Practice Algebra as Language in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
The perspective that algebra is a formal language with syntax and grammar for expressing mathematical ideas and relationships precisely.
Just as English has grammar, algebra has rules for combining symbols meaningfully.
Showing a random 20 of 50 problems.
Example 1
mediumExpress in algebra: 'The product of two consecutive integers is 12 more than twice their sum.'
Example 2
mediumExpress: 'The square of the sum of and ' vs 'The sum of the squares of and '. Are they equal?
Example 3
easyTranslate 'eight less than three times a number ' into an algebraic expression.
Example 4
easyTranslate 'five more than a number ' into algebra.
Example 5
mediumRead in plain English.
Example 6
mediumTranslate Pythagoras's relation 'the square on the hypotenuse equals the sum of the squares on the other two sides' with legs and hypotenuse .
Example 7
challengeExpress 'a function is injective' in formal logic.
Example 8
easyTranslate 'half of a number decreased by 4' into algebra.
Example 9
mediumA taxi charges $3 plus $2 per mile. Write the cost for miles as an equation.
Example 10
mediumA student writes '' to mean and . Why is this a grammar violation?
Example 11
easyTranslate 'the sum of three consecutive even integers' starting from into an expression.
Example 12
hardRead as a sentence.
Example 13
easyTranslate 'a number is positive' into an inequality with variable .
Example 14
easyTranslate ' is between 2 and 8 inclusive' into a compound inequality.
Example 15
easyRead the expression in words.
Example 16
mediumRead in words, then simplify.
Example 17
mediumTranslate the constraint 'a number is no more than twice another, and they sum to 12' into a system using .
Example 18
easyIs the expression '' grammatically valid algebra?
Example 19
easyWrite an equation: 'A number decreased by 7 equals 15.'
Example 20
mediumRead in words and express it as a compound inequality without absolute value.