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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. This model is at the forefront of probability research. Mathematicians use it to model traffic patterns in an attempt to understand flow rates and gridlock - among other things.
De Bruijn Sequence
Exponents
The BML Traffic Model
a - c = b - c
2. A topological object that can be used to study the allowable states of a given system.
evaluate the expression in the innermost pair of grouping symbols first.
The Prime Number Theorem
Configuration Space
Factor Tree Alternate Approach
3. 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
Prime Deserts
Answer the Question
Intrinsic View
Multiplicative Identity:
4. 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
4 + x = 12
The Commutative Property of Addition
Dimension
5. An instrument's _____ - the sound it produces - is a complex mixture of waves of different frequencies.
Rarefactior
One equal sign per line
Tone
Group
6. 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
Commensurability
Set up an Equation
repeated addition
perimeter
7. 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.
Law of Large Numbers
The Multiplicative Identity Property
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.
Ramsey Theory
8. Are the fundamental building blocks of arithmetic.
Primes
Figurate Numbers
Fundamental Theorem of Arithmetic
Markov Chains
9. (a · b) · c = a · (b · c)
Probability
Noether's Theorem
Spherical Geometry
Associative Property of Multiplication:
10. 1. Find the prime factorizations of each number.
A number is divisible by 9
a
Greatest Common Factor (GCF)
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.
11. 4 more than a certain number is 12
4 + x = 12
The inverse of multiplication is division
Genus
Distributive Property:
12. Let a - b - and c be any whole numbers. Then - a
Noether's Theorem
evaluate the expression in the innermost pair of grouping symbols first.
The Distributive Property (Subtraction)
Tone
13. 1. Parentheses (or any grouping symbol {braces} - [square brackets] - |absolute value|)
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14. Means approximately equal.
perimeter
a - c = b - c
Galton Board
˜
15. A way to measure how far away a given individual result is from the average result.
a + c = b + c
Additive Identity:
Standard Deviation
Geometry
16. An algebraic 'sentence' containing an unknown quantity.
Polynomial
Division is not Associative
Commutative Property of Multiplication:
Aleph-Null
17. Division by zero is undefined. Each of the expressions 6
perimeter
Division by Zero
The inverse of multiplication is division
Equivalent Equations
18. This means that for any two magnitudes - one should always be able to find a fundamental unit that fits some whole number of times into each of them (i.e. - a unit whose magnitude is a whole number factor of each of the original magnitudes)
Commensurability
Spaceland
Genus
Line Land
19. A factor tree is a way to visualize a number's
4 + x = 12
prime factors
left to right
Associative Property of Multiplication:
20. Collection of objects. list all the objects in the set and enclosing the list in curly braces.
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
Polynomial
set
Standard Deviation
21. A + (-a) = (-a) + a = 0
Solve the Equation
The index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.
Additive Inverse:
Comparison Property
22. 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
Look Back
Commutative Property of Multiplication:
Poincare Disk
The inverse of subtraction is addition
23. The process of taking a complicated signal and breaking it into sine and cosine components.
per line
Fourier Analysis
counting numbers
Multiplication by Zero
24. We can think of the space between primes as 'prime deserts -' strings of consecutive numbers - none of which are prime.
Prime Deserts
Expected Value
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
Frequency
25. Points in two-dimensional space require two numbers to specify them completely. The Cartesian plane is a good way to envision two-dimensional space.
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
Modular Arithmetic
Flat Land
In Euclidean four-space
26. 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.
Stereographic Projection
Multiplying both Sides of an Equation by the Same Quantity
Unique Factorization Theorem
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
27. 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.
Aleph-Null
Spherical Geometry
Properties of Equality
Rational
28. When writing mathematical statements - follow the mantra:
Unique Factorization Theorem
Overtone
Stereographic Projection
One equal sign per line
29. 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.
The Same
Answer the Question
does not change the solution set.
Fundamental Theorem of Arithmetic
30. The multitude concept presented numbers as collections of discrete units - rather like indivisible atoms.
Box Diagram
Standard Deviation
Discrete
Principal Curvatures
31. 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
Genus
Symmetry
De Bruijn Sequence
1. The unit 2. Prime numbers 3. Composite numbers
32. Non-Euclidean geometries abide by some - but not all of Euclid's five postulates.
Hypercube
Irrational
Non-Euclidian Geometry
Denominator
33. Determines the likelihood of events that are not independent of one another.
set
Conditional Probability
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
inline
34. Some numbers make geometric shapes when arranged as a collection of dots - for example - 16 makes a square - and 10 makes a triangle.
Irrational
Associative Property of Multiplication:
A number is divisible by 5
Figurate Numbers
35. Rules for Rounding - To round a number to a particular place - follow these steps:
Answer the Question
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 Prime Number Theorem
The BML Traffic Model
36. If a and b are any whole numbers - then a
Equation
˜
Factor Trees
Commutative Property of Multiplication
37. A number is divisible by 2
Rational
division
The Prime Number Theorem
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
38. This method can create a flat map from a curved surface while preserving all angles in any features present.
Hamilton Cycle
Sign Rules for Division
A number is divisible by 9
Stereographic Projection
39. 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
The BML Traffic Model
Greatest Common Factor (GCF)
Amplitude
The inverse of multiplication is division
40. This result says that the symmetries of geometric objects can be expressed as groups of permutations.
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41. An arrangement where order matters.
Bijection
˜
The inverse of addition is subtraction
Permutation
42. The whole number zero is called the additive identity. If a is any whole number - then a + 0 = a.
Dividing both Sides of an Equation by the Same Quantity
Commensurability
The Additive Identity Property
a - c = b - c
43. Because of the associate property of addition - when presented with a sum of three numbers - whether you start by adding the first two numbers or the last two numbers - the resulting sum is
Standard Deviation
Spaceland
Order of Operations - PEMDAS 'Please Excuse My Dear Aunt Sally'
The Same
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.
1. The unit 2. Prime numbers 3. Composite numbers
Pigeonhole Principle
Prime Number
Public Key Encryption
45. Is a path that visits every node in a graph and ends where it began.
Galton Board
Hamilton Cycle
Order of Operations - PEMDAS 'Please Excuse My Dear Aunt Sally'
Grouping Symbols
46. Has no factors other than 1 and itself
evaluate the expression in the innermost pair of grouping symbols first.
Spaceland
Torus
A prime number
47. Codifies the 'average behavior' of a random event and is a key concept in the application of probability.
De Bruijn Sequence
Least Common Multiple (LCM)
a - c = b - c
Expected Value
48. 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
In Euclidean four-space
Figurate Numbers
Dimension
Factor Trees
49. 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.
Set up an Equation
a
Solution
Galton Board
50. 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.
Flat Land
Line Land
Geometry
Non-Orientability