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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. 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.






2. A way to analyze sequences of events where the outcomes of prior events affect the probability of outcomes of subsequent events.






3. A · 1/a = 1/a · a = 1






4. 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.






5. If a = b then






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






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






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






9. To describe and extend a numerical pattern






10. 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).






11. 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.






12. N = {1 - 2 - 3 - 4 - 5 - . . .}.






13. A + 0 = 0 + a = a






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






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






16. Writing Mathematical equations - arrange your work one equation






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






18. 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






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






20. 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.






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






22. When writing mathematical statements - follow the mantra:






23. 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.'






24. 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






25. 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






26. 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.






27. Some numbers make geometric shapes when arranged as a collection of dots - for example - 16 makes a square - and 10 makes a triangle.






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






29. 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.'






30. If grouping symbols are nested






31. 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






32. (a






33. 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.






34. 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.






35. Are the fundamental building blocks of arithmetic.






36. Also known as gluing diagrams - are a convenient way to examine intrinsic topology.






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






38. Requirements for Word Problem Solutions.






39. All integers are thus divided into three classes:






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






41. A number is divisible by 2






42. 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.






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






44. Negative






45. The state of appearing unchanged.






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






47. ____________ 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






48. 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






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






50. Is a symbol (usually a letter) that stands for a value that may vary.