Umar Zaheer

Note: This is the Solution of review exercise 5.1 from newly published book by PCTB (Punjab Curriculum and Textbook Board, Pakistan) for new 9th session 2025 Onward. Exercise 5.1 Question # 01: Solve and represent the solution on a real line: \((i)\) \(\quad\) \( 12x+30=-6\) \((ii)\) \(\quad\) \(\frac{x}{3}+6=-12\) \((iii)\) \(\quad\) \(\frac{x}{2}-\frac{3x}{4}=\frac{1}{12} \) \((iv)\) \(\quad \)\(2=7(2x+4)+12x … Read more

Note: This is the Solution of review exercise 4 from newly published book by PCTB (Punjab Curriculum and Textbook Board, Pakistan) for new 9th session 2025 Onward. Review Exercise 4 Question # 01: Four option are given against each statement. Encircle the correct option. \((i)\) The factorization of \(12x+36\) is: \( a) \quad \) \( … Read more

Note: This is the Solution of review exercise 2 from newly published book by PCTB (Punjab Curriculum and Textbook Board, Pakistan) for new 9th session 2025 Onward. Review Exercise 2 Question # 01: Four option are given against each statement. Encircle the correct option. \((i)\) The standard form of \(5.2\times10^6\) is: \( a) \quad \) … Read more

Note: This is the Solution of exercise 2.4 from newly published book by PCTB (Punjab Curriculum and Textbook Board, Pakistan) for new 9th session 2025 Onward. Exercise 2.4 Question # 01: Without using calculator, evaluate the following: \((i)\) \(\quad\) \(log_2\ 18 – log_2\ 9 \) \((ii)\) \(\quad\) \(log_2\ 64 + log_2\ 2 \) \((iii)\) \(\quad\) … Read more

Note: This is the Solution of exercise 2.3 from newly published book by PCTB (Punjab Curriculum and Textbook Board, Pakistan) for new 9th session 2025 Onward. Exercise 2.3 Question # 01: Find characteristic of the following numbers: \((i)\) \(\quad\) \(5287 \) \((ii)\) \(\quad\) \(59.28 \) \((iii)\) \(\quad\) \(0.0567\) \((iv)\) \(\quad\) \(234.7 \) \((v)\) \(\quad\)\( 0.000049 … Read more

Note: This is the Solution of exercise 2.2 from newly published book by PCTB (Punjab Curriculum and Textbook Board, Pakistan) for new 9th session 2025 Onward. Exercise 2.2 Question # 01: Express each of the following in logarithmic form: \((i)\) \(\quad\) \(10^3=1000 \) \((ii)\) \(\quad\) \(2^8=256 \) \((iii)\) \(\quad\) \(3^{-3}=\frac{1}{27}\) \((iv)\) \(\quad\) \(20^2=400 \) \((v)\) … Read more

Note: This is the Solution of exercise 2.1 from newly published book by PCTB (Punjab Curriculum and Textbook Board, Pakistan) for new 9th session 2025 Onward. Exercise 2.1 Question # 01: Express the following numbers in scientific notation. \((i)\) \(\quad\) \(2000000 \) \((ii)\) \(\quad\) \(48900 \) \((iii)\) \(\quad\) \( 0.0042\) \((iv)\) \(\quad\) \(0.0000009 \) \((v)\) … Read more

Note: This is the Solution of review exercise 1 from newly published book by PCTB (Punjab Curriculum and Textbook Board, Pakistan) for new 9th session 2025 Onward. Review Exercise 1 Question # 01: Four option are given against each statement. Encircle the correct option. \((i)\)\(\quad\)\(\sqrt{7}\) is: \( a) \quad \) integer \( b) \quad \) … Read more

Note: This is the Solution of exercise 1.3 from newly published book by PCTB (Punjab Curriculum and Textbook Board, Pakistan) for new 9th session 2025 Onward. Exercise 1.3 Question # 01: The sum of three consecutive integers is forty two, find the three integers. Question # 02: The diagram shows right angled \(\triangle ABC\) in … Read more

Note: This is the Solution of exercise 1.2 from newly published book by PCTB (Punjab Curriculum and Textbook Board, Pakistan) for new 9th session 2025 Onward. Exercise 1.2 Question # 01: Rationalize the denominator of following: \((i)\) \(\quad \large{\frac{13}{4+\sqrt{3}}} \) \((ii)\) \(\quad \large{\frac{\sqrt{2}+\sqrt{5}}{\sqrt{3}}} \) \((iii)\) \(\quad \large{\frac{\sqrt{2}-1}{\sqrt{5}}}\) \((iv)\) \(\quad \large{\frac{6-4\sqrt{2}}{6+4\sqrt{2}}} \) \((v)\) \(\quad \large{\frac{\sqrt{3}-\sqrt{2}}{\sqrt{3}+\sqrt{2}}} \) … Read more