Practice Structure Recognition in Math

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

Quick Recap

The skill of identifying that a given mathematical expression or problem belongs to a known family or matches a recognizable pattern.

Seeing 'Oh, this is really a quadratic' or 'This has the same structure as...'

Showing a random 20 of 50 problems.

Example 1

easy
What type of equation is 3x+2=11?

Example 2

medium
Recognize the hidden quadratic in 9x−4⋅3x+3=0 and solve.

Example 3

medium
Recognize the structure to solve 1x+1x+1=1x⋅1x+1⋅k ... instead, factor x2+5x+6.

Example 4

easy
Recognize the structure and factor x2−25.

Example 5

easy
What known sequence type is 2,5,8,11,…?

Example 6

medium
Recognize the structure: what is eln⁡7?

Example 7

challenge
Recognize the structure to solve x4−5x2+4=0.

Example 8

challenge
Recognize the structure of 11⋅2+12⋅3+⋯+19⋅10 and evaluate.

Example 9

medium
Recognize the structure to sum 1+2+3+⋯+100.

Example 10

medium
Recognize the structure: factor x3−8.

Example 11

hard
Recognize the structure: compute (100)+(101)+⋯+(1010).

Example 12

easy
What known identity does a2−2ab+b2 match?

Example 13

medium
Recognize the structure and simplify x2−9x2+6x+9.

Example 14

easy
Recognise and name the algebraic structure in x2−6x+9, then factorise.

Example 15

medium
Recognize the structure: solve x+1x=2 for x>0.

Example 16

hard
Recognize the structure: factor 4x2−12x+9.

Example 17

easy
Factor x2−9 by recognizing its structure.

Example 18

medium
Recognize the structure of 1+3+9+27+81 and compute via formula.

Example 19

easy
Is y=mx+b structurally linear or quadratic?

Example 20

easy
Identify the structure of the sequence 5,10,20,40,….