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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. 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 -






2. A '___________' infinite set is one that can be put into one-to-one correspondence with the set of natural numbers.






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






4. 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).






5. Codifies the 'average behavior' of a random event and is a key concept in the application of probability.






6. Means approximately equal.






7. When writing mathematical statements - follow the mantra:






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






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






10. 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.'






11. Mathematical statement that equates two mathematical expressions.






12. Add and subtract






13. Multiplication is equivalent to






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






15. Einstein's famous theory - relates gravity to the curvature of spacetime.






16. If grouping symbols are nested






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






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






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






20. Writing Mathematical equations - arrange your work one equation






21. Our standard notions of Pythagorean distance and angle via the inner product extend quite nicely from three-space.






22. If a = b then






23. 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






24. (a · b) · c = a · (b · c)






25. Negative






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






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






28. × - ( )( ) - · - 1. Multiply the numbers (ignoring the signs)2. The answer is positive if they have the same signs. 3. The answer is negative if they have different signs. 4. Alternatively - count the amount of negative numbers. If there are an even






29. 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






30. An important part of problem solving is identifying






31. The study of shape from an external perspective.






32. Of central importance in Ramsey Theory - and in combinatorics in general - is the 'pigeonhole principle -' also known as Dirichlet's box. This principle simply states that we cannot fit n+1 pigeons into n pigeonholes in such a way that only one pigeo






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






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






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






36. Uses second derivatives to relate acceleration in space to acceleration in time.






37. 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.






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






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






40. 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.






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






42. An arrangement where order matters.






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






44. The fundamental theorem of arithmetic says that






45. You must always solve the equation set up in the previous step.






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






47. 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






48. 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






49. 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.






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