Essential algebra to complement the previous essential biology and chemistry posts. The long term goal of this project is to support marketing and sustainability projects.
Essential Algebra Questions
Below are questions generated by ChatGPT for which it considers essential algebra. ChatGPT scored the answers, then provided additional information to bring the result from 85% to a 100%.
The Fundamentals of Linear Equations
What is an equation?
An equation is a mathematical statement that demonstrates that two expressions are equal.
What is an unknown in an equation?
An unknown, also known as a variable, is part of an equation that represents an unknown value.
How do you identify the left and right part of an equation?
The left part appears before the = symbol, while the right part appears after it.
What does it mean to resolve an equation?
It means to find the value of the unknown variable that makes the equation true.
How do you interpret the solution of an equation?
First you have to determine whether there is one solution, infinite solutions or none. Afterwards, you have to explain how it applies to the real world.
Introduction to linear equations
What is a linear equation in one unknown?
It is an equation where the highest power of the unknown is 1. This means it will form a straight line when depicted on a graph.
How do you distinguish a linear equation from other forms of equation?
An exponent in a linear equation cannot exceed 1, whereas the non linear equations have higher exponents.
How do you solve the equation 2π₯ + 3 = 9?
2π₯ + 3 = 9
2π₯ = 9 – 3
2π₯ = 6
π₯ = 6 / 2
π₯ = 3
How do you solve the equation 5 β π₯ = 8?
5 – π₯ = 8
-π₯ = 8 – 5
-π₯ = 3
π₯ = -3
What does it mean to clear the unknown in an equation?
It means to find the value of the variable that makes the equation correct.
Linear equations with fractions?
What are linear equations with fractions?
They are equations that include fractions in the expression.
How do you solve the equation 3π₯ / 4 = 6?
3π₯ / 4 = 6
3π₯ = 6 Γ 4
3π₯ = 24
π₯ = 24 / 3
π₯ = 8
How do you simplify equations with fractions before resolving them?
You have to find the highest common factor for the denominator and the numerator, then divide them both by the factor to simplify the fraction.
How do you solve the equation π₯/2 + 5 = 9?
π₯/2 + 5 = 9
π₯/2 = 9 – 5
π₯/2 = 4
π₯ = 4 Γ 2
π₯ = 8
Why do you have to eliminate fractions before resolving an equation?
Eliminating a fraction makes an equation easier to solve.
Basic concepts of systems of equations
What is a system of linear equations?
It is a set of two more more linear equations.
Why are systems of linear equations used in Algebra?
They are used to solve real world problems that involve multiple variables.
How are the equations of a system identified as linear?
They have the form of y = mx + b where m is the slope and b is the intersection on y.
How do you resolve systems of equations by substitution?
Resolve an equation for a variable then substitute it in the other equation.
How do you solve systems of linear equations by linear combination?
You have to multiply the equations to obtain equal coefficients of the variables. Afterwards, you add or take away the eliminate the variable.
Introduction to properties of real numbers
What are real numbers?
They are classified as:
- Natural
- Whole
- Integer
- Rational
- Irrational
How do you perform addition with real numbers?
Addition is performed by combining two or more numbers to obtain a total.
How do you perform subtraction with real numbers?
Subtraction is performed by taking away a quantity from another to obtain a difference. It is the quantity that remains after removing another.
How do you perform multiplication of real numbers?
Multiplication is the operation of adding a number to itself a certain number of times. You can consider it as the repetition of addition.
Essential Algebra and AI – Pros and Cons
The difficult thing was getting a good set of questions that focussed on theory and the how. If it’s been a long time since you’ve solved equations, you’ll need a refresher.
As a result there was also fair bit of prerequisite knowledge to complete this and the next part.
However, it’s very fortunate that ChatGPT is very good clarifying some things that weren’t clear in the resources used to find the answers.
Having said that cuemaths is a decent resource.