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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. 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.






2. The system that Euclid used in The Elements






3. Negative






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






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






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






7. Arise from the attempt to measure all quantities with a common unit of measure.






8. A · 1 = 1 · a = a






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






10. 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






11. A sphere can be thought of as a stack of circular discs of increasing - then decreasing - radii. The process of slicing is one way to visualize higher-dimensional objects via level curves and surfaces. A hypersphere can be thought of as a 'stack' of






12. Mathematical statement that equates two mathematical expressions.






13. Trigonometric functions - such as sine and cosine - are useful for modeling sound waves - because they oscillate between values






14. (a






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






16. All integers are thus divided into three classes:






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






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






19. 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).






20. 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.






21. 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.






22. 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.






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






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






25. 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.'






26. Some favor repeatedly dividing by 2 until the result is no longer divisible by 2. Then try repeatedly dividing by the next prime until the result is no longer divisible by that prime. The process terminates when the last resulting quotient is equal t






27. Is the length around an object. Used to calculate such things as fencing around a yard - trimming a piece of material - and the amount of baseboard needed for a room.It is not necessary to have a formula since it is always just calculated by adding t






28. Let a - b - and c be any whole numbers. Then - a






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






30. 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.






31. If a = b then






32. An arrangement where order matters.






33. 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






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






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






36. Let a and b be whole numbers. Then a is _______________ by b if and only if the remainder is zero when a is divided by b. In this case - we say that 'b is a divisor of a.'






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 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






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






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






41. 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.






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






43. 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






44. 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.






45. Points in two-dimensional space require two numbers to specify them completely. The Cartesian plane is a good way to envision two-dimensional space.






46. If we start with a number x and multiply by a number a - then dividing the result by the number a returns us to the original number x. In symbols - a






47. When writing mathematical statements - follow the mantra:






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






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 · b = b · a