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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. If a = b then






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






3. Has no factors other than 1 and itself






4. This important result says that every natural number greater than one can be expressed as a product of primes in exactly one way.






5. The surface of a standard 'donut shape'.






6. This method can create a flat map from a curved surface while preserving all angles in any features present.






7. This means that for any two magnitudes - one should always be able to find a fundamental unit that fits some whole number of times into each of them (i.e. - a unit whose magnitude is a whole number factor of each of the original magnitudes)






8. × - ( )( ) - · - 1. Multiply the numbers (ignoring the signs)2. The answer is positive if they have the same signs. 3. The answer is negative if they have different signs. 4. Alternatively - count the amount of negative numbers. If there are an even






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






10. The process of taking a complicated signal and breaking it into sine and cosine components.






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






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






13. The fundamental theorem of arithmetic says that






14. 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.






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






16. 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






17. A + 0 = 0 + a = a






18. A number is divisible by 2






19. 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).






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






21. 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.






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






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






24. 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.






25. 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






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






27. A flat map of hyperbolic space.






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






29. A · 1/a = 1/a · a = 1






30. Means approximately equal.






31. This famous - as yet unproven - result relates to the distribution of prime numbers on the number line.






32. The four-dimensional analog of the cube - square - and line segment. A hypercube is formed by taking a 3-D cube - pushing a copy of it into the fourth dimension - and connecting it with cubes. Envisioning this object in lower dimensions requires that






33. 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






34. An equation is a numerical value that satisfies the equation. That is - when the variable in the equation is replaced by the solution - a true statement results.






35. 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






36. Originally known as analysis situs






37. 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






38. This result relates conserved physical quantities - like conservation of energy - to continuous symmetries of spacetime.

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39. The multitude concept presented numbers as collections of discrete units - rather like indivisible atoms.






40. Add and subtract






41. Writing Mathematical equations - arrange your work one equation






42. Also known as 'clock math -' incorporates 'wrap around' effects by having some number other than zero play the role of zero in addition - subtraction - multiplication - and division.






43. The study of shape from the perspective of being on the surface of the shape.






44. 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






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






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






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






48. Requirements for Word Problem Solutions.






49. The identification of a 'one-to-one' correspondence--enables us to enumerate a set that may be difficult to count in terms of another set that is more easily counted.






50. 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.