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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 a and b are any whole numbers - then a






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






3. (a






4. The distribution of averages of many trials is always normal - even if the distribution of each trial is not.






5. A point in one dimension requires only one number to define it. The number line is a good example of a one-dimensional space.






6. 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






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






8. 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






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






10. Writing Mathematical equations - arrange your work one equation






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






12. In this type of geometry the angles of a triangle add up to less than 180 degrees. In such a system - one has to replace the parallel postulate with a version that admits many parallel lines.






13. 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.






14. 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.






15. The process of taking a complicated signal and breaking it into sine and cosine components.






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






17. An arrangement where order matters.






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






19. 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.






20. 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






21. 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.






22. An important part of problem solving is identifying






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






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






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






26. 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).






27. 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






28. 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






29. The system that Euclid used in The Elements






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






31. Assuming that the air is of uniform density and pressure to begin with - a region of high pressure will be balanced by a region of low pressure - called rarefaction - immediately following the compression






32. All integers are thus divided into three classes:






33. If we start with a number x and multiply by a number a - then dividing the result by the number a returns us to the original number x. In symbols - a






34. 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).






35. 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.






36. 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)






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






38. Public key encryption allows two parties to communicate securely over an un-secured computer network using the properties of prime numbers and modular arithmetic. RSA is the modern standard for public key encryption.






39. A






40. Requirements for Word Problem Solutions.






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






42. A + b = b + a






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






44. The study of shape from the perspective of being on the surface of the shape.






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






46. 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.






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






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






49. Rules for Rounding - To round a number to a particular place - follow these steps:






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