Practice Variable as Generalization in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
A variable standing for any arbitrary member of a specified set, used to express statements that hold universally.
'For any number , ' works for ALL numbers, not just one.
Showing a random 20 of 50 problems.
Example 1
mediumGeneralize: the area of a triangle with base and height is what?
Example 2
hardWrite a general formula for the th term of .
Example 3
mediumClassify: '' — identity or conditional equation?
Example 4
challengeProve or disprove: 'For every integer , is even.' Give a general argument.
Example 5
mediumA pattern: , , . Generalize the sum of the first odd numbers.
Example 6
challengeProve that the product of two consecutive integers is even.
Example 7
mediumExplain why is true for every integer .
Example 8
mediumIs '' a generalization that holds for all ? Justify.
Example 9
mediumWrite a general formula for the sum of the first even positive integers.
Example 10
mediumIs odd for every integer ? Justify.
Example 11
easyDoes hold for every number ?
Example 12
mediumIs '' true for every number ? Explain the exception.
Example 13
mediumIdentify the domain: ' is defined for every ____.'
Example 14
easyIs '' a generalization or a single arithmetic fact?
Example 15
hardFind a counterexample to ' for every real '.
Example 16
mediumIs the equation true for every real ?
Example 17
mediumWrite a general formula for the sum of the first positive integers.
Example 18
hardProve the sum of two consecutive integers is always odd.
Example 19
hardIs '' true for every real ? If not, restrict the domain.
Example 20
mediumGeneralize: the perimeter of a square with side is what?