Practice Symbolic Abstraction in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

Using letter symbols to represent mathematical concepts in a form that holds independent of any specific numerical values.

Instead of 2+3=3+2 and 5+7=7+5, write a+b=b+a for ALL numbers.

Example 1

medium
The area of a circle is A = \pi r^2. Without knowing r, what happens to A if r is doubled?

Example 2

hard
If f(x) = ax^2 + bx + c and f(0) = 5, what is c?

Example 3

easy
If y = kx and y = 15 when x = 3, find k.

Example 4

medium
If V = lwh, what happens to V when all three dimensions are halved?
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