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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. 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






2. GThe mathematical study of space. The geometry of a space goes hand in hand with how one defines the shortest distance between two points in that space.






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






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






5. 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






6. If a = b then






7. A · 1/a = 1/a · a = 1






8. When writing mathematical statements - follow the mantra:






9. A + b = b + a






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






11. An arrangement where order matters.






12. If grouping symbols are nested






13. 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






14. 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.






15. 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.






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






17. The state of appearing unchanged.






18. In the expression 3






19. Original Balance minus River Tam's Withdrawal is Current Balance






20. Points in two-dimensional space require two numbers to specify them completely. The Cartesian plane is a good way to envision two-dimensional space.






21. 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.






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






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






24. Index p radicand






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






26. 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






27. If we start with a number x and subtract a number a - then adding a to the result will return us to the original number x. In symbols - x - a + a = x. So -






28. The identification of a 'one-to-one' correspondence--enables us to enumerate a set that may be difficult to count in terms of another set that is more easily counted.






29. When comparing two whole numbers a and b - only one of three possibilities is true: a < b or a = b or a > b.






30. A way to extrinsically measure the curvature of a surface by looking at a given point and finding the contour line with the greatest curvature and the contour line with the least curvature.






31. This result relates conserved physical quantities - like conservation of energy - to continuous symmetries of spacetime.

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






33. Non-Euclidean geometries abide by some - but not all of Euclid's five postulates.






34. The multitude concept presented numbers as collections of discrete units - rather like indivisible atoms.






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






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






37. The inverse of multiplication






38. Multiplication is equivalent to






39. 1. Find the prime factorizations of each number. To find the prime factorization one method is a factor tree where you begin with any two factors and proceed by dividing the numbers until all the ends are prime factors. 2. Star factors which are shar






40. Collection of objects. list all the objects in the set and enclosing the list in curly braces.






41. To describe and extend a numerical pattern






42. The expression a/b means






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






44. 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.






45. 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.'






46. Is a path that visits every node in a graph and ends where it began.






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






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






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






50. An important part of problem solving is identifying