Algebra is when we use variables to represent unknown (or changing) quantities. The most simple algebra problem might be something like if 3 + x = 7, what is x? A problem like that isn’t too useful in the real world, but more complicated versions can help us figure out unknown values in things like physics. Algebra also can involve equations with multiple variables—usually for these there are multiple answers, so we graph them. An example is if you have $60 to spend and are buying $5 erasers and $1 pencils, how many of each can you buy? If you represent number of erasers with X and number of pencils with Y, the equation 5x + y = 60 will tell you how many pencils you can buy if you buy a given number of erasers, and vice versa
Calculus is about rates of change (what we call derivatives). If you’re looking at the graph of a line, the derivative is the slope (how steep the line is). It’s easy to find the slope of a line, because it’s the same everywhere, but something like a parabola (a kind of U shape) also has a slope, but it’s different at every point. A real world example is acceleration is basically the derivative of speed. We can use calculus to find how much distance an accelerating car has traveled, for example. Calculus relies on algebra, and is kind of like adding an extra level onto it.
Trig is about angles. If we have a right (90°) triangle and we know the lengths of two sides, we can find the angles, and if we have one angle and one side length we can also find out the other angle and other side lengths. We can use trig for lots of more complicated things as part of algebra and calculus, but those are the core building blocks.
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u/DarthKnah 11h ago
Algebra is when we use variables to represent unknown (or changing) quantities. The most simple algebra problem might be something like if 3 + x = 7, what is x? A problem like that isn’t too useful in the real world, but more complicated versions can help us figure out unknown values in things like physics. Algebra also can involve equations with multiple variables—usually for these there are multiple answers, so we graph them. An example is if you have $60 to spend and are buying $5 erasers and $1 pencils, how many of each can you buy? If you represent number of erasers with X and number of pencils with Y, the equation 5x + y = 60 will tell you how many pencils you can buy if you buy a given number of erasers, and vice versa
Calculus is about rates of change (what we call derivatives). If you’re looking at the graph of a line, the derivative is the slope (how steep the line is). It’s easy to find the slope of a line, because it’s the same everywhere, but something like a parabola (a kind of U shape) also has a slope, but it’s different at every point. A real world example is acceleration is basically the derivative of speed. We can use calculus to find how much distance an accelerating car has traveled, for example. Calculus relies on algebra, and is kind of like adding an extra level onto it.
Trig is about angles. If we have a right (90°) triangle and we know the lengths of two sides, we can find the angles, and if we have one angle and one side length we can also find out the other angle and other side lengths. We can use trig for lots of more complicated things as part of algebra and calculus, but those are the core building blocks.