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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. 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.'






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






3. Originally known as analysis situs






4. 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






5. To describe and extend a numerical pattern






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






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






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






9. A






10. 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






11. 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






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






13. A number is divisible by 2






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






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






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






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






18. The cardinality of sets that cannot be put into one-to-one correspondence with the counting numbers - such as the set of real numbers - is referred to as c. The designations A_0 and c are known as 'transfinite' cardinalities.






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






20. When writing mathematical statements - follow the mantra:






21. 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.






22. If grouping symbols are nested






23. Multiplication is equivalent to






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






25. 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.






26. 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.






27. This ubiquitous result describes the outcomes of many trials of events from a wide array of contexts. It says that most results cluster around the average with few results far above or far below average.






28. 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.






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






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. A flat map of hyperbolic space.






32. In the expression 3






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






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






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






36. 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






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






38. If a = b then






39. 1. Parentheses (or any grouping symbol {braces} - [square brackets] - |absolute value|)

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40. 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.'






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






42. 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 -






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






44. A graph in which every node is connected to every other node is called a complete graph.






45. Perform all additions and subtractions in the order presented






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






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






48. If on a surface there is no meaningful way to tell an object's orientation (left or right handedness) - the surface is said to be non-orientable.






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






50. 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






Can you answer 50 questions in 15 minutes?



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