9th Grade Math Challenge

Order of Operations

• To solve the expression 3 + 4 x 5, follow the correct order of operations: Parentheses, Exponents, Multiplication and Division, and finally Addition and Subtraction.

Slope of a Line

• The slope of the line passing through points (2, 3) and (4, 5) can be calculated using the formula m = (y2 - y1) / (x2 - x1).

Linear Equations

• To solve the equation 2x + 5 = 3x - 1, isolate the variable x by adding 1 to both sides, then subtracting 5 from both sides, and finally dividing both sides by 1.

Rational Expressions

• The expression (x^2 + 2x - 8)/(x - 2) can be simplified by factoring the numerator and canceling out the common terms.

Quadratic Equations

• The sum of the roots of the quadratic equation x^2 - 5x + 6 = 0 can be found using Vieta's formulas or by factoring the equation.

Geometry

• The area of a triangle with vertices at (1, 2), (3, 4), and (5, 6) can be calculated using the formula A = (1/2) |(x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2))|.

Limits

• The value of the limit as x approaches infinity of (1+1/x)^x is e, where e is the base of the natural logarithm.

Derivatives

• The derivative of the function f(x) = ln(sin(x)) can be found using the chain rule and the derivative of the natural logarithm.

Integrals

• The value of the integral from 0 to pi/2 of sin(x^2) can be evaluated using substitution or numerical methods.