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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. An algebraic 'sentence' containing an unknown quantity.






2. The expression a/b means






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






4. The answer to the question of why the primes occur where they do on the number line has eluded mathematicians for centuries. Gauss's Prime Number Theorem is perhaps one of the most famous attempts to find the 'pattern behind the primes.'






5. If a = b then






6. Rules for Rounding - To round a number to a particular place - follow these steps:






7. If a is any whole number - then a






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

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9. A · 1/a = 1/a · a = 1






10. 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






11. A whole number (other than 1) is a _____________ if its only factors (divisors) are 1 and itself. Equivalently - a number is prime if and only if it has exactly two factors (divisors).






12. The state of appearing unchanged.






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






14. 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






15. A factor tree is a way to visualize a number's






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






17. 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.






18. 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.






19. If a = b then






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






21. 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.






22. TA model of a sequence of random events. Each marble that passes through the system represents a trial consisting of as many random events as there are rows in the system.






23. A + b = b + a






24. Reveals why we tend to find structure in seemingly random sets. Ramsey numbers indicate how big a set must be to guarantee the existence of certain minimal structures.






25. A · b = b · a






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






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






28. 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.






29. 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.






30. Originally known as analysis situs






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






32. Breaks a complicated signal into a combination of simple sine waves. Fourier synthesis does the opposite - constructing a complicated signal from simple sine waves.






33. 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






34. A(b + c) = a · b + a · c a(b - c) = a · b - a · c






35. Let a - b - and c represent whole numbers. Then - (a + b) + c = a + (b + c).






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






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






38. The study of shape from an external perspective.






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






40. If a = b then a + c = b + c If a = b then a - c = b - c If a = b then a






41. (a · b) · c = a · (b · c)






42. Are the fundamental building blocks of arithmetic.






43. If a represents any whole number - then a






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






45. 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






46. Has no factors other than 1 and itself






47. An arrangement where order matters.






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






49. 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.'






50. A + 0 = 0 + a = a