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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. An arrangement where order matters.






2. 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.






3. 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






4. 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.






5. In the expression 3






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






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






8. A point in one dimension requires only one number to define it. The number line is a good example of a one-dimensional space.






9. Positive integers are






10. 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.






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






12. Is the length around an object. Used to calculate such things as fencing around a yard - trimming a piece of material - and the amount of baseboard needed for a room.It is not necessary to have a formula since it is always just calculated by adding t






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






14. 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).






15. A · b = b · a






16. 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






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






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






19. 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.






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






21. 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.






22. ____________ theory enables us to use mathematics to characterize and predict the behavior of random events. By 'random' we mean 'unpredictable' in the sense that in a given specific situation - our knowledge of current conditions gives us no way to






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






24. 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.






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






26. 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






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






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






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






30. 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.






31. If a is any whole number - then a






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






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






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






35. Add and subtract






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






37. 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






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






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






40. Originally known as analysis situs






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






42. 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






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






44. 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.






45. Are the fundamental building blocks of arithmetic.






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






47. A + 0 = 0 + a = a






48. A + b = b + a






49. Perform all additions and subtractions in the order presented






50. A