MathProblemsBank Math Problems Bank
  • Home
  • Forum
  • About Us
  • Contact Us
  • Login
  • Register
  • language
 MathProblemsBank banner

MathProblemsBank banner

Math Problems and solutions

Mathematics sections
  • Algebra
    • Vector Algebra
    • Determinant calculation
    • Permutation group
    • Matrix transformations
    • Linear transformations
    • Quadratic forms
    • Fields, Groups, Rings
    • Systems of algebraic equations
    • Linear spaces
    • Polynomials
    • Tensor calculus
    • Vector analysis
  • Analytic geometry
    • Curves of the 2-nd order
    • Surfaces of the 2-nd order
    • Lines on a plane
    • Line and plane in space
    • Tangents and normals
  • Complex analysis
    • Operations with complex numbers
    • Singular points and residues
    • Integral of a complex variable
    • Laplace transform
    • Conformal mappings
    • Analytic functions
    • Series with complex terms
    • Calculating integrals of a real variable using residues
  • Differential equations
    • Ordinary differential equations
      • First order differential equations
      • Second order differential equations
      • Higher order differential equations
      • Geometric and physical applications
    • Systems of ordinary differential equations
    • Stability
      • Stability of the equations
      • Stability of the systems of equations
    • Operating method
      • Differential equations
      • Systems of differential equations
  • Differential geometry
  • Discret mathematics
    • Boolean algebra
    • Set theory
    • Combinatorics
    • Graph theory
    • Binary relations
    • Propositional algebra
      • Propositional calculus
      • Sequent calculus
    • Predicate calculus
    • Theory of algorithms and formal languages
    • Automata theory
    • Recursive functions
  • Functional analysis
    • Metric spaces
      • Properties of metric spaces
      • Orthogonal systems
      • Convergence in metric spaces
    • Normed spaces
      • Properties of normed spaces
      • Convergence in normed spaces
    • Measure theory
      • Lebesgue measure and integration
      • Measurable functions and sets
      • Convergence (in measure, almost everywhere)
    • Compactness
    • Linear operators
    • Integral equations
    • Properties of sets
    • Generalized derivatives
    • Riemann-Stieltjes integral
  • Geometry
    • Planimetry
      • Transformations on the plane
      • Construction problems
      • Complex numbers in geometry
      • Various problems on the plane
      • Locus of points
    • Stereometry
      • Construction of sections
      • Various problems in the space
    • Affine transformations
  • Mathematical analysis
    • Gradient and directional derivative
    • Graphing functions using derivatives
    • Plotting functions
    • Fourier series
      • Trigonometric Fourier series
      • Fourier integral
    • Number series
    • Function extrema
    • Power series
    • Function properties
    • Derivatives and differentials
    • Functional sequences and series
    • Calculation of limits
    • Asymptotic analysis
  • Mathematical methods and models in economics
  • Mathematical physics
    • First order partial differential equations
    • Second order partial differential equations
      • d'Alembert method
      • Fourier method
      • With constant coefficients
      • With variable coefficients
      • Mixed problems
    • Convolution of functions
    • Nonlinear equations
    • Sturm-Liouville problem
    • Systems of equations in partial derivatives of the first order
  • Mathematical statistics
  • Numerical methods
    • Golden section search method
    • Least square method
    • Sweep method
    • Simple-Iteration method
    • Approximate calculation of integrals
    • Approximate solution of differential equations
    • Approximate numbers
    • Function Interpolation
    • Approximate solution of algebraic equations
  • Olympiad problems
    • Olympic geometry
    • Number theory
    • Olympic algebra
    • Various Olympiad problems
    • Inequalities
      • Algebraic
      • Geometric
    • Higher mathematics
  • Probability theory
    • One dimensional random variables and their characteristics
    • Theory of random processes
    • Markov chains
    • Queuing systems
    • Two-dimensional random variables and their characteristics
    • Definition and properties of probability
    • Limit theorems
  • Real integrals
    • Integrals of functions of a single variable
      • Indefinite integrals
      • Definite Integrals
      • Improper integrals
    • Double integrals
    • Triple integrals
    • The area of a region
    • Volume of a solid
    • Volume of a solid of revolution
    • Flux of the vector field
    • Surface integrals
    • Curvilinear integrals
    • Potential and solenoidal fields
    • Vector field circulation
    • Integrals depending on a parameter
  • Topology
  • USE problems
  • Variational calculus
Problem list Free problems

Attention! If a subsection is selected, then the search will be performed in it!

