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CLEP General Math: Number Sense - Patterns - Algebraic Thinking

Subjects : clep, math, algebra
Instructions:
  • Answer 50 questions in 15 minutes.
  • If you are not ready to take this test, you can study here.
  • Match each statement with the correct term.
  • Don't refresh. All questions and answers are randomly picked and ordered every time you load a test.

This is a study tool. The 3 wrong answers for each question are randomly chosen from answers to other questions. So, you might find at times the answers obvious, but you will see it re-enforces your understanding as you take the test each time.
1. The whole number zero is called the additive identity. If a is any whole number - then a + 0 = a.






2. A topological object that can be used to study the allowable states of a given system.






3. A '___________' infinite set is one that can be put into one-to-one correspondence with the set of natural numbers.






4. Dimension is how mathematicians express the idea of degrees of freedom






5. The inverse of multiplication






6. Of central importance in Ramsey Theory - and in combinatorics in general - is the 'pigeonhole principle -' also known as Dirichlet's box. This principle simply states that we cannot fit n+1 pigeons into n pigeonholes in such a way that only one pigeo






7. Solving Equations






8. Our standard notions of Pythagorean distance and angle via the inner product extend quite nicely from three-space.






9. A topological invariant that relates a surface's vertices - edges - and faces.






10. Einstein's famous theory - relates gravity to the curvature of spacetime.






11. The system that Euclid used in The Elements






12. At each level of the tree - break the current number into a product of two factors. The process is complete when all of the 'circled leaves' at the bottom of the tree are prime numbers. Arranging the factors in the 'circled leaves' in order. The fina






13. Add and subtract






14. In this type of geometry the angles of a triangle add up to more than 180 degrees. In such a system - one has to replace the parallel postulate with a version that admits no parallel lines as well as modify Euclid's first two postulates.






15. Aka The Osculating Circle - a way to measure the curvature of a line.






16. Originally known as analysis situs






17. Two equations if they have the same solution set.






18. If the sum of its digits is divisible by 3 (ex: 3591 is divisible by 3 since 3 + 5 + 9 + 1 = 18 is divisible by 3).






19. If a = b then






20. An arrangement where order matters.






21. A point in three-dimensional space requires three numbers to fix its location.






22. Requirements for Word Problem Solutions.






23. Does not change the solution set. That is - if a = b - then multiplying both sides of the equation by c produces the equivalent equation a






24. A






25. If a - b - and c are any whole numbers - then a






26. The study of shape from an external perspective.






27. 1. Find the prime factorizations of each number. To find the prime factorization one method is a factor tree where you begin with any two factors and proceed by dividing the numbers until all the ends are prime factors. 2. Star factors which are shar






28. Because of the associate property of addition - when presented with a sum of three numbers - whether you start by adding the first two numbers or the last two numbers - the resulting sum is






29. Cantor called the cardinality of all the sets that can be put into one-to-one correspondence with the counting numbers - or 'Aleph Null.'






30. If a and b are any whole numbers - then a






31. All integers are thus divided into three classes:






32. ____________ theory enables us to use mathematics to characterize and predict the behavior of random events. By 'random' we mean 'unpredictable' in the sense that in a given specific situation - our knowledge of current conditions gives us no way to






33. A + 0 = 0 + a = a






34. When comparing two whole numbers a and b - only one of three possibilities is true: a < b or a = b or a > b.






35. If its final digit is a 0 or 5.






36. A group is just a collection of objects (i.e. - elements in a set) that obey a few rules when combined or composed by an operation. In order for a set to be considered a group under a certain operation - each element must have an inverse - the set mu






37. Three is the common property of the group of sets containing three members. This idea is called '__________ -' which is a synonym for 'size.' The set {a -b -c} is a representative set of the cardinal number 3.






38. Every solution to a word problem must include a carefully crafted equation that accurately describes the constraints in the problem statement.






39. Writing Mathematical equations - arrange your work one equation






40. A point in four-space - also known as 4-D space - requires four numbers to fix its position. Four-space has a fourth independent direction - described by 'ana' and 'kata.'






41. Says that when a random process - such as dropping marbles through a Galton board - is repeated many times - the frequencies of the observed outcomes get increasingly closer to the theoretical probabilities.






42. In a mathematical sense - it is a transformation that leaves an object invariant. Symmetry is perhaps most familiar as an artistic or aesthetic concept. Designs are said to be symmetric if they exhibit specific kinds of balance - repetition - and/or






43. If a = b then






44. An instrument's _____ - the sound it produces - is a complex mixture of waves of different frequencies.






45. This model is at the forefront of probability research. Mathematicians use it to model traffic patterns in an attempt to understand flow rates and gridlock - among other things.






46. (a + b) + c = a + (b + c)






47. To describe and extend a numerical pattern






48. Division by zero is undefined. Each of the expressions 6






49. Cannot be written as a ratio of natural numbers.






50. The distribution of averages of many trials is always normal - even if the distribution of each trial is not.