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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. 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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2. 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.






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. Multiplication is equivalent to






5. 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






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






7. You must let your readers know what each variable in your problem represents. This can be accomplished in a number of ways: Statements such as 'Let P represent the perimeter of the rectangle.' - Labeling unknown values with variables in a table - Lab






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






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






10. 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






11. A + (-a) = (-a) + a = 0






12. All integers are thus divided into three classes:






13. 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






14. A · 1/a = 1/a · a = 1






15. 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.






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






17. The study of shape from an external perspective.






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






19. 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.'






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






21. To describe and extend a numerical pattern






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






23. Codifies the 'average behavior' of a random event and is a key concept in the application of probability.






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






25. A + 0 = 0 + a = a






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






28. 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.






29. 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.






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






31. A + b = b + a






32. Mathematical statement that equates two mathematical expressions.






33. The fundamental theorem of arithmetic says that






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






35. Are the fundamental building blocks of arithmetic.






36. 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.






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

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38. (a · b) · c = a · (b · c)






39. 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






40. The inverse of multiplication






41. If a is any whole number - then a






42. If a and b are any whole numbers - then a






43. Writing Mathematical equations - arrange your work one equation






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






45. 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).






46. 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.






47. 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.






48. 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.






49. 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).






50. A topological object that can be used to study the allowable states of a given system.