Download PDF Class 9 Mathematics — Chapter 7: Coordinate Geometry Punjab Board | 2026 Exercise 7.1 Q1. Find the distance between the following pairs of points. Distance Formula [ d=sqrt{(x_2-x_1)^2+(y_2-y_1)^2} ] (i) A(2, 3), B(6, 6) Step 1: Identify the coordinates. [ x_1=2,quad y_1=3,quad x_2=6,quad y_2=6 ] Step 2: Apply the distance formula. […
Download PDF Class 9 Mathematics — Chapter 6: Trigonometry Punjab Board | 2026 Exercise 6.1 Q1. Find the quadrant in which each angle lies. Write a co-terminal angle for each. (i) 65° Quadrant: Since (0^circ<65^circ<90^circ), the angle lies in Quadrant I. Co-terminal angle: [ 65^circ+360^circ=boxed{425^circ} ] (ii) 135° Quadrant: Since (90^circ<135^circ<180^circ), the angle lies…
Download PDF Class 9 Mathematics Notes – Chapter 5: Linear Equations and Inequalities Punjab Board | 2026 Exercise 5.1 Q1. Solve and represent the solution on a real line. (i) (12x+30=-6) Subtract 30 from both sides: [ 12x=-6-30=-36 ] Divide both sides by 12: [ x=frac{-36}{12}=-3 ] Solution Set: ({-3}) Real Line Representation: Mark…
Download PDF Class 9 Mathematics Notes – Chapter 4: Factorization and Algebraic Manipulation Punjab Board | 2026 Exercise 4.1 Q1. Factorize by identifying common factors. (i) (6x+12) Answer: [ 6x+12=6(x+2) ] (ii) (15y^2+20y) Answer: [ 15y^2+20y=5y(3y+4) ] (iii) (-12x^2-3x) Answer: [ -12x^2-3x=-3x(4x+1) ] (iv) (4a^2b+8ab^2) Answer: [ 4a^2b+8ab^2=4ab(a+2b) ] (v) (xy-3x^2+2x) Answer: [ xy-3x^2+2x=x(y-3x+2)…
Download PDF Class 9 Mathematics Notes – Chapter 3: Sets and Functions Punjab Board · 2026 Exercise 3.1 Q1. Write the following sets in set-builder notation. (i) ({1,4,9,16,25,36,ldots,484}) Answer: [ {xmid x=n^2, ninmathbb N, nleq22} ] (ii) ({2,4,8,16,32,64,ldots,150}) Answer: [ {xmid x=2^n, ninmathbb N, 2^nleq150} ] (iii) ({0,pm1,pm2,ldots,pm1000}) Answer: [ {xmid xinmathbb Z, -1000leq…
Download PDF Class 9 Mathematics Notes — Chapter 2: Logarithms Punjab Board · Class 9 · Chapter 02 Exercise 2.1 Q1. Express the following numbers in scientific notation. (i) (2,000,000) [ 2,000,000=2times10^6 ] Move the decimal point 6 places to the left. (ii) (48,900) [ 48,900=4.89times10^4 ] Move the decimal point 4 places to…
Download PDF Class 9 Mathematics Notes – Chapter 1: Real Numbers Board: Punjab BoardSubject: MathematicsClass: 9thChapter: 1 Exercise 1.1 Q1. Identify each of the following as a rational or irrational number. (i) (2.353535) Answer: Rational number. Reason: It is a terminating decimal number. (ii) (0.overline{6}) Answer: Rational number. Reason: It is a non-terminating, recurring…
Download PDF Class 9 Computer Science Notes Chapter 12 Chapter 12: Entrepreneurship in Digital Age Exercise Solution PART I: MULTIPLE-CHOICE QUESTIONS (MCQs) 1. What is entrepreneurship? (a) The process of starting a new business or organization(b) The process of buying and selling stocks(c) The process of working for a large company(d) The process of creating…
Download PDF Class 9 Computer Science Notes Chapter 11 Chapter 11: Ethical, Social, and Legal Concerns in Computer Usage Exercise Solution PART I: MULTIPLE-CHOICE QUESTIONS (MCQs) Q1. Why is it important to use computers safely and responsibly? (a) To ensure we can use them more frequently(b) To protect our personal information and make wise choices…
Download PDF Class 9 Computer Science Notes Chapter 10 Chapter 10: Emerging Technologies in Computer Science Exercise Solution PART I: MULTIPLE-CHOICE QUESTIONS (MCQs) Q1. Which of the following is not a subfield of AI? (a) Machine Learning(b) Natural Language Processing(c) Computer Vision(d) Robotics Answer: All listed options (Machine Learning, Natural Language Processing, Computer Vision, and…
