GMAT Exam > GMAT Videos > Quantitative for GMAT > Algebra Practice Question - 2
Algebra Practice Question - 2 Video Lecture | Quantitative for GMAT
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FAQs on Algebra Practice Question - 2 Video Lecture - Quantitative for GMAT
| 1. How to solve a system of equations with two variables? |  |
Ans. To solve a system of equations with two variables, you can use either the substitution method or the elimination method. In the substitution method, solve one equation for one variable and substitute it into the other equation. In the elimination method, multiply one or both equations by suitable constants to make the coefficients of one variable opposite in sign. Then, add or subtract the equations to eliminate one variable and solve for the other.
| 2. What is the difference between an expression and an equation in algebra? | |
Ans. In algebra, an expression is a combination of numbers, variables, and operators, but it does not have an equal sign. It can be simplified or evaluated to obtain a single value. On the other hand, an equation is a mathematical statement that contains an equal sign, showing that two expressions are equal. Equations can be solved to find the values of the variables that make the equation true.
| 3. How can I factorize a quadratic expression? | |
Ans. To factorize a quadratic expression, you can use the method of grouping or the quadratic formula. In the method of grouping, look for two numbers that multiply to give the constant term of the quadratic expression and add up to give the coefficient of the linear term. Then, split the middle term of the quadratic expression using these two numbers and factor by grouping. The quadratic formula, on the other hand, can be used to directly find the roots of a quadratic equation and hence factorize the quadratic expression.
| 4. What are the properties of exponents in algebra? | |
Ans. In algebra, there are several properties of exponents that help simplify expressions involving powers. These properties include the product rule (a^m * a^n = a^(m+n)), the power rule ((a^m)^n = a^(m*n)), the quotient rule (a^m / a^n = a^(m-n)), and the zero exponent rule (a^0 = 1). Additionally, there are rules for negative exponents (a^(-m) = 1/a^m) and fractional exponents (a^(m/n) = nth root of a^m).
| 5. How can I solve a linear inequality in one variable? | |
Ans. To solve a linear inequality in one variable, treat it like an equation, but with one exception: when multiplying or dividing both sides by a negative number, reverse the direction of the inequality. Solve the inequality by isolating the variable on one side of the inequality sign. Remember to use the correct inequality signs (>, <, ≥, ≤) depending on whether the solution includes the boundary points or not. The solution will be expressed as a range of values that satisfies the inequality.
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Nov 24, 2024 Last updated |
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