# 50 ChatGPT Prompts for Math Problems: Enhance Your Problem-Solving Skills

- Author: Noreen Niazi
- Last Updated on: February 12, 2024

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ToggleMathematics is the foundation of many disciplines and sectors, ranging from engineering to finance, and being good at problem is a key to success in these areas. ChatGPT, AI language model developed by OpenAI, can be a useful instrument for practicing math problems to sharpen your problem-solving skills. In this blog post, we will look into 50 math prompt on ChatGPT with solved examples and frequently asked questions which will help you in getting a better understanding of the math concepts.

## Section 1: Algebra

**Prompt**: Solve for $$x: 2x + 5 = 17.$$**Example**: $$2x + 5 = 17 $$

$$2x = 17 – 5$$

$$2x = 12$$

$$x = 12 / 2 $$

$$x = 6.$$**Prompt**: Factor the quadratic expression: x^2 + 5x + 6.**Example**: $$x^2 + 5x + 6 = (x + 2)(x + 3).$$**Prompt**: Simplify the expression: $$(3x^2 + 2x – 8) / (x – 2).$$**Example**: $$(3x^2 + 2x – 8) / (x – 2) = 3x + 4.$$

## Section 2: Geometry

**Prompt**: Find the area of a triangle with base 6 units and height 8 units.**Example**: Area = (1/2) * base * height = (1/2) * 6 * 8 = 24 square units.**Prompt**: Calculate the volume of a sphere with radius 5 units.**Example**: Volume = (4/3) * π * radius^3 = (4/3) * π * 5^3 ≈ 523.6 cubic units.**Prompt**: Determine the perimeter of a rectangle with length 10 units and width 4 units.**Example**: Perimeter = 2 * (length + width) = 2 * (10 + 4) = 28 units.

## Section 3: Calculus

**Prompt**: Find the derivative of the function f(x) = 3x^2 + 2x – 5.**Example**: f'(x) = 6x + 2.**Prompt**: Calculate the integral of the function f(x) = 2x + 3 with respect to x.**Example**: ∫(2x + 3) dx = x^2 + 3x + C.**Prompt**: Determine the critical points of the function f(x) = x^3 – 6x^2 + 9x.**Example**: Critical points are where f'(x) = 0 or is undefined. So, f'(x) = 3x^2 – 12x + 9 = 0 Solving, we get x = 1 or x = 3.

## Section 4: Probability and Statistics

**Prompt**: Calculate the probability of rolling a sum of 7 with two fair six-sided dice.**Example**: There are 6 possible outcomes that result in a sum of 7 out of a total of 36 outcomes. So, the probability is 6/36 = 1/6.**Prompt**: Find the mean of the following set of numbers: {2, 4, 6, 8, 10}.**Example**: Mean = (2 + 4 + 6 + 8 + 10) / 5 = 30 / 5 = 6.**Prompt**: Determine the standard deviation of the data set: {5, 10, 15, 20, 25}.**Example**: First, find the mean (μ) which is 15. Then, calculate the variance = ((5-15)^2 + (10-15)^2 + (15-15)^2 + (20-15)^2 + (25-15)^2) / 5 = (100 + 25 + 0 + 25 + 100) / 5 = 50. Finally, take the square root of the variance to find the standard deviation ≈ 7.07.

## Section 5: Number Theory

**Prompt**: Find the prime factorization of the number 72.**Example**: Prime factorization of 72 = 2^3 * 3^2.**Prompt**: Determine if the number 37 is prime.**Example**: 37 is a prime number because it is only divisible by 1 and itself.**Prompt**: Find the least common multiple (LCM) of 12 and 18.**Example**: LCM(12, 18) = 36.

## Section 6: Trigonometry

**Prompt**: Calculate the sine of an angle of 30 degrees.**Example**: sin(30°) = 1/2.**Prompt**: Find the value of cos(45°).**Example**: cos(45°) = √2 / 2.**Prompt**: Determine the tangent of an angle of 60 degrees.**Example**: tan(60°) = √3.

