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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. Every whole number can be uniquely factored as a product of primes. This result guarantees that if the prime factors are ordered from smallest to largest - everyone will get the same result when breaking a number into a product of prime factors.






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






3. If a = b then






4. 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)






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






6. Division by zero is undefined. Each of the expressions 6






7. In the expression 3






8. If a and b are any whole numbers - then a






9. 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






10. 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.






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






12. A · b = b · a






13. Topological objects are categorized by their _______ (number of holes). The genus of a surface is a feature of its global topology.






14. 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.






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






16. ____________ theory enables us to use mathematics to characterize and predict the behavior of random events. By 'random' we mean 'unpredictable' in the sense that in a given specific situation - our knowledge of current conditions gives us no way to






17. 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.






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






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






20. 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.






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






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. The system that Euclid used in The Elements






24. 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






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






26. If a = b then






27. The inverse of multiplication






28. The fundamental theorem of arithmetic says that






29. 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






30. 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






31. Aka The Osculating Circle - a way to measure the curvature of a line.






32. Solving Equations






33. This model is at the forefront of probability research. Mathematicians use it to model traffic patterns in an attempt to understand flow rates and gridlock - among other things.






34. Negative






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






36. 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.






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






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






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






40. All integers are thus divided into three classes:






41. The state of appearing unchanged.






42. Requirements for Word Problem Solutions.






43. W = {0 - 1 - 2 - 3 - 4 - 5 - . . .} is called






44. 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.






45. 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.






46. 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






47. 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.'






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






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






50. A flat map of hyperbolic space.