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






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






3. 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.






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

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






6. ____________ 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






7. 4 more than a certain number is 12






8. (a · b) · c = a · (b · c)






9. 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.






10. If a = b then






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






12. 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).






13. If the sum of its digits is divisible by 9 (ex: 3591 is divisible by 9 since 3 + 5 + 9 + 1 = 18 is divisible by 9).






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






15. 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






16. A + b = b + a






17. If a represents any whole number - then a






18. A · 1/a = 1/a · a = 1






19. The system that Euclid used in The Elements






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






21. 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.






22. The fundamental theorem of arithmetic says that






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






24. 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






25. All integers are thus divided into three classes:






26. An important part of problem solving is identifying






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






28. 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






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






30. 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).






31. When writing mathematical statements - follow the mantra:






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






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






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






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






37. 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






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






39. If a whole number is not a prime number - then it is called a...






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






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






42. A point in four-space - also known as 4-D space - requires four numbers to fix its position. Four-space has a fourth independent direction - described by 'ana' and 'kata.'






43. A number is divisible by 2






44. 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 -






45. A · b = b · a






46. 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






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






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






49. If a = b then






50. 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