Practice Concept Networks in Math

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

Worksheet PDF Free Answer-key PDF Family

Quick Recap

The web of relationships between mathematical concepts, where each node is an idea and edges represent logical dependence, analogy, or application.

Math concepts don't exist in isolation—they're all connected.

Showing a random 20 of 50 problems.

Example 1

easy
Fractions, decimals, and percentages can all represent 1/2. What single concept do they all express?

Example 2

medium
Logical AND and set intersection are linked. If A={1,2,3}A=\{1,2,3\} and B={2,3,4}B=\{2,3,4\}, give A∩BA\cap B.

Example 3

easy
Draw (describe) the concept network connecting: set, subset, union, intersection, complement, and De Morgan's laws.

Example 4

easy
Slope of a line, rate of change, and the derivative all express the same core idea. What is that shared idea linking them in the concept network?

Example 5

challenge
Show that the identities sin^2 + cos^2 = 1, the Pythagorean theorem, and the equation of a unit circle x^2 + y^2 = 1 are the same network node by mapping (x, y) on the unit circle to (cos t, sin t).

Example 6

medium
Identify three connections between set theory and logic in the concept network. For each, give the corresponding pair of concepts.

Example 7

easy
Vectors (a,b)(a,b) and complex numbers a+bia+bi are isomorphic as 2D objects. Give the magnitude of 4+3i4+3i.

Example 8

medium
In a concept network, 'functions' connects to graphs, equations, calculus, and sequences. If a student strengthens 'functions,' which network property explains why many other topics improve at once?

Example 9

medium
Geometric series, repeating decimals, and infinite limits connect via the formula ∑n=0∞arn=a1−r\sum_{n=0}^\infty ar^n=\frac{a}{1-r}, ∣r∣<1|r|<1. Evaluate 0.3‾0.\overline{3}.

Example 10

easy
Graphs of y=2xy=2x and tables doubling input both express linear scaling. What is the slope of y=2xy=2x?

Example 11

easy
Multiplication is repeated addition; exponentiation is repeated multiplication. What operation is exponentiation built on in this chain?

Example 12

medium
GCD and the Euclidean algorithm rely on the same divisibility network. Compute gcd⁡(48,18)\gcd(48,18).

Example 13

challenge
A knowledge network is 'fragile' if removing one node disconnects many others. Given a star graph with center H connected to 6 leaves, compute how many pairwise connections are lost if H is removed, and explain the lesson for learning.

Example 14

medium
Sequences, functions of nn, and discrete dynamical systems are linked. For an=2na_n=2^n, give a5a_5.

Example 15

medium
Probability density and frequency histogram are linked: both have area = total probability. What is the total area under any valid probability density function?

Example 16

medium
Symmetry in algebra (even/odd functions) and symmetry in geometry (mirror/rotation) share a network node. f(x)=x4f(x)=x^4 has which kind of symmetry?

Example 17

hard
Probability and integration are linked via density functions. For density f(x)=2xf(x)=2x on [0,1][0,1], give P(X≤0.5)P(X\le 0.5).

Example 18

easy
Name three concepts that are directly connected to 'mathematical induction' in the concept network and explain each connection.

Example 19

easy
The Pythagorean theorem connects to the distance formula. What does the distance formula essentially compute?

Example 20

challenge
Information, entropy, and probability share a node via H=−∑pilog⁡2piH=-\sum p_i\log_2 p_i. Compute HH for a fair coin.
← Back to Concept Networks Worked Examples

Related Concepts

Conceptual Dependency