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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. 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






2. This result says that the symmetries of geometric objects can be expressed as groups of permutations.

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3. Public key encryption allows two parties to communicate securely over an un-secured computer network using the properties of prime numbers and modular arithmetic. RSA is the modern standard for public key encryption.






4. An object possessing continuous symmetries can remain invariant while one symmetry is turned into another. A circle is an example of an object with continuous symmetries.






5. Codifies the 'average behavior' of a random event and is a key concept in the application of probability.






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






7. Solving Equations






8. Writing Mathematical equations - arrange your work one equation






9. This area of mathematics relates symmetry to whether or not an equation has a 'simple' solution.






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






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






12. Does not change the solution set. That is - if a = b - then dividing both sides of the equation by c produces the equivalent equation a/c = b/c - provided c = 0.






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






14. 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).






15. In the expression 3






16. This step is easily overlooked. For example - the problem might ask for Jane's age - but your equation's solution gives the age of Jane's sister Liz. Make sure you answer the original question asked in the problem. Your solution should be written in






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






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






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






20. Adding the same quantity to both sides of an equation - if a = b - then adding c to both sides of the equation produces the equivalent equation a + c = b + c.






21. A way to measure how far away a given individual result is from the average result.






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






23. (a · b) · c = a · (b · c)






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

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25. 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






26. The system that Euclid used in The Elements






27. 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






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






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






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






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






32. 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.






33. 1. Find the prime factorizations of each number.






34. 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.






35. Mathematical statement that equates two mathematical expressions.






36. A · 1 = 1 · a = a






37. If a is any whole number - then a






38. 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






39. If a = b then






40. 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






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






42. It is important to note that this step does not imply that you should simply check your solution in your equation. After all - it's possible that your equation incorrectly models the problem's situation - so you could have a valid solution to an inco






43. Perform all additions and subtractions in the order presented






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






45. Assuming that the air is of uniform density and pressure to begin with - a region of high pressure will be balanced by a region of low pressure - called rarefaction - immediately following the compression






46. If on a surface there is no meaningful way to tell an object's orientation (left or right handedness) - the surface is said to be non-orientable.






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






48. 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.






49. The solutions to this gambling dilemma is traditionally held to be the start of modern probability theory.






50. A