Algebra
Problems related to equations, functions, polynomials, etc.
Problems in this category
Given that $x^2 + y^2 + xy = 0$, we want to find the value of $(\frac{x-y}{x})^{80} + (\frac{x-y}{y}...
Complex NumbersCube Roots of UnityAlgebraic ManipulationPolynomial Equations
2025/6/18
The problem consists of two questions. Question 1 asks to evaluate five expressions involving expone...
ExponentsExponential EquationsSimplification
2025/6/18
The problem has two parts. Part a: Sketch the graph of the function $y = (1+x)(x-3)$. Part b: Find t...
Quadratic FunctionsGraphingInequalitiesLinear Equations
2025/6/18
The problem consists of two parts. Part a requires sketching the graph of the function $y = (1+x)(x-...
Quadratic FunctionsGraphingInequalitiesMinimum ValueParabola
2025/6/18
The problem is divided into two parts. The first part asks to sketch the graph of the function $y = ...
Quadratic FunctionsGraphingInequalitiesLinear EquationsCoordinate GeometryVertex of a ParabolaMinimum Value
2025/6/17
The problem consists of two parts. Part 1: Convert the given matrix $\begin{bmatrix} 5 & -7 & 1 \\ 6...
Linear AlgebraMatricesDeterminantsMatrix Transformations
2025/6/17
The problem presents three separate mathematical questions: 1. Find a number that when multiplied b...
Linear EquationsWord ProblemsAge ProblemsRectangle Perimeter
2025/6/17
Sophat is 51 years old, and Rasmei is 21 years old. In how many years will Sophat be twice the age o...
Age ProblemsLinear EquationsWord Problems
2025/6/17
The problem consists of two parts. Part 1: Solve the equation $5(1 + 4e^{0.1x-1}) = 25$ for $x$. Par...
Exponential EquationsLogarithmic EquationsQuadratic EquationsLogarithm PropertiesEquation Solving
2025/6/17
The problem presents a formula for $a_n$, which is $a_n = a_1 \cdot r^{n-1}$. This is the formula fo...
Sequences and SeriesGeometric SequenceFormula
2025/6/17