Problem: Solve the inequality for all values of the parameter \( a \) : \[ \sqrt{|x+1|} \leq a-x \text {. } \]

17.9 USE problems

2.57 $

Problem: Find all the values of the parameter a, for which the function is even: \[ f(x)=|x-a+1|+|x+3 a| . \]

17.10 USE problems

2.57 $

Problem: Solve the system of equations: \[ \left\{\begin{array}{l} x-2 y+\frac{3}{x-2 y}=4 \\ \frac{y}{x-2 y-3}=5 \end{array}\right. \]

17.11 USE problems

0 $

Problem: Solve the system of equations: \[ \left\{\begin{array}{l} \sqrt{3 x-5}=\sqrt{3 y+7} \\ y^{2}+x=10 \end{array}\right. \]

17.12 USE problems

0 $

Problem: Solve the irrational equation: \[ \left(x^{2}-4\right) \sqrt{3+5 x-2 x^{2}}=0 \text {. } \]

17.13 USE problems

0 $

Problem: Solve the irrational equation: \[ \sqrt{x-1}+\sqrt{x+2}=\sqrt{x+34}-\sqrt{x+7} . \]

17.14 USE problems

0 $

Problem: Find all values of the parameter a, for which 1) the equation \( a x^{2}+x+17=0 \) has only one root; 2) the equation \( a x^{2}+(5-3 a) x-a=0 \) has two roots of different signs.

17.15 USE problems

0 $

Problem: Find all values of the parameter a, for which 1) the equation \( 4 x^{2}+4 x=a^{2}-1 \) has two different positive roots. 2) the equation \( (a-2) x^{2}+2(a-2) x+ \) \( +2=0 \) has no roots.

17.16 USE problems

0 $

Problem: Determine the number of roots of the equation for each value of the parameter a. \[ a x^{2}+(a+1)^{2} x+a+2=0 . \]

17.17 USE problems

0 $

Problem: Find all values of \( a \) for which the sum of the real roots' squares of the equation \[ x^{2}-a x+a-2=0 \text { is minimal. } \]

17.18 USE problems

0 $

Problem: The quadratic equation \( x^{2}+p x+q=0 \) has two different roots \( x_{1} \) and \( x_{2} \). Find \( p \) and \( q \), if the numbers of \( x_{1}+1 \) и \( x_{2}+1 \) are the roots of the equation \( x^{2}-p^{2} x+p q=0 \).

17.19 USE problems

2.57 $

Problem: In the cuboid \( A B C D A_{1} B_{1} C_{1} D_{1} \) the lengths of the edges are \( A D=12, A B=5, A A_{1}=8 \). Find the volume of the pyramid \( M B_{1} C_{1} D \), if \( M \) is a point on \( A A_{1} \) moreover \( A M=5 \).

17.21 USE problems

2.57 $

Problem: We have \( A B C \) right triangle, with the right angle \( C \). On the line, containing \( A D \) median, point \( E \) is taken, which is at a distance of 4 from the vertex \( A \). Find the area of the triangle \( B C E \), if \( B C=6 \), \( A C=4 \).

17.23 USE problems

3.08 $

Problem: 1) Appliances are connected to the power outlet, the total resistance of which is \( 60 \mathrm{Ohm} \). An electric heater is supposed to be connected to the outlet in parallel with them. Determine (in ohms) the smallest possible resistance of this electric heater, if it is known that in case of a parallel connection of two conductors with resistances \( R_{1} \) and \( R_{2} \) their total resistance is given by the formla \( R=\frac{R_{1} \cdot R_{2}}{R_{1}+R_{2}} \), and for the normal functioning of the electrical network the total resistance of it must be not less than \( 10 \mathrm{Ohm} \). 2) Find the biggest value of the function: \( y=17 x-5 \sin x+7 \) on the segment \( \left[-\frac{\pi}{2} ; 0\right] \). 3) The first pipe passes 1 liter less water per minute, than the second pipe. How many liters of water per minute passes through the second pipe, if it fills the reservoir with the volume of 624 liters 2 minutes faster, than the first pipe fills the reservoir with the volume of 650 liters?

17.25 USE problems

3.08 $

Problem: Solve for all values of the parameter: \[ a^{2}(x-1)-a(2 x-5)=3 x-6 \text {. } \]

17.26 USE problems

0 $

  • ‹
  • 1
  • 2
  • ...
  • 41
  • ...
  • 116
  • 117
  • ›

mathproblemsbank.net

Terms of use Privacy policy

© Copyright 2025, MathProblemsBank

Trustpilot
Order a solution
Order a solution to a problem?
Order a solution
Order a solution to a problem?
home.button.login