## Section 7: Advance algebra

**Prompt**: Solve the system of equations: $\mathrm{\$3x+2y-z=5\$}$$\mathrm{\$2x-y+3z=-4\$}$$\mathrm{\$x+3y-2z=10\$.}$**Prompt**: Find the eigenvalues and eigenvectors of the matrix: $\left(\begin{array}{cc}{\textstyle 2}& {\textstyle -1}\\ {\textstyle -1}& {\textstyle 2}\end{array}\right)$**Prompt**: Determine the characteristic polynomial of the matrix: $\left(\begin{array}{ccc}{\textstyle 3}& {\textstyle 0}& {\textstyle 1}\\ {\textstyle 1}& {\textstyle 2}& {\textstyle 2}\\ {\textstyle 4}& {\textstyle 1}& {\textstyle -1}\end{array}\right)$**Prompt**: Factorize the polynomial ${x}^{4}-5{x}^{3}+8{x}^{2}-4\mathrm{\$x\$}$**Prompt**: Solve the inequality: $2{x}^{2}-3x-2>0$.**Prompt**: Find the inverse of the matrix: $\left(\begin{array}{ccc}{\textstyle 1}& {\textstyle 2}& {\textstyle 3}\\ {\textstyle 0}& {\textstyle 1}& {\textstyle 4}\\ {\textstyle 5}& {\textstyle 6}& {\textstyle 0}\end{array}\right)$**Prompt**: Determine the rank of the matrix: $\left(\begin{array}{ccc}{\textstyle 1}& {\textstyle 2}& {\textstyle 3}\\ {\textstyle 4}& {\textstyle 5}& {\textstyle 6}\\ {\textstyle 7}& {\textstyle 8}& {\textstyle 9}\end{array}\right)$**Prompt**: Solve the equation for $x$: ${\mathrm{log}}_{2}(x+3)+{\mathrm{log}}_{2}(x-2)=2$**Prompt**: Find the roots of the equation: ${x}^{3}-6{x}^{2}+11x-6=0$**Prompt**: Calculate the determinant of the matrix: $\left(\begin{array}{ccc}{\textstyle 4}& {\textstyle 2}& {\textstyle -1}\\ {\textstyle 3}& {\textstyle 0}& {\textstyle 5}\\ {\textstyle -2}& {\textstyle 1}& {\textstyle 3}\end{array}\right)$

## Section 8: Basic math

**Prompt**: Calculate the sum of 25 and 13.**Prompt**: Find the product of 8 and 6.**Prompt**: Subtract 17 from 35.**Prompt**: Divide 48 by 6.**Prompt**: What is the result of adding 9, 12, and 15?**Prompt**: Multiply 5 by 4, then subtract 7.**Prompt**: If you have $50 and spend $28, how much money do you have left?**Prompt**: What is the double of 16?**Prompt**: Add 3 to the difference of 20 and 8.**Prompt**: If a box contains 24 candies and you take out 6, how many candies are left in the box?

## Section 8: Basic math

**Number Sense:**

Problem: Sally has 7 apples. She ate 3 of them. And how many apples are there left with her?

Solution: We can represent this as 7 = 3 + _. In that case, Sally has 4 apples left, then.**Geometry:**

Problem: Sarah has a cuboid box. What is the number of faces, edges, and vertices of the cube?

Solution: A cube has 6 sides, 12 edges, and is eight-sided.**Measurement:**

Problem: Tom owns a ribbon of 12 cubes length. If each cube is 2 centimeters then length of the ribbon is in centimeters.

Solution: Since one cube stands for 2 centimeters, 12 cubes would be $12\cdot 2 = 24$ centimeters long.

## Section 9:Applied math

**Prompt**: A car travels at a constant speed of 65 miles per hour. How long will it take to travel 260 miles?**Prompt**: If a rectangular garden has a length of 20 feet and a width of 12 feet, what is the area of the garden in square feet?**Prompt**: A company’s profit is given by the function $P(x)=3{x}^{2}+5x-20$$x$ represents the number of units sold. Find the profit when 100 units are sold.**Prompt**: The population of a town is 10,000 and is increasing at a rate of 5% per year. What will the population be after 5 years?**Prompt**: A cylindrical tank has a radius of 3 meters and a height of 8 meters. Calculate the volume of water the tank can hold in cubic meters.**Prompt**: A triangle has side lengths of 6 inches, 8 inches, and 10 inches. Determine the area of the triangle in square inches.**Prompt**: An investment of $5000 earns an annual interest rate of 8%. How much money will be in the account after 5 years, compounded annually?**Prompt**: The temperature in a city increased from 60°F to 80°F over the course of a day. What was the percentage increase in temperature?**Prompt**: A baseball team wins 60% of their games. If they play 80 games in a season, how many games can they expect to win?**Prompt**: A piece of equipment depreciates at a rate of 10% per year. If the initial value of the equipment is $10,000, what will be its value after 5 years?

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