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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. 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






2. A · b = b · a






3. 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






4. If its final digit is a 0 or 5.






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






6. 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






7. In the expression 3






8. 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.






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

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10. If a = b then






11. A · 1/a = 1/a · a = 1






12. Trigonometric functions - such as sine and cosine - are useful for modeling sound waves - because they oscillate between values






13. Dimension is how mathematicians express the idea of degrees of freedom






14. 4 more than a certain number is 12






15. Negative






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






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






18. A topological object that can be used to study the allowable states of a given system.






19. 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






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






21. (a






22. Are the fundamental building blocks of arithmetic.






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






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






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






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






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






28. ____________ 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






29. 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.






30. In a mathematical sense - it is a transformation that leaves an object invariant. Symmetry is perhaps most familiar as an artistic or aesthetic concept. Designs are said to be symmetric if they exhibit specific kinds of balance - repetition - and/or






31. 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.






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






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






34. 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.'






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






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






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






38. 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).






39. 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.






40. A + 0 = 0 + a = a






41. 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






42. 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






43. 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.






44. × - ( )( ) - · - 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






45. 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.






46. The state of appearing unchanged.






47. 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






48. 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 -






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






50. 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.