Following the first round of study, some issues arose which has led to a change in approach and the creation of this algebra preparation post. Two things were obvious trying to study some subjects with AI using the previous method:
- Maths and chemistry are too hierarchal to study some aspects simultaneously
- ChatGPT’s concept of “for beginners” overestimates the capability of a novice
With both approaches the limit of the task set does mean that some pre-requisite knowledge gets missed, which this post will address as the project progresses.
So this is a reset for studying algebra with AI which will contribute to the study of chemistry and biology to later support sustainable marketing projects.
Algebra Preparation Questions
The questions below for algebra preparation are the result of two things. Firstly, the lack of required information to answer the questions in the upcoming posts for studying algebra with AI. Secondly, ChatGPT produced some additional information based on the missing information to find a few more potential gaps.
Number Properties
What is a Commutative Property?
For addition and multiplication, the order of the numbers does not change the result. Example:
- a + b = b + a
- a × b = b × a
What is an Associative Property?
For addition and multiplication, the grouping of the numbers does not change the result. Example:
- (a + b) + c = a + (b + c)
- (a × b) × c = a × (b × c)
What is a Distributive Property?
The distributive property connects multiplication and addition. Example:
- a(b + c) = ab + ac
Basic Mathematical Concepts
What is a term?
A term is a single mathematical expression that can be a number, a variable, or the product of numbers and variables. For example, in the expression 5x + 3, both 5x and 3 are terms.
What is a power?
A power refers to the exponent in an expression, which indicates how many times a number (the base) is multiplied by itself. For example, in 23, the number 2 is the base and 3 is the power.
What is an expression?
An expression is a combination of terms joined by addition or subtraction operators. For example, 4x – 7 + 3y is an expression.
What is a coefficient?
A coefficient is a numerical or constant factor that multiplies a variable in a term. In the term 5x, 5 is the coefficient.
What is a constant?
A constant is a value that does not change. In the expression 4x + 7, 7 is a constant.
What is a variable?
A variable is a symbol, usually a letter, that represents one or more unknown numbers or values. For example, in the equation x + 5 = 9, x is the variable.
What is a denominator and a numerator?
In a fraction, the numerator is the top number and represents the number of parts we have, while the denominator is the bottom number and represents the number of equal parts the whole is divided into. For example, in 3/4, 3 is the numerator and 4 is the denominator.
What is a factor?
A factor is a number or expression that divides another number or expression evenly. For example, 2 and 3 are factors of 6 because 2 × 3 = 6.
What is a highest common factor (HCF)?
The highest common factor, or greatest common divisor (GCD), or even greatest common factor (GCF) is the largest number that divides two or more numbers without leaving a remainder. For example, the HCF of 12 and 18 is 6.
What is an integer?
An integer is a whole number that can be positive, negative, or zero. Examples include -3, 0, and 7.
What is a rational number?
A rational number is any number that can be expressed as the quotient or fraction of two integers, with the denominator not equal to zero. For example, 1/2 and -3 are rational numbers.
What is an irrational number?
An irrational number is a number that cannot be expressed as a simple fraction; its decimal form is non-repeating and non-terminating. Examples include π and √2.
What is a prime number?
A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. Examples include 2, 3, 5, and 7.
What is a composite number?
A composite number is a natural number greater than 1 that is not prime, meaning it has factors other than 1 and itself. Examples include 4, 6, 8, and 9.
What is the order of operations?
The order of operations is the set of rules that defines the correct sequence to evaluate a mathematical expression. The common acronym PEMDAS stands for Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
What is absolute value?
The absolute value of a number is its distance from zero on the number line, regardless of direction. For example, the absolute value of both -5 and 5 is 5.
What is a percentage?
A percentage is a fraction or ratio expressed as a part of 100. For example, 45% is equivalent to 45/100 or 0.45.
What is a ratio?
A ratio is a relationship between two numbers showing how many times the first number contains the second. For example, the ratio of 8 to 4 is written as 8:4 or simplified to 2:1.
What is a proportion?
A proportion is an equation that states that two ratios are equal. For example, 1/2 = 2/4 is a proportion.
What is a mean?
The mean is the average of a set of numbers, found by dividing the sum of the numbers by the count of the numbers. For example, the mean of 2, 3, and 5 is (2 + 3 + 5)/3 = 3.33.
What is a median?
The median is the middle value in a set of numbers ordered from least to greatest. If the set has an even number of observations, the median is the average of the two middle numbers. For example, the median of 1, 3, and 5 is 3.
What is a mode?
The mode is the number that appears most frequently in a set of numbers. For example, in the set 1, 2, 2, 3, 4, the mode is 2.
What is a range?
The range is the difference between the highest and lowest values in a set of numbers. For example, in the set 2, 3, 7, 9, the range is 9 – 2 = 7.
What is the area, perimeter and volume of a shape?
The perimeter represents the total length of a shape’s sides – the circumference in the case of a circle.
The area is the space taken up by the 2d shape, whereas volume represents how much space is taken up by a 3d shape
How do you reduce a fraction to its simplest form?
You have to divide the numerator and denominator by their Highest Common Factor.
Algebraic Concepts
What are x and y intercepts?
The x-intercept is the point where a graph crosses the x-axis, meaning the y-value is zero at this point. The y-intercept is the point where a graph crosses the y-axis, meaning the x-value is zero at this point. For example, in the equation y = 2x + 3, the y-intercept is 3 (where x = 0).
What is a linear equation?
A linear equation is an equation between two variables that produces a straight line when graphed. For example, y = 2x + 3 is a linear equation.
What is a quadratic equation?
A quadratic equation is a second-order polynomial equation in a single variable x, with the form ax2 + bx + c = 0. For example, x2 – 4x + 4 = 0.
What is a polynomial?
A polynomial is an expression consisting of variables and coefficients, involving only addition, subtraction, multiplication, and non-negative integer exponents of variables. For example, 3x3 + 2x2 – x + 7 is a polynomial.
What is an inequality?
An inequality refers to an equation where both sides are not equal. For example, x > 5 or y ≤ 2.
Cue math also mentions some rules regarding inequalities.
What is a function?
A function is a relation between a set of inputs and a set of permissible outputs, where each input is related to exactly one output. For example, f(x) = x2.
What is the domain and range of a function?
The domain of a function is the set of all possible input values (x-values), while the range is the set of all possible output values (y-values). For example, for f(x) = x2, the domain is all real numbers, and the range is all non-negative real numbers.
What is a cartesian coordinate system?
A Cartesian coordinate system in a plane refers to a coordinate system defined by two perpendicular lines called axes: the x-axis (horizontal) and the y-axis (vertical). These axes intersect at a point called the origin (0, 0). Any point on the plane can be described by an ordered pair of numbers (x, y), known as coordinates, which represent its position relative to the origin. The x-coordinate shows the horizontal distance from the origin, while the y-coordinate shows the vertical distance. This system is commonly used to plot points, graph lines, and represent geometric shapes in mathematics
Ready for Algebra
This algebra preparation should mean that you are ready to continue with the upcoming Algebra post. However there will be links back to this one in the future articles; it is likely new things will be added as the project advances.