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






2. Also known as gluing diagrams - are a convenient way to examine intrinsic topology.






3. 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.'






4. 4 more than a certain number is 12






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






6. If grouping symbols are nested






7. 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.






8. If a is any whole number - then a






9. (a · b) · c = a · (b · c)






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






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

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12. 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.






13. 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.






14. Add and subtract






15. 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.






16. ____________ 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






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






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






19. 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.'






20. 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






21. 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 -






22. 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






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






24. A · b = b · a






25. 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.






26. A flat map of hyperbolic space.






27. Used to display measurements. The measurement was taken is placed on the horizontal axis - and the height of each bar equals the amount during that year.






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






29. A number is divisible by 2






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






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






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






33. A point in three-dimensional space requires three numbers to fix its location.






34. 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).






35. 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.'






36. A factor tree is a way to visualize a number's






37. An arrangement where order matters.






38. 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.






39. If a = b then






40. Originally known as analysis situs






41. In the expression 3






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






43. If a represents any whole number - then a






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






45. 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).






46. The state of appearing unchanged.






47. × - ( )( ) - · - 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






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






49. At each level of the tree - break the current number into a product of two factors. The process is complete when all of the 'circled leaves' at the bottom of the tree are prime numbers. Arranging the factors in the 'circled leaves' in order. The fina






50. 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







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