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Test your basic knowledge |
CLEP General Math: Number Sense - Patterns - Algebraic Thinking
Start Test
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. You must always solve the equation set up in the previous step.
Solve the Equation
Public Key Encryption
The Prime Number Theorem
Figurate Numbers
2. If a = b then a + c = b + c If a = b then a - c = b - c If a = b then a
Set up a Variable Dictionary.
Hamilton Cycle
Properties of Equality
Countable
3. Public key encryption allows two parties to communicate securely over an un-secured computer network using the properties of prime numbers and modular arithmetic. RSA is the modern standard for public key encryption.
The inverse of addition is subtraction
Pigeonhole Principle
The Same
Public Key Encryption
4. A way to extrinsically measure the curvature of a surface by looking at a given point and finding the contour line with the greatest curvature and the contour line with the least curvature.
Principal Curvatures
Central Limit Theorem
Hamilton Cycle
Equation
5. 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.'
Hyperland
Irrational
Fourier Analysis and Synthesis
Spaceland
6. We can think of the space between primes as 'prime deserts -' strings of consecutive numbers - none of which are prime.
Invarient
Prime Deserts
per line
Least Common Multiple (LCM)
7. Division by zero is undefined. Each of the expressions 6
A number is divisible by 10
Division by Zero
set
Box Diagram
8. A way to analyze sequences of events where the outcomes of prior events affect the probability of outcomes of subsequent events.
Markov Chains
Galois Theory
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.
The inverse of addition is subtraction
9. Means approximately equal.
The Prime Number Theorem
Conditional Probability
Unique Factorization Theorem
˜
10. A '___________' infinite set is one that can be put into one-to-one correspondence with the set of natural numbers.
perimeter
Countable
The Commutative Property of Addition
Continuous
11. 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.
Topology
Unique Factorization Theorem
˜
Products and Factors
12. If grouping symbols are nested
Commutative Property of Multiplication
A number is divisible by 3
Multiplicative Inverse:
evaluate the expression in the innermost pair of grouping symbols first.
13. Also known as gluing diagrams - are a convenient way to examine intrinsic topology.
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.
Box Diagram
Polynomial
Prime Number
14. At each level of the tree - break the current number into a product of two factors. The process is complete when all of the 'circled leaves' at the bottom of the tree are prime numbers. Arranging the factors in the 'circled leaves' in order. The fina
Factor Trees
Poincare Disk
Set up an Equation
Tone
15. This method can create a flat map from a curved surface while preserving all angles in any features present.
4 + x = 12
Factor Trees
Order of Operations - PEMDAS 'Please Excuse My Dear Aunt Sally'
Stereographic Projection
16. A flat map of hyperbolic space.
Multiplicative Inverse:
Poincare Disk
Factor Tree Alternate Approach
Set up a Variable Dictionary.
17. (a
Division is not Associative
Fourier Analysis and Synthesis
˜
The Set of Whole Numbers
18. Instruments produce notes that have a fundamental frequency in combination with multiples of that frequency known as partials or overtones
Overtone
Tone
Look Back
Bijection
19. Used to display measurements. The measurement was taken is placed on the horizontal axis - and the height of each bar equals the amount during that year.
The Additive Identity Property
bar graph
Discrete
counting numbers
20. Mathematical statement that equates two mathematical expressions.
Equation
Configuration Space
a
Topology
21. A factor tree is a way to visualize a number's
Commensurability
Public Key Encryption
prime factors
1. Simplify the expression on either side of the equation. 2. Gather the variable term on the left-hand side (LHS) by adding to both sides. the opposite of the variable term on the right-hand side (RHS). Note: either side is fine but we will consiste
22. 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
Geometry
Frequency
Principal Curvatures
23. An important part of problem solving is identifying
Fundamental Theorem of Arithmetic
variable
Probability
Bijection
24. 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
Set up a Variable Dictionary.
The Additive Identity Property
The Prime Number Theorem
Rational
25. If a is any whole number - then a
Euler Characteristic
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
The Kissing Circle
The Multiplicative Identity Property
26. In some ways - the opposite of a multitude is a magnitude - which is ___________. In other words - there are no well defined partitions.
Properties of Equality
Distributive Property:
Flat Land
Continuous
27. 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.
a
Division is not Commutative
Dividing both Sides of an Equation by the Same Quantity
Topology
28. TA model of a sequence of random events. Each marble that passes through the system represents a trial consisting of as many random events as there are rows in the system.
A prime number
Euler Characteristic
Galton Board
Multiplying both Sides of an Equation by the Same Quantity
29. Trigonometric functions - such as sine and cosine - are useful for modeling sound waves - because they oscillate between values
Periodic Function
A number is divisible by 9
Noether's Theorem
variable
30. Some numbers make geometric shapes when arranged as a collection of dots - for example - 16 makes a square - and 10 makes a triangle.
Dividing both Sides of an Equation by the Same Quantity
Additive Inverse:
The Multiplicative Identity Property
Figurate Numbers
31. Add and subtract
left to right
A number is divisible by 5
inline
Frequency
32. In the expression 3
Non-Orientability
The Additive Identity Property
bar graph
Products and Factors
33. 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.
Extrinsic View
Cardinality
Conditional Probability
Overtone
34. Are the fundamental building blocks of arithmetic.
Look Back
does not change the solution set.
Primes
Commutative Property of Addition:
35. W = {0 - 1 - 2 - 3 - 4 - 5 - . . .} is called
A number is divisible by 5
Invarient
The Set of Whole Numbers
Distributive Property:
36. 1. Find the prime factorizations of each number. To find the prime factorization one method is a factor tree where you begin with any two factors and proceed by dividing the numbers until all the ends are prime factors. 2. Star factors which are shar
Sign Rules for Division
Least Common Multiple (LCM)
The Same
Symmetry
37. Our standard notions of Pythagorean distance and angle via the inner product extend quite nicely from three-space.
In Euclidean four-space
Continuous Symmetry
Non-Euclidian Geometry
Axiomatic Systems
38. 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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39. The multitude concept presented numbers as collections of discrete units - rather like indivisible atoms.
Discrete
Line Land
Galton Board
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
40. Original Balance minus River Tam's Withdrawal is Current Balance
Division is not Associative
a - c = b - c
The index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.
B - 125 = 1200
41. If a and b are any whole numbers - then a
Sign Rules for Division
Variable
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
Commutative Property of Multiplication
42. 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.
Torus
a
De Bruijn Sequence
Non-Orientability
43. If a - b - and c are any whole numbers - then a
Denominator
Dividing both Sides of an Equation by the Same Quantity
The Associative Property of Multiplication
Multiplication
44. This result says that the symmetries of geometric objects can be expressed as groups of permutations.
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45. If a whole number is not a prime number - then it is called a...
a - c = b - c
Discrete
Composite Numbers
The Kissing Circle
46. Uses second derivatives to relate acceleration in space to acceleration in time.
Wave Equation
The inverse of addition is subtraction
Hypercube
Markov Chains
47. Topological objects are categorized by their _______ (number of holes). The genus of a surface is a feature of its global topology.
Flat Land
per line
Law of Large Numbers
Genus
48. 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.
Axiomatic Systems
Law of Large Numbers
left to right
The inverse of addition is subtraction
49. 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
does not change the solution set.
Hypercube
Set up a Variable Dictionary.
Exponents
50. Dimension is how mathematicians express the idea of degrees of freedom
Normal Distribution
Dimension
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
Divisible