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Test your basic knowledge |
CLEP General Math: Number Sense - Patterns - Algebraic Thinking
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Study First
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. The identification of a 'one-to-one' correspondence--enables us to enumerate a set that may be difficult to count in terms of another set that is more easily counted.
Greatest Common Factor (GCF)
In Euclidean four-space
Bijection
Irrational
2. To describe and extend a numerical pattern
does not change the solution set.
1. Find a relationship between the first and second numbers. 2. Then we see if the relationship is true for the second and third numbers - the third and fourth - and so on.
Normal Distribution
Commutative Property of Addition:
3. If a - b - and c are any whole numbers - then a
Probability
The Associative Property of Multiplication
a · c = b · c for c does not equal 0
Group
4. The fundamental theorem of arithmetic says that
each whole number can be uniquely decomposed into products of primes.
Continuous
Division by Zero
Figurate Numbers
5. Trigonometric functions - such as sine and cosine - are useful for modeling sound waves - because they oscillate between values
Public Key Encryption
Periodic Function
Continuous
Hypercube
6. 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
Rarefactior
Periodic Function
Primes
The Riemann Hypothesis
7. A graph in which every node is connected to every other node is called a complete graph.
Complete Graph
a
Set up a Variable Dictionary.
1. Mark the place you wish to round to. This is called the rounding digit . 2. Check the next digit to the right of your digit marked in step 1. This is called the test digit . If the test digit is greater than or equal to 5 - add 1 to the rounding d
8. 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 -
The index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.
Stereographic Projection
The inverse of subtraction is addition
Multiplication by Zero
9. A '___________' infinite set is one that can be put into one-to-one correspondence with the set of natural numbers.
Spherical Geometry
Countable
Aleph-Null
1. Find a relationship between the first and second numbers. 2. Then we see if the relationship is true for the second and third numbers - the third and fourth - and so on.
10. Breaks a complicated signal into a combination of simple sine waves. Fourier synthesis does the opposite - constructing a complicated signal from simple sine waves.
a · c = b · c for c does not equal 0
Prime Number
Division is not Commutative
Fourier Analysis and Synthesis
11. × - ( )( ) - · - 1. Multiply the numbers (ignoring the signs)2. The answer is positive if they have the same signs. 3. The answer is negative if they have different signs. 4. Alternatively - count the amount of negative numbers. If there are an even
Multiplication
A number is divisible by 10
Associative Property of Multiplication:
Principal Curvatures
12. An instrument's _____ - the sound it produces - is a complex mixture of waves of different frequencies.
Division by Zero
Amplitude
Distributive Property:
Tone
13. 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).
variable
Polynomial
Prime Number
Fourier Analysis
14. 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
The Riemann Hypothesis
Properties of Equality
A number is divisible by 3
Multiplying both Sides of an Equation by the Same Quantity
15. The answer to the question of why the primes occur where they do on the number line has eluded mathematicians for centuries. Gauss's Prime Number Theorem is perhaps one of the most famous attempts to find the 'pattern behind the primes.'
The Prime Number Theorem
Multiplying both Sides of an Equation by the Same Quantity
Irrational
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
16. The state of appearing unchanged.
Multiplication by Zero
Continuous Symmetry
Non-Euclidian Geometry
Invarient
17. An important part of problem solving is identifying
variable
left to right
Multiplication
The inverse of addition is subtraction
18. 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.
Continuous
Answer the Question
Discrete
Hyperbolic Geometry
19. 1. Find the prime factorizations of each number.
The Set of Whole Numbers
Box Diagram
Greatest Common Factor (GCF)
Galois Theory
20. Mathematical statement that equates two mathematical expressions.
Additive Inverse:
Equation
Galton Board
Non-Euclidian Geometry
21. 4 more than a certain number is 12
1. The unit 2. Prime numbers 3. Composite numbers
Solve the Equation
4 + x = 12
Public Key Encryption
22. A topological object that can be used to study the allowable states of a given system.
Configuration Space
A number is divisible by 9
The inverse of subtraction is addition
The inverse of multiplication is division
23. 1. Parentheses (or any grouping symbol {braces} - [square brackets] - |absolute value|)
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24. Points in two-dimensional space require two numbers to specify them completely. The Cartesian plane is a good way to envision two-dimensional space.
A number is divisible by 9
Modular Arithmetic
Flat Land
Division is not Associative
25. Determines the likelihood of events that are not independent of one another.
Fourier Analysis and Synthesis
Principal Curvatures
Conditional Probability
The inverse of addition is subtraction
26. A · 1/a = 1/a · a = 1
Multiplicative Inverse:
Unique Factorization Theorem
Geometry
Aleph-Null
27. Codifies the 'average behavior' of a random event and is a key concept in the application of probability.
Bijection
Expected Value
1. The unit 2. Prime numbers 3. Composite numbers
B - 125 = 1200
28. 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
Non-Euclidian Geometry
Associative Property of Multiplication:
Frequency
Solution
29. Is the shortest string that contains all possible permutations of a particular length from a given set.
Multiplicative Inverse:
The inverse of addition is subtraction
left to right
De Bruijn Sequence
30. An arrangement where order matters.
Flat Land
Permutation
a
Line Land
31. A + b = b + a
General Relativity
Continuous Symmetry
Permutation
Commutative Property of Addition:
32. 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.
Hyperbolic Geometry
Spherical Geometry
Fourier Analysis
The Multiplicative Identity Property
33. A way to measure how far away a given individual result is from the average result.
Factor Tree Alternate Approach
Standard Deviation
Non-Orientability
Noether's Theorem
34. 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).
The Same
A number is divisible by 9
Comparison Property
Irrational
35. 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
perimeter
The inverse of subtraction is addition
Continuous Symmetry
variable
36. We can think of the space between primes as 'prime deserts -' strings of consecutive numbers - none of which are prime.
One equal sign per line
Prime Deserts
4 + x = 12
Multiplicative Inverse:
37. Our standard notions of Pythagorean distance and angle via the inner product extend quite nicely from three-space.
Solve the Equation
In Euclidean four-space
The inverse of addition is subtraction
Equation
38. A(b + c) = a · b + a · c a(b - c) = a · b - a · c
Distributive Property:
Sign Rules for Division
Invarient
Set up an Equation
39. Uses second derivatives to relate acceleration in space to acceleration in time.
Commutative Property of Multiplication
Law of Large Numbers
Wave Equation
Geometry
40. 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 -
Fourier Analysis
Public Key Encryption
Spaceland
The inverse of addition is subtraction
41. 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
each whole number can be uniquely decomposed into products of primes.
Group
Overtone
Hypercube
42. In the expression 3
a
Products and Factors
perimeter
a - c = b - c
43. If a is any whole number - then a
Fundamental Theorem of Arithmetic
Flat Land
The Multiplicative Identity Property
prime factors
44. The inverse of multiplication
De Bruijn Sequence
division
Continuous Symmetry
left to right
45. A
A prime number
The Prime Number Theorem
Division is not Commutative
The inverse of multiplication is division
46. 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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47. The expression a/b means
Unique Factorization Theorem
Periodic Function
Probability
a divided by b
48. 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.'
Divisible
1. The unit 2. Prime numbers 3. Composite numbers
Properties of Equality
Solution
49. Cannot be written as a ratio of natural numbers.
One equal sign per line
Geometry
Galois Theory
Irrational
50. Are the fundamental building blocks of arithmetic.
Equivalent Equations
General Relativity
Permutation
Primes