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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. Solving Equations






2. 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).






3. 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






4. 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






5. Perform all additions and subtractions in the order presented






6. 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.






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






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






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






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






11. The inverse of multiplication






12. 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.






13. An important part of problem solving is identifying






14. 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 -






15. In some ways - the opposite of a multitude is a magnitude - which is ___________. In other words - there are no well defined partitions.






16. The system that Euclid used in The Elements






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






18. 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.






19. An arrangement where order matters.






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

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21. Let a - b - and c represent whole numbers. Then - (a + b) + c = a + (b + c).






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






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






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






26. 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






27. 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.






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






29. × - ( )( ) - · - 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






30. N = {1 - 2 - 3 - 4 - 5 - . . .}.






31. The expression a/b means






32. Multiplication is equivalent to






33. Originally known as analysis situs






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






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






36. It is important to note that this step does not imply that you should simply check your solution in your equation. After all - it's possible that your equation incorrectly models the problem's situation - so you could have a valid solution to an inco






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






38. 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.'






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






40. Some numbers make geometric shapes when arranged as a collection of dots - for example - 16 makes a square - and 10 makes a triangle.






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






42. 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.






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






44. 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






45. In the expression 3






46. Has no factors other than 1 and itself






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






48. 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






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

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