Umar Zaheer

Note: This is the Solution of review exercise 7.1 from newly published book by PCTB (Punjab Curriculum and Textbook Board, Pakistan) for new 9th session 2025 Onward. Exercise 7.1 Question # 01: Describe the location in the plane of the point \(\small{P(x,y)}\), for which \((i)\) \(\quad\) \( x>0\) \((ii)\) \(\quad\) \(x>0\) and \(y>0\) \((iii)\) \(\quad\) … Read more

Note: This is the Solution of review exercise 6 from newly published book by PCTB (Punjab Curriculum and Textbook Board, Pakistan) for new 9th session 2025 Onward. Review Exercise 6 Question # 01: Four option are given against each statement. Encircle the correct option. \((i)\) The value of \(\tan^{-1} 2\) in radians is: \( a) … Read more

Note: This is the Solution of review exercise 6.5 from newly published book by PCTB (Punjab Curriculum and Textbook Board, Pakistan) for new 9th session 2025 Onward. Exercise 6.5 Question # 01: Find the values of \(\small{x,y}\) and \(\small{z}\) from the following right angled triangles. Question 2: Find the unknown side and angles of the … Read more

Note: This is the Solution of review exercise 6.6 from newly published book by PCTB (Punjab Curriculum and Textbook Board, Pakistan) for new 9th session 2025 Onward. Exercise 6.6 Question # 01: The angle of elevation of the top of a flag post from a point on the ground level \(\small{40\ m}\) away from the … Read more

Note: This is the Solution of review exercise 6.4 from newly published book by PCTB (Punjab Curriculum and Textbook Board, Pakistan) for new 9th session 2025 Onward. Exercise 6.4 Question # 01: Find the value of the following trigonometric ratios without using the calculator. \((i)\) \(\quad\) \( \sin 30^\circ\) \((ii)\) \(\quad\) \(\cos 30^\circ\) \((iii)\) \(\quad\) … Read more

Note: This is the Solution of review exercise 6.3 from newly published book by PCTB (Punjab Curriculum and Textbook Board, Pakistan) for new 9th session 2025 Onward. Exercise 6.3 Question # 01: If \(\small{\theta}\) lies in first quadrant, find the remaining trigonometric ratios of \(\small{\theta}\). \((i)\) \(\quad\) \( \sin \theta =\frac{2}{3}\) \((ii)\) \(\quad\) \(\cos \theta … Read more

Note: This is the Solution of review exercise 6.2 from newly published book by PCTB (Punjab Curriculum and Textbook Board, Pakistan) for new 9th session 2025 Onward. Exercise 6.2 Question # 01: For each of the following right-angles triangles, find the trignometric ratios: \((i)\) \(\quad\) \( \sin \theta\) \((ii)\) \(\quad\) \(\cos \theta \) \((iii)\) \(\quad\) … Read more

Note: This is the Solution of review exercise 6.1 from newly published book by PCTB (Punjab Curriculum and Textbook Board, Pakistan) for new 9th session 2025 Onward. Exercise 6.1 Question # 01: Find in which quadrant the following angles lie. Write a co-terminal angle for each: \((i)\) \(\quad\) \( 65^\circ\) \((ii)\) \(\quad\) \(135^\circ\) \((iii)\) \(\quad\) … Read more

Note: This is the Solution of review exercise 5 from newly published book by PCTB (Punjab Curriculum and Textbook Board, Pakistan) for new 9th session 2025 Onward. Review Exercise 5 Question # 01: Four option are given against each statement. Encircle the correct option. \((i)\) In the following, linear equation is: \( a) \quad \) … Read more

Note: This is the Solution of review exercise 5.2 from newly published book by PCTB (Punjab Curriculum and Textbook Board, Pakistan) for new 9th session 2025 Onward. Exercise 5.2 Question # 01: Maximize \(\small{f(x,y)=2x+5y}\); subject to the constraints: \(2y-x\le 8\) \(x-y\le4\) \(x \ge 0\; ; y\ge 0\) Question # 02: Maximize \(\small{f(x,y)=x+3y}\); subject to the … Read more