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CLEP General Math: Number Sense - Patterns - Algebraic Thinking
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Subjects
:
clep
,
math
,
algebra
Instructions:
Answer 50 questions in 15 minutes.
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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. Let a and b represent two whole numbers. Then - a + b = b + a.
Greatest Common Factor (GCF)
a
Division by Zero
The Commutative Property of Addition
2. The study of shape from an external perspective.
Spaceland
Flat Land
Extrinsic View
Permutation
3. A point in one dimension requires only one number to define it. The number line is a good example of a one-dimensional space.
bar graph
A number is divisible by 3
Line Land
Associative Property of Multiplication:
4. In any ratio of two whole numbers - expressed as a fraction - we can interpret the first (top) number to be the 'counter -' or numerator
Denominator
Factor Trees
Continuous Symmetry
The inverse of subtraction is addition
5. An instrument's _____ - the sound it produces - is a complex mixture of waves of different frequencies.
Transfinite
Associative Property of Addition:
Tone
Torus
6. The state of appearing unchanged.
Invarient
In Euclidean four-space
The Kissing Circle
Products and Factors
7. If a is any whole number - then a
Intrinsic View
Principal Curvatures
Fundamental Theorem of Arithmetic
The Multiplicative Identity Property
8. Some numbers make geometric shapes when arranged as a collection of dots - for example - 16 makes a square - and 10 makes a triangle.
Figurate Numbers
Probability
Principal Curvatures
Dividing both Sides of an Equation by the Same Quantity
9. Also known as gluing diagrams - are a convenient way to examine intrinsic topology.
Grouping Symbols
Exponents
Frequency
Box Diagram
10. A · 1 = 1 · a = a
Rational
Figurate Numbers
The inverse of subtraction is addition
Multiplicative Identity:
11. This important result says that every natural number greater than one can be expressed as a product of primes in exactly one way.
Frequency
Fundamental Theorem of Arithmetic
Discrete
The index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.
12. A way to analyze sequences of events where the outcomes of prior events affect the probability of outcomes of subsequent events.
The BML Traffic Model
Group
Invarient
Markov Chains
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
De Bruijn Sequence
B - 125 = 1200
Look Back
Order of Operations - PEMDAS 'Please Excuse My Dear Aunt Sally'
14. 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 -
Dimension
The inverse of addition is subtraction
Factor Tree Alternate Approach
prime factors
15. Collection of objects. list all the objects in the set and enclosing the list in curly braces.
Dimension
Sign Rules for Division
set
Overtone
16. (a + b) + c = a + (b + c)
Noether's Theorem
Order of Operations - PEMDAS 'Please Excuse My Dear Aunt Sally'
B - 125 = 1200
Associative Property of Addition:
17. Requirements for Word Problem Solutions.
Genus
Non-Orientability
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
Intrinsic View
18. Are the fundamental building blocks of arithmetic.
Primes
Distributive Property:
a - c = b - c
Standard Deviation
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.'
Continuous Symmetry
Grouping Symbols
Additive Inverse:
Hyperland
20. 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.
Hypercube
The Prime Number Theorem
Law of Large Numbers
Modular Arithmetic
21. Positive integers are
counting numbers
Composite Numbers
One equal sign per line
Overtone
22. 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).
Aleph-Null
A number is divisible by 9
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
Cayley's Theorem
23. Topological objects are categorized by their _______ (number of holes). The genus of a surface is a feature of its global topology.
Set up an Equation
Genus
Exponents
The inverse of subtraction is addition
24. This result relates conserved physical quantities - like conservation of energy - to continuous symmetries of spacetime.
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25. Use parentheses - brackets - or curly braces to delimit the part of an expression you want evaluated first.
The index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.
Grouping Symbols
Exponents
Countable
26. 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
The Associative Property of Multiplication
The Set of Whole Numbers
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
Rarefactior
27. If a = b then
Countable
a - c = b - c
Permutation
perimeter
28. ____________ 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
Non-Euclidian Geometry
prime factors
Hypersphere
29. An important part of problem solving is identifying
Products and Factors
variable
Amplitude
Fundamental Theorem of Arithmetic
30. A '___________' infinite set is one that can be put into one-to-one correspondence with the set of natural numbers.
evaluate the expression in the innermost pair of grouping symbols first.
Associative Property of Addition:
Countable
De Bruijn Sequence
31. × - ( )( ) - · - 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
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.
Multiplication
Division is not Commutative
variable
32. Division by zero is undefined. Each of the expressions 6
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
Division by Zero
Spherical Geometry
A number is divisible by 10
33. A way to measure how far away a given individual result is from the average result.
Standard Deviation
Solve the Equation
Equation
Figurate Numbers
34. Dimension is how mathematicians express the idea of degrees of freedom
Dimension
Prime Deserts
Associative Property of Addition:
Cardinality
35. Breaks a complicated signal into a combination of simple sine waves. Fourier synthesis does the opposite - constructing a complicated signal from simple sine waves.
Multiplication by Zero
Fourier Analysis and Synthesis
Exponents
Standard Deviation
36. 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.
Principal Curvatures
Greatest Common Factor (GCF)
The Distributive Property (Subtraction)
Spherical Geometry
37. Is a symbol (usually a letter) that stands for a value that may vary.
Division is not Associative
Variable
set
a - c = b - c
38. 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.
a
Continuous Symmetry
Geometry
Rarefactior
39. Trigonometric functions - such as sine and cosine - are useful for modeling sound waves - because they oscillate between values
Prime Number
Periodic Function
Sign Rules for Division
Tone
40. (a · b) · c = a · (b · c)
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
Associative Property of Multiplication:
Factor Tree Alternate Approach
Polynomial
41. 4 more than a certain number is 12
Associative Property of Multiplication:
4 + x = 12
Euclid's Postulates
Factor Trees
42. This method can create a flat map from a curved surface while preserving all angles in any features present.
General Relativity
Transfinite
Stereographic Projection
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
43. Index p radicand
Ramsey Theory
The Commutative Property of Addition
The index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.
Rational
44. In some ways - the opposite of a multitude is a magnitude - which is ___________. In other words - there are no well defined partitions.
Overtone
Sign Rules for Division
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.
Continuous
45. If a = b then
Probability
a
Prime Deserts
General Relativity
46. 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
Euclid's Postulates
A prime number
Factor Trees
each whole number can be uniquely decomposed into products of primes.
47. If a = b then
a + c = b + c
Genus
Axiomatic Systems
Hypercube
48. When writing mathematical statements - follow the mantra:
Axiomatic Systems
The Additive Identity Property
Geometry
One equal sign per line
49. (a
division
Markov Chains
Division is not Associative
One equal sign per line
50. 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.
Law of Large Numbers
Properties of Equality
The inverse of subtraction is addition
Exponents
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