Algebra
Problems related to equations, functions, polynomials, etc.
Problems in this category
The sum of the first 3 terms of a sequence is 9. The sum of the first 6 terms is -63. Given that thi...
Arithmetic SequencesLinear EquationsSystems of Equations
2025/6/11
The problem has three parts: (a) Factorize completely $2\pi h + 2\pi r^2$. (b) Express $\frac{4}{x+5...
FactorizationRational ExpressionsSimultaneous EquationsLinear Equations
2025/6/11
The problem is to solve the following five linear equations: 1. $8 - 8x = 9 - 9x$
Linear EquationsSolving Equations
2025/6/10
The problem is about the quadratic function $y = -2x^2 + (a+3)x + a - 3$. (1) Find the condition on ...
Quadratic FunctionsDiscriminantVieta's FormulasVertex of ParabolaIsosceles Right Triangle
2025/6/10
The problem consists of several sub-problems covering various topics in algebra. These include expre...
Scientific NotationEngineering NotationSimplificationPolynomial Remainder TheoremSimultaneous EquationsLogarithmic EquationsLinear EquationsGradientY-interceptEquation of a LinePartial Fractions
2025/6/10
We are given four problems: a) i. Use the vertical line test to show that $f(x) = \sqrt{x}$ is a fun...
FunctionsVertical Line TestRangeLinear FunctionsInverse FunctionsAlgebraic Manipulation
2025/6/10
We are given the equation $x^3 + 2x^2y - x^2 + 2xy + 4y^2 - 2y = 44$. The problem asks us to factor...
Polynomial FactorizationEquation SolvingInteger Properties
2025/6/10
We are given the equation $f(x) - g(x) = 3ax^2 + 2(a+1)x + a + 1$. We are also given that $a = \fra...
Quadratic EquationsParabolasIntersection of CurvesSystems of Equations
2025/6/10
Given that $f(x) - g(x) = 3ax^2 + 2(a+1)x + a+1$, we need to find the range of values for $a$ such t...
Quadratic InequalitiesQuadratic EquationsDiscriminantParabolasIntersection Points
2025/6/10
The problem is a fill-in-the-blank question. Given that for all real numbers $x$, $f(x) > g(x)$, det...
InequalitiesQuadratic FunctionsIntersection of CurvesProblem Solving
2025/6/10