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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. 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.






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






3. A topological invariant that relates a surface's vertices - edges - and faces.






4. 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.






5. 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






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






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






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






9. An arrangement where order matters.






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. When writing mathematical statements - follow the mantra:






12. 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.






13. Says that when a random process - such as dropping marbles through a Galton board - is repeated many times - the frequencies of the observed outcomes get increasingly closer to the theoretical probabilities.






14. A · b = b · a






15. Also known as 'clock math -' incorporates 'wrap around' effects by having some number other than zero play the role of zero in addition - subtraction - multiplication - and division.






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






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






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






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






20. 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 -






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






22. A + 0 = 0 + a = a






23. (a · b) · c = a · (b · c)






24. 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






25. If a = b then






26. 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






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






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






29. A






30. 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.






31. To describe and extend a numerical pattern






32. 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).






33. If a = b then






34. The system that Euclid used in The Elements






35. Uses second derivatives to relate acceleration in space to acceleration in time.






36. The expression a/b means






37. 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.'






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






39. Positive integers are






40. 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.






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






43. × - ( )( ) - · - 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






44. If its final digit is a 0.






45. 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 -






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






47. 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






48. (a






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






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