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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. 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






2. Cannot be written as a ratio of natural numbers.






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






4. 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.






5. (a






6. A number is divisible by 2






7. 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.'






8. Add and subtract






9. An object possessing continuous symmetries can remain invariant while one symmetry is turned into another. A circle is an example of an object with continuous symmetries.






10. If a is any whole number - then a






11. Does not change the solution set. That is - if a = b - then multiplying both sides of the equation by c produces the equivalent equation a






12. Cantor called the cardinality of all the sets that can be put into one-to-one correspondence with the counting numbers - or 'Aleph Null.'






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






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

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15. The expression a/b means






16. 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






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






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






19. To describe and extend a numerical pattern






20. Rules for Rounding - To round a number to a particular place - follow these steps:






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

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22. 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.






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






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






25. An arrangement where order matters.






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






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






28. 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






29. 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.






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






31. 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.






32. Of central importance in Ramsey Theory - and in combinatorics in general - is the 'pigeonhole principle -' also known as Dirichlet's box. This principle simply states that we cannot fit n+1 pigeons into n pigeonholes in such a way that only one pigeo






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






34. Let a - b - and c be any whole numbers. Then - a






35. This famous - as yet unproven - result relates to the distribution of prime numbers on the number line.






36. 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.






37. Some favor repeatedly dividing by 2 until the result is no longer divisible by 2. Then try repeatedly dividing by the next prime until the result is no longer divisible by that prime. The process terminates when the last resulting quotient is equal t






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






39. Originally known as analysis situs






40. The system that Euclid used in The Elements






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






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






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






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






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






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






47. Means approximately equal.






48. Has no factors other than 1 and itself






49. Multiplication is equivalent to






50. 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 -