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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. 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.






2. If a = b then






3. A · 1 = 1 · a = a






4. Use parentheses - brackets - or curly braces to delimit the part of an expression you want evaluated first.






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






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






7. If we start with a number x and add a number a - then subtracting a from the result will return us to the original number x. x + a - a = x. so -






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






9. Writing Mathematical equations - arrange your work one equation






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






11. 1. Any two points can be joined by a straight line. 2. Any straight line segment can be extended indefinitely in a straight line. 3. Given any straight line segment - a circle can be drawn having the segment as radius and one endpoint as center. 4. A

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12. Multiplication is equivalent to






13. In the expression 3






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

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15. An important part of problem solving is identifying






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






17. An object possessing continuous symmetries can remain invariant while one symmetry is turned into another. A circle is an example of an object with continuous symmetries.






18. 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)






19. Perform all additions and subtractions in the order presented






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






21. 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






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






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






24. 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.'






25. Determines the likelihood of events that are not independent of one another.






26. 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






27. 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.






28. Are the fundamental building blocks of arithmetic.






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






30. All integers are thus divided into three classes:






31. 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.






32. A + 0 = 0 + a = a






33. When writing mathematical statements - follow the mantra:






34. 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).






35. 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






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






37. Used to display measurements. The measurement was taken is placed on the horizontal axis - and the height of each bar equals the amount during that year.






38. ____________ 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






39. 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






40. 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.






41. Requirements for Word Problem Solutions.






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

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43. 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.






44. If its final digit is a 0.






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






46. Means approximately equal.






47. 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.






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






49. 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.






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






Can you answer 50 questions in 15 minutes?



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