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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. 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.
Amplitude
Law of Large Numbers
Standard Deviation
B - 125 = 1200
2. Objects are topologically equivalent if they can be continuously deformed into one another. Properties that are preserved during this process are called topological invariants.
Continuous
a · c = b · c for c does not equal 0
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
Irrational
3. 4 more than a certain number is 12
Rarefactior
A number is divisible by 3
Pigeonhole Principle
4 + x = 12
4. If its final digit is a 0.
Euler Characteristic
A number is divisible by 10
Hypercube
Unique Factorization Theorem
5. 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
Periodic Function
a + c = b + c
repeated addition
Answer the Question
6. ____________ 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
Probability
Multiplicative Inverse:
Poincare Disk
Factor Tree Alternate Approach
7. Are the fundamental building blocks of arithmetic.
Discrete
Cardinality
Commutative Property of Addition:
Primes
8. The distribution of averages of many trials is always normal - even if the distribution of each trial is not.
Multiplicative Inverse:
Multiplication by Zero
Central Limit Theorem
Extrinsic View
9. A point in one dimension requires only one number to define it. The number line is a good example of a one-dimensional space.
Properties of Equality
Line Land
Division by Zero
˜
10. To describe and extend a numerical pattern
Solve the Equation
A number is divisible by 3
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.
Geometry
11. This result says that the symmetries of geometric objects can be expressed as groups of permutations.
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12. 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 -
The inverse of addition is subtraction
Principal Curvatures
Equivalent Equations
Continuous
13. Adding the same quantity to both sides of an equation - if a = b - then adding c to both sides of the equation produces the equivalent equation a + c = b + c.
does not change the solution set.
Geometry
Commutative Property of Addition:
Hypercube
14. 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
variable
Look Back
The inverse of multiplication is division
Order of Operations - PEMDAS 'Please Excuse My Dear Aunt Sally'
15. Trigonometric functions - such as sine and cosine - are useful for modeling sound waves - because they oscillate between values
a
Periodic Function
B - 125 = 1200
Associate Property of Addition
16. N = {1 - 2 - 3 - 4 - 5 - . . .}.
a · c = b · c for c does not equal 0
Additive Inverse:
the set of natural numbers
Composite Numbers
17. An algebraic 'sentence' containing an unknown quantity.
Polynomial
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.
Public Key Encryption
Division is not Commutative
18. Topological objects are categorized by their _______ (number of holes). The genus of a surface is a feature of its global topology.
Solve the Equation
Flat Land
Genus
a divided by b
19. If a represents any whole number - then a
Non-Euclidian Geometry
Multiplication by Zero
Euclid's Postulates
Group
20. W = {0 - 1 - 2 - 3 - 4 - 5 - . . .} is called
Overtone
The Set of Whole Numbers
the set of natural numbers
Unique Factorization Theorem
21. The process of taking a complicated signal and breaking it into sine and cosine components.
Cardinality
Fourier Analysis
Commutative Property of Multiplication:
Denominator
22. 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
Configuration Space
Associate Property of Addition
Factor Trees
Overtone
23. Is a symbol (usually a letter) that stands for a value that may vary.
De Bruijn Sequence
Central Limit Theorem
Ramsey Theory
Variable
24. In the expression 3
The Prime Number Theorem
Products and Factors
the set of natural numbers
Bijection
25. The solutions to this gambling dilemma is traditionally held to be the start of modern probability theory.
Problem of the Points
Non-Orientability
Poincare Disk
Aleph-Null
26. A
division
Tone
Divisible
Division is not Commutative
27. A topological object that can be used to study the allowable states of a given system.
Configuration Space
Prime Number
Distributive Property:
Group
28. Is a path that visits every node in a graph and ends where it began.
Continuous Symmetry
Hamilton Cycle
Ramsey Theory
Multiplication
29. The study of shape from an external perspective.
Galois Theory
Hyperbolic Geometry
Solution
Extrinsic View
30. Determines the likelihood of events that are not independent of one another.
Set up an Equation
Conditional Probability
Euclid's Postulates
Comparison Property
31. 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 -
counting numbers
The inverse of subtraction is addition
Order of Operations - PEMDAS 'Please Excuse My Dear Aunt Sally'
Cardinality
32. 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.
Bijection
B - 125 = 1200
A number is divisible by 5
Hypersphere
33. The surface of a standard 'donut shape'.
Fourier Analysis
Euler Characteristic
Torus
A number is divisible by 9
34. Requirements for Word Problem Solutions.
Commutative Property of Addition:
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
Multiplying both Sides of an Equation by the Same Quantity
Cardinality
35. Originally known as analysis situs
Complete Graph
Standard Deviation
Topology
Spaceland
36. The whole number zero is called the additive identity. If a is any whole number - then a + 0 = a.
Products and Factors
Dividing both Sides of an Equation by the Same Quantity
The Additive Identity Property
Tone
37. 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
Multiplicative Identity:
Group
The Same
Overtone
38. Rules for Rounding - To round a number to a particular place - follow these steps:
Galton Board
Exponents
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
1. The unit 2. Prime numbers 3. Composite numbers
39. This result relates conserved physical quantities - like conservation of energy - to continuous symmetries of spacetime.
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40. An instrument's _____ - the sound it produces - is a complex mixture of waves of different frequencies.
Group
Tone
counting numbers
Set up an Equation
41. 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
Complete Graph
Rarefactior
division
General Relativity
42. Index p radicand
per line
counting numbers
The index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.
4 + x = 12
43. The amount of displacement - as measured from the still surface line.
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
Commutative Property of Addition:
Amplitude
Dimension
44. 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.
Properties of Equality
Grouping Symbols
each whole number can be uniquely decomposed into products of primes.
Public Key Encryption
45. 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.
General Relativity
Commutative Property of Multiplication
Law of Large Numbers
bar graph
46. This method can create a flat map from a curved surface while preserving all angles in any features present.
Variable
Galois Theory
Grouping Symbols
Stereographic Projection
47. 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.
Tone
Primes
A number is divisible by 3
Modular Arithmetic
48. If a is any whole number - then a
The Multiplicative Identity Property
˜
Box Diagram
4 + x = 12
49. If grouping symbols are nested
Divisible
evaluate the expression in the innermost pair of grouping symbols first.
Non-Orientability
A prime number
50. 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.
Normal Distribution
Transfinite
Least Common Multiple (LCM)
Primes