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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 instrument's _____ - the sound it produces - is a complex mixture of waves of different frequencies.






2. 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)






3. 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).






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






5. 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






6. 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.






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

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8. 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.






9. The fundamental theorem of arithmetic says that






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

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






12. 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.






13. Perform all additions and subtractions in the order presented






14. 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






15. (a · b) · c = a · (b · c)






16. In the expression 3






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






18. If a = b then






19. The whole number zero is called the additive identity. If a is any whole number - then a + 0 = a.






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






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






22. An arrangement where order matters.






23. The amount of displacement - as measured from the still surface line.






24. 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.






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






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






28. 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.






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






30. A + b = b + a






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






32. A · b = b · a






33. A topological invariant that relates a surface's vertices - edges - and faces.






34. 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






35. 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).






36. In any ratio of two whole numbers - expressed as a fraction - we can interpret the first (top) number to be the 'counter -' or numerator






37. (a






38. Solving Equations






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






40. A topological object that can be used to study the allowable states of a given system.






41. Add and subtract






42. Index p radicand






43. Has no factors other than 1 and itself






44. The system that Euclid used in The Elements






45. Multiplication is equivalent to






46. The study of shape from an external perspective.






47. 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.






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

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49. 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






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