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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. An important part of problem solving is identifying
variable
Modular Arithmetic
Solve the Equation
Associative Property of Multiplication:
2. All integers are thus divided into three classes:
The Same
1. The unit 2. Prime numbers 3. Composite numbers
Hypercube
Extrinsic View
3. 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
The Same
Additive Inverse:
Modular Arithmetic
Set up a Variable Dictionary.
4. Collection of objects. list all the objects in the set and enclosing the list in curly braces.
set
variable
each whole number can be uniquely decomposed into products of primes.
Rational
5. (a
The Commutative Property of Addition
Division is not Associative
set
a · c = b · c for c does not equal 0
6. Original Balance minus River Tam's Withdrawal is Current Balance
Conditional Probability
B - 125 = 1200
Periodic Function
Hypersphere
7. Some favor repeatedly dividing by 2 until the result is no longer divisible by 2. Then try repeatedly dividing by the next prime until the result is no longer divisible by that prime. The process terminates when the last resulting quotient is equal t
Discrete
Factor Tree Alternate Approach
Solution
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.
8. If a and b are any whole numbers - then a
Multiplication by Zero
Torus
Commutative Property of Multiplication
Intrinsic View
9. To describe and extend a numerical pattern
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.
Spaceland
Composite Numbers
Solve the Equation
10. Positive integers are
Amplitude
counting numbers
Euclid's Postulates
Non-Euclidian Geometry
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.
Unique Factorization Theorem
prime factors
Configuration Space
does not change the solution set.
12. 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
bar graph
left to right
Factor Trees
Extrinsic View
13. A(b + c) = a · b + a · c a(b - c) = a · b - a · c
The Prime Number Theorem
Distributive Property:
Genus
Multiplication
14. Arise from the attempt to measure all quantities with a common unit of measure.
a · c = b · c for c does not equal 0
bar graph
Grouping Symbols
Rational
15. If a whole number is not a prime number - then it is called a...
Line Land
Composite Numbers
Dimension
The index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.
16. 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 -
De Bruijn Sequence
left to right
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
17. If a = b then a + c = b + c If a = b then a - c = b - c If a = b then a
Extrinsic View
Fourier Analysis
Properties of Equality
Central Limit Theorem
18. Cantor called the cardinality of all the sets that can be put into one-to-one correspondence with the counting numbers - or 'Aleph Null.'
Aleph-Null
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
a · c = b · c for c does not equal 0
Hypersphere
19. A point in one dimension requires only one number to define it. The number line is a good example of a one-dimensional space.
Line Land
Law of Large Numbers
Sign Rules for Division
The Riemann Hypothesis
20. If a = b then
Transfinite
Configuration Space
a · c = b · c for c does not equal 0
Irrational
21. Mathematical statement that equates two mathematical expressions.
Associative Property of Addition:
Equation
Continuous
The Associative Property of Multiplication
22. Two equations if they have the same solution set.
Figurate Numbers
Variable
Equivalent Equations
Look Back
23. Some numbers make geometric shapes when arranged as a collection of dots - for example - 16 makes a square - and 10 makes a triangle.
One equal sign per line
does not change the solution set.
Figurate Numbers
Commensurability
24. 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.
Exponents
Cayley's Theorem
Hypercube
Modular Arithmetic
25. This famous - as yet unproven - result relates to the distribution of prime numbers on the number line.
Continuous
Box Diagram
The Riemann Hypothesis
Divisible
26. 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.
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
Commutative Property of Multiplication
Geometry
Configuration Space
27. Solving Equations
Commutative Property of Addition:
Additive Identity:
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
Euler Characteristic
28. In the expression 3
Galton Board
Complete Graph
A number is divisible by 3
Products and Factors
29. Let a and b represent two whole numbers. Then - a + b = b + a.
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
Box Diagram
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
The Commutative Property of Addition
30. If its final digit is a 0 or 5.
Extrinsic View
Rational
Aleph-Null
A number is divisible by 5
31. This method can create a flat map from a curved surface while preserving all angles in any features present.
Bijection
Primes
Least Common Multiple (LCM)
Stereographic Projection
32. 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).
Denominator
The Associative Property of Multiplication
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
A number is divisible by 9
33. If a is any whole number - then a
Poincare Disk
a + c = b + c
The Multiplicative Identity Property
per line
34. 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.
Poincare Disk
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.
A number is divisible by 3
Normal Distribution
35. The cardinality of sets that cannot be put into one-to-one correspondence with the counting numbers - such as the set of real numbers - is referred to as c. The designations A_0 and c are known as 'transfinite' cardinalities.
A number is divisible by 9
Transfinite
Divisible
Probability
36. Uses second derivatives to relate acceleration in space to acceleration in time.
A number is divisible by 3
Complete Graph
Wave Equation
In Euclidean four-space
37. If the sum of its digits is divisible by 3 (ex: 3591 is divisible by 3 since 3 + 5 + 9 + 1 = 18 is divisible by 3).
Wave Equation
Comparison Property
Greatest Common Factor (GCF)
A number is divisible by 3
38. When comparing two whole numbers a and b - only one of three possibilities is true: a < b or a = b or a > b.
Comparison Property
Markov Chains
Commutative Property of Multiplication
Continuous Symmetry
39. This result says that the symmetries of geometric objects can be expressed as groups of permutations.
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40. × - ( )( ) - · - 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
Poincare Disk
Topology
Fourier Analysis and Synthesis
41. 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.'
Stereographic Projection
Principal Curvatures
The Prime Number Theorem
a - c = b - c
42. Negative
Sign Rules for Division
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
each whole number can be uniquely decomposed into products of primes.
Euler Characteristic
43. 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
Commutative Property of Multiplication:
Answer the Question
Galton Board
Divisible
44. We can think of the space between primes as 'prime deserts -' strings of consecutive numbers - none of which are prime.
Line Land
Intrinsic View
Public Key Encryption
Prime Deserts
45. Writing Mathematical equations - arrange your work one equation
Genus
Products and Factors
The inverse of addition is subtraction
per line
46. An arrangement where order matters.
Factor Tree Alternate Approach
Probability
Associative Property of Multiplication:
Permutation
47. A factor tree is a way to visualize a number's
prime factors
Additive Identity:
The inverse of addition is subtraction
The Commutative Property of Addition
48. A
Intrinsic View
B - 125 = 1200
Problem of the Points
Division is not Commutative
49. 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.
Modular Arithmetic
In Euclidean four-space
a + c = b + c
left to right
50. A + b = b + a
A number is divisible by 3
Factor Trees
Commensurability
Commutative Property of Addition:
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