Umar Zaheer

Class 9th math 1.2 solution english PCTB

by

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

Class 9th math 1.1 solution english PCTB

by

Note: This is the Solution of exercise 1.1 from newly published book by PCTB (Punjab Curriculum and Textbook Board, Pakistan) for new 9th session 2025 Onward. Exercise 1.1 Question # 01: Identify each of the following as rational or irrational number. \((i)\) \(\quad 2.353535 \) \((ii)\) \(\quad 0.\overline{6} \) \((iii)\) \(\quad 2.236067… \) \((iv)\) \(\quad … Read more

Exercise 1.1 FBISE NBF Solution

by

Exercise 1.1 Question 1: Represent each number on the number line. \((i)\) \(\quad \frac{3}{4} \) \((ii)\) \(\quad -\frac{1}{3} \) \((iii)\) \(\quad 4\frac{1}{2} \) \((iv)\) \(\quad -\sqrt{8} \) \((v)\) \(\quad \sqrt{8} \) \((vi)\) \(\quad -4\frac{1}{2} \) \((vii)\) \(\quad \frac{1}{3} \) \((viii)\) \(\quad -\frac{7}{8} \) Question 2: Identify the property that justifies. \((i)\) \(\quad 1\times \left( y-2 … Read more

Sat Linear Equations Practice Problems

by

\(Q1.\:\) If \(x+3y=c\) and \(\left(1,2\right)\) is a solution of the equation, then the value of \(c\) is: \( a) \quad \) \(0\) \( b) \quad \) \(7\) \(c) \quad \) \(5\) \( d) \quad \) \(6\) \( \text{Answer/Explanation}\) \(Q2.\:\) \(2x+5=3x+4\) is equivalent to \( a) \quad \) \(x=1\) \( b) \quad \) \(2x+1=3\) \(c) \quad … Read more

Sat Absolute Value Practice Problems

by

Questions related to basic arithmetic involving absolute values. \(Q1.\quad |-2|=\_\_\_\_ \) \( a) \qquad 2 \) \( b) \quad -2\) \(c) \qquad 0 \) \( d) \qquad \text{Both a and b} \) \( \text{Answer/Explanation}\) \(Q2.\quad -|-3|=\_\_\_\_ \) \( a) \qquad 3 \) \( b) \quad -3\) \(c) \qquad 0 \) \( d) \qquad \text{Both a … Read more

Sat Inequality Practice Problems

by

\(Q1.\:\) Solve for \( x: 5x-1 \le 3 \) \( a) \quad x \le \frac{5}{4} \) \( b) \quad x \le \frac{4}{5}\) \(c) \quad x \le \frac{2}{5} \) \( d) \quad x \le \frac{5}{2} \) \( \text{Answer/Explanation}\) \(Q2.\: \) if \( \frac{1}{3}x \le 1\) then \( a) \quad x \in (3, \infty) \) \( b) … Read more

Gauss Jordan’s elimination In Sagemath

by

In sagemath, a system of linear equations can be solved with built-in functions matrix(), augment(), solve_right(), solve_left(), rref(), and by row, and column operations. Gauss Jordan elimination method is to solve \(n\) linear system of equations in \(n\) variables. Gauss Jordon method is similar to the Gauss elimination method, except entries above and below pivot … Read more