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






2. The state of appearing unchanged.






3. 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.'






4. The multitude concept presented numbers as collections of discrete units - rather like indivisible atoms.






5. A factor tree is a way to visualize a number's






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






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






8. Objects are topologically equivalent if they can be continuously deformed into one another. Properties that are preserved during this process are called topological invariants.






9. 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.






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






11. 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






12. 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






13. If a is any whole number - then a






14. Collection of objects. list all the objects in the set and enclosing the list in curly braces.






15. This means that for any two magnitudes - one should always be able to find a fundamental unit that fits some whole number of times into each of them (i.e. - a unit whose magnitude is a whole number factor of each of the original magnitudes)






16. 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.






17. 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.






18. An instrument's _____ - the sound it produces - is a complex mixture of waves of different frequencies.






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






20. If a = b then






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






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






23. When writing mathematical statements - follow the mantra:






24. 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.






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






26. A · 1 = 1 · a = a






27. Positive integers are






28. 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






29. The fundamental theorem of arithmetic says that






30. 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.






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






32. 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.






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






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






35. 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






36. 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.






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






38. The process of taking a complicated signal and breaking it into sine and cosine components.






39. A + b = b + a






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






41. 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 -






42. 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 -






43. If the sum of its digits is divisible by 9 (ex: 3591 is divisible by 9 since 3 + 5 + 9 + 1 = 18 is divisible by 9).






44. 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.






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






46. Index p radicand






47. 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.






48. If a represents any whole number - then a






49. Are the fundamental building blocks of arithmetic.






50. Arise from the attempt to measure all quantities with a common unit of measure.