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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. Originally known as analysis situs






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






3. Has no factors other than 1 and itself






4. The amount of displacement - as measured from the still surface line.






5. Writing Mathematical equations - arrange your work one equation






6. 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.'






7. Let a and b represent two whole numbers. Then - a + b = b + a.






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






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






10. Perform all additions and subtractions in the order presented






11. To describe and extend a numerical pattern






12. 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.






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






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






15. The inverse of multiplication






16. 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






17. Is a symbol (usually a letter) that stands for a value that may vary.






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






19. A






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






21. If a = b then






22. An important part of problem solving is identifying






23. 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 -






24. If a = b then






25. 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.






26. 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






27. In this type of geometry the angles of a triangle add up to more than 180 degrees. In such a system - one has to replace the parallel postulate with a version that admits no parallel lines as well as modify Euclid's first two postulates.






28. Assuming that the air is of uniform density and pressure to begin with - a region of high pressure will be balanced by a region of low pressure - called rarefaction - immediately following the compression






29. 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






30. A flat map of hyperbolic space.






31. A · 1 = 1 · a = a






32. 1. Any two points can be joined by a straight line. 2. Any straight line segment can be extended indefinitely in a straight line. 3. Given any straight line segment - a circle can be drawn having the segment as radius and one endpoint as center. 4. A

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33. 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.'






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. An algebraic 'sentence' containing an unknown quantity.






36. If grouping symbols are nested






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






38. 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.






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






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

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41. An arrangement where order matters.






42. An equation is a numerical value that satisfies the equation. That is - when the variable in the equation is replaced by the solution - a true statement results.






43. If a - b - and c are any whole numbers - then a






44. Are the fundamental building blocks of arithmetic.






45. 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.






46. When writing mathematical statements - follow the mantra:






47. Positive integers are






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






49. If a = b then






50. 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).