverse proportion, increasing one quantity decreases the other.
- What is a cheque? A written order instructing a bank to pay a specific amount from a specified account to the holder of the cheque.
- How is percentage profit calculated? Percentage Profit = (Profit ÷ Cost Price) × 100.
- What is taxable income? The difference between a person’s annual income and their exempted income.
Chapter 5: Polynomials
This chapter defines a polynomial as an algebraic expression whose variable exponents are whole numbers, and explains the degree and coefficient of a polynomial term. It teaches how to recognize polynomials in one, two, and more variables, and classifies them by degree into linear, quadratic, cubic, and biquadratic polynomials, with examples of each type.
Important Questions:
- What is a polynomial? An algebraic expression with one or more terms in which the exponent of the variable is zero or a positive integer.
- What is the degree of a polynomial? The highest sum of the exponents of the variables found in any single term of the polynomial.
- What is a quadratic polynomial? A polynomial of degree two, such as x²-3x+1.
- In the term 4x, what is the coefficient of x? 4, since the coefficient is the number multiplied with the variable.
Chapter 6: Factorization, Simultaneous Equations
This chapter teaches the basic algebraic formulas (a+b)², (a-b)², and a²-b² = (a+b)(a-b), and uses them to factorize expressions and simplify calculations. It covers recognizing and solving simultaneous linear equations in two variables, forming equations from word statements, and solving systems of equations using the elimination method.
Important Questions:
- State the formula for a²-b². a²-b² = (a+b)(a-b).
- What is factorization? The process of expressing a given algebraic expression as a product of its factors.
- What are simultaneous linear equations? Two or more linear equations in the same variables that are satisfied by the same values of those variables.
- What is the elimination method used for? Removing one variable from a system of equations so a single equation in one variable remains, called the eliminant.
Chapter 7: Fundamentals of Geometry
This chapter defines parallel lines and demonstrates their properties, including that lines parallel to the same line are parallel to each other, and the angle relationships formed when a transversal cuts two parallel lines, vertically opposite, corresponding, alternate interior, and interior angles. It then covers polygons, the properties of parallelograms, regular pentagons, hexagons, and octagons, and points lying in the interior and exterior of a circle.
Important Questions:
- What are parallel lines? Lines on the same plane that never meet, touch, or intersect at any point, and are always the same distance apart.
- What are corresponding angles? Pairs of angles formed on the same side of a transversal and in the same position relative to two parallel lines.
- What does the midpoint theorem for triangles state? A line through the midpoint of one side of a triangle, parallel to a second side, bisects the third side.
- What is a regular polygon? A polygon whose sides are all equal in length and whose angles are all equal in measure, such as a regular hexagon.
Chapter 8: Practical Geometry
This chapter covers geometric constructions using compass and ruler, starting with finding the angle between two converging (non-parallel) lines and bisecting that angle without extending the lines. It then teaches how to construct a rhombus, a parallelogram, a kite given two unequal sides and a diagonal, and regular pentagons and hexagons when one side length is given.
Important Questions:
- What are converging lines? Lines that intersect at a single point rather than running parallel to each other.
- What is needed to construct a kite? Two unequal sides and a diagonal of the kite.
- What tools are used for geometric constructions in this chapter? A compass and a straightedge (ruler).
- What information is needed to construct a regular hexagon? The length of one side of the hexagon.
Chapter 9: Areas and Volumes
This chapter proves and applies the Pythagoras theorem (Base² + Altitude² = Hypotenuse²) for right-angled triangles, then introduces Hero’s Formula for finding the area of a triangle when all three side lengths are known. It closes with the surface area and volume of a sphere, showing that a sphere’s surface area equals 4πr², derived by comparing it to the curved surface area of a cylinder with the same radius.
Important Questions:
- State the Pythagoras theorem. In a right-angled triangle, the square of the hypotenuse equals the sum of the squares of the other two sides: a²+b²=c².
- When is Hero’s Formula used? When the lengths of all three sides of a triangle are known but the height is not.
- What is the formula for the surface area of a sphere? Surface area = 4πr², where r is the radius of the sphere.
- Find the surface area of a sphere with radius 21cm (π=22/7). Surface area = 4×22/7×21×21 = 5544 cm².
Chapter 10: Information Handling
This chapter explains frequency and frequency distribution, showing how to organize raw data like students’ weights into a grouped frequency distribution table and represent it as a histogram. It covers the measures of central tendency, mean, weighted mean, median, and mode, and how to calculate and apply each one to real-life data sets.
Important Questions:
- What is the frequency of a value in a data set? The number of times that value occurs in the data.
- What is a frequency distribution? A table that organizes data into classes so the frequency of each class can be seen at a glance.
- Name the four measures of central tendency covered in this chapter. Mean, weighted mean, median, and mode.
- What is a histogram used for? To visually represent a frequency distribution using adjacent bars over class intervals.
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⬇ Download PDF (2016-17)Who Should Read This
This textbook is for Class 8 students studying Mathematics in English medium under Punjab Textbook Board. It is especially useful for students preparing for annual board exams and those who want to build a solid foundation in algebra and geometry for Class 9 and beyond.
Applicable Boards
This textbook is published by Punjab Textbook Board (PTB) and is used in all Punjab Board affiliated schools. Students from Federal Board and other provincial boards may also find it useful as the Class 8 Math syllabus is largely similar.
FAQs
Is this the official PTB Mathematics book for Class 8 English medium?
Yes, this is the official Punjab Textbook Board Mathematics textbook for Class 8 in English medium, covering all 10 chapters of the current syllabus.
Is there a Urdu medium version of this book?
Yes, the Urdu medium version of Class 8 Mathematics is also available for download separately on our website.
Which topics are covered in Class 8 Math?
The book covers Operations on Sets, Real Numbers, Number Systems, Financial Arithmetic, Polynomials, Factorization and Simultaneous Equations, Fundamentals of Geometry, Practical Geometry, Areas and Volumes, and Information Handling.
Is this book helpful for Class 9 preparation?
Yes, Class 8 Mathematics builds a strong foundation for Class 9. Topics like polynomials, factorization, geometry, and statistics directly connect to the Class 9 syllabus.
Are multiple versions available?
Yes, both the latest version and the 2016-17 version of Class 8 Mathematics English medium are available for download on this page.
Does this page include solved examples?
This page summarizes every chapter with its key formulas and concepts, plus important questions for revision, alongside the full worked examples and exercises in the downloadable PDF.