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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. Objects are topologically equivalent if they can be continuously deformed into one another. Properties that are preserved during this process are called topological invariants.






2. In this type of geometry the angles of a triangle add up to less than 180 degrees. In such a system - one has to replace the parallel postulate with a version that admits many parallel lines.






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






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






5. Are the fundamental building blocks of arithmetic.






6. You must let your readers know what each variable in your problem represents. This can be accomplished in a number of ways: Statements such as 'Let P represent the perimeter of the rectangle.' - Labeling unknown values with variables in a table - Lab






7. 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






8. We can think of the space between primes as 'prime deserts -' strings of consecutive numbers - none of which are prime.






9. The system that Euclid used in The Elements






10. If we start with a number x and add a number a - then subtracting a from the result will return us to the original number x. x + a - a = x. so -






11. A way to extrinsically measure the curvature of a surface by looking at a given point and finding the contour line with the greatest curvature and the contour line with the least curvature.






12. A · b = b · a






13. In some ways - the opposite of a multitude is a magnitude - which is ___________. In other words - there are no well defined partitions.






14. The cardinality of sets that cannot be put into one-to-one correspondence with the counting numbers - such as the set of real numbers - is referred to as c. The designations A_0 and c are known as 'transfinite' cardinalities.






15. Perform all additions and subtractions in the order presented






16. Is a path that visits every node in a graph and ends where it began.






17. This ubiquitous result describes the outcomes of many trials of events from a wide array of contexts. It says that most results cluster around the average with few results far above or far below average.






18. 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






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






20. Writing Mathematical equations - arrange your work one equation






21. Instruments produce notes that have a fundamental frequency in combination with multiples of that frequency known as partials or overtones






22. The expression a^m means a multiplied by itself m times. The number a is called the base of the exponential expression and the number m is called the exponent. The exponent m tells us to repeat the base a as a factor m times.






23. If a whole number is not a prime number - then it is called a...






24. 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).






25. 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






26. If its final digit is a 0.






27. A + b = b + a






28. If a represents any whole number - then a






29. 4 more than a certain number is 12






30. An algebraic 'sentence' containing an unknown quantity.






31. ____________ 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






32. A flat map of hyperbolic space.






33. 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






34. Let a and b represent two whole numbers. Then - a + b = b + a.






35. The state of appearing unchanged.






36. Whether or not we hear waves as sound has everything to do with their _____________ - or how many times every second the molecules switch from compression to rarefaction and back to compression again - and their intensity - or how much the air is com






37. Also known as gluing diagrams - are a convenient way to examine intrinsic topology.






38. A + 0 = 0 + a = a






39. You must always solve the equation set up in the previous step.






40. Means approximately equal.






41. If a = b then






42. Is the shortest string that contains all possible permutations of a particular length from a given set.






43. Add and subtract






44. The expression a/b means






45. Originally known as analysis situs






46. A + (-a) = (-a) + a = 0






47. 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






48. If a = b then






49. Collection of objects. list all the objects in the set and enclosing the list in curly braces.






50. 1. Parentheses (or any grouping symbol {braces} - [square brackets] - |absolute value|)

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