Math FAQ
Find answers to common questions about learning math, algebra, calculus, geometry, statistics, and solving math problems.
How do I solve algebra equations?
Solve algebra equations by: 1) Simplify both sides by combining like terms, 2) Isolate the variable term by moving constants to one side, 3) Divide by the coefficient to isolate the variable, 4) Check your answer by substituting back into the original equation. Remember: whatever you do to one side, do to the other.
What is the quadratic formula?
The quadratic formula solves equations of the form ax² + bx + c = 0. The formula is x = (-b ± √(b² - 4ac)) / 2a. This gives two solutions (one with +, one with -). The discriminant (b² - 4ac) tells you about the solutions: positive = two real solutions, zero = one solution, negative = complex solutions.
How do I find the derivative of a function?
Find derivatives using rules: Power rule: d/dx(xⁿ) = nxⁿ⁻¹. Product rule: d/dx(fg) = f'g + fg'. Quotient rule: d/dx(f/g) = (f'g - fg')/g². Chain rule: d/dx(f(g(x))) = f'(g(x))g'(x). Choose the rule that matches the function structure.
What is the difference between mean, median, and mode?
Mean is the average (sum divided by count). Median is the middle value when data is ordered. Mode is the most frequent value. For example, in {2, 3, 3, 5, 8}: mean = 4.2, median = 3, mode = 3. Mean is affected by outliers, median is more robust.
How do I calculate the area of a circle?
The area of a circle is A = πr², where r is the radius and π ≈ 3.14159. For example, a circle with radius 5 has area A = π(5)² = 25π ≈ 78.54 square units. If you know the diameter, divide by 2 to get the radius first.
What is the Pythagorean theorem?
The Pythagorean theorem states that in a right triangle, a² + b² = c², where a and b are the legs and c is the hypotenuse (longest side). It's used to find missing side lengths. For example, if legs are 3 and 4, the hypotenuse is √(3² + 4²) = 5.
How do I solve calculus problems?
Solve calculus problems by: 1) Identify the problem type (limit, derivative, integral), 2) Simplify the expression algebraically, 3) Choose the appropriate rule or technique, 4) Apply the rule step by step showing all work, 5) Check your answer by differentiation (for integrals) or special cases.
What is the difference between permutation and combination?
Permutations count arrangements where order matters (nPr = n!/(n-r)!). Combinations count selections where order doesn't matter (nCr = n!/(r!(n-r)!)). For example, choosing 2 people from 3: permutations count AB and BA as different, combinations count them as the same.