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Test your basic knowledge |
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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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. If a = b then a + c = b + c If a = b then a - c = b - c If a = b then a
division
Rarefactior
set
Properties of Equality
2. Also known as gluing diagrams - are a convenient way to examine intrinsic topology.
The Riemann Hypothesis
Box Diagram
Grouping Symbols
The Commutative Property of Addition
3. 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.'
The Prime Number Theorem
Greatest Common Factor (GCF)
Rational
A number is divisible by 3
4. 4 more than a certain number is 12
Intrinsic View
Spherical Geometry
4 + x = 12
Poincare Disk
5. You must always solve the equation set up in the previous step.
Line Land
Genus
Solve the Equation
Multiplicative Identity:
6. If grouping symbols are nested
evaluate the expression in the innermost pair of grouping symbols first.
a - c = b - c
Set up a Variable Dictionary.
Overtone
7. 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.
Transfinite
Commutative Property of Multiplication
Least Common Multiple (LCM)
Fourier Analysis and Synthesis
8. If a is any whole number - then a
each whole number can be uniquely decomposed into products of primes.
Factor Tree Alternate Approach
The inverse of subtraction is addition
The Multiplicative Identity Property
9. (a · b) · c = a · (b · c)
perimeter
Complete Graph
Associative Property of Multiplication:
Symmetry
10. A way to analyze sequences of events where the outcomes of prior events affect the probability of outcomes of subsequent events.
Associate Property of Addition
Stereographic Projection
Ramsey Theory
Markov Chains
11. This result relates conserved physical quantities - like conservation of energy - to continuous symmetries of spacetime.
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12. 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 Kissing Circle
Configuration Space
Poincare Disk
Public Key Encryption
13. 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.
Denominator
set
Properties of Equality
Principal Curvatures
14. Add and subtract
The inverse of subtraction is addition
Invarient
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
inline
15. 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.
Multiplicative Identity:
Cardinality
Flat Land
Noether's Theorem
16. ____________ 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
Irrational
Rational
Probability
Factor Tree Alternate Approach
17. Is the shortest string that contains all possible permutations of a particular length from a given set.
Fourier Analysis
Spaceland
De Bruijn Sequence
Denominator
18. We can think of the space between primes as 'prime deserts -' strings of consecutive numbers - none of which are prime.
Prime Deserts
Principal Curvatures
General Relativity
each whole number can be uniquely decomposed into products of primes.
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.'
a - c = b - c
Polynomial
Hyperland
Prime Deserts
20. 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
Expected Value
˜
Fundamental Theorem of Arithmetic
Answer the Question
21. 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 -
Set up an Equation
Euler Characteristic
The inverse of addition is subtraction
Comparison Property
22. 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
Probability
Principal Curvatures
The BML Traffic Model
Group
23. When comparing two whole numbers a and b - only one of three possibilities is true: a < b or a = b or a > b.
A number is divisible by 9
Comparison Property
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
Spaceland
24. A · b = b · a
Normal Distribution
Sign Rules for Division
1. The unit 2. Prime numbers 3. Composite numbers
Commutative Property of Multiplication:
25. 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.
Distributive Property:
Order of Operations - PEMDAS 'Please Excuse My Dear Aunt Sally'
Bijection
evaluate the expression in the innermost pair of grouping symbols first.
26. A flat map of hyperbolic space.
Commensurability
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.
The inverse of subtraction is addition
27. 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.
Cayley's Theorem
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
Equivalent Equations
bar graph
28. A + (-a) = (-a) + a = 0
Denominator
Transfinite
The Kissing Circle
Additive Inverse:
29. A number is divisible by 2
Division by Zero
Periodic Function
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
Configuration Space
30. Einstein's famous theory - relates gravity to the curvature of spacetime.
Commutative Property of Multiplication
The Associative Property of Multiplication
General Relativity
Standard Deviation
31. A point in one dimension requires only one number to define it. The number line is a good example of a one-dimensional space.
Law of Large Numbers
Ramsey Theory
Euclid's Postulates
Line Land
32. Instruments produce notes that have a fundamental frequency in combination with multiples of that frequency known as partials or overtones
does not change the solution set.
Overtone
Sign Rules for Division
Products and Factors
33. A point in three-dimensional space requires three numbers to fix its location.
Spaceland
perimeter
Bijection
inline
34. A whole number (other than 1) is a _____________ if its only factors (divisors) are 1 and itself. Equivalently - a number is prime if and only if it has exactly two factors (divisors).
a - c = b - c
Prime Number
Overtone
Associative Property of Addition:
35. Let a and b be whole numbers. Then a is _______________ by b if and only if the remainder is zero when a is divided by b. In this case - we say that 'b is a divisor of a.'
Extrinsic View
Divisible
1. The unit 2. Prime numbers 3. Composite numbers
The Same
36. A factor tree is a way to visualize a number's
prime factors
Exponents
Associate Property of Addition
Set up a Variable Dictionary.
37. An arrangement where order matters.
Expected Value
a · c = b · c for c does not equal 0
Permutation
Frequency
38. 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.
Distributive Property:
evaluate the expression in the innermost pair of grouping symbols first.
Box Diagram
Dividing both Sides of an Equation by the Same Quantity
39. If a = b then
a · c = b · c for c does not equal 0
Multiplication by Zero
Commensurability
The inverse of addition is subtraction
40. Originally known as analysis situs
Primes
Multiplication by Zero
Topology
Factor Trees
41. In the expression 3
Products and Factors
The Additive Identity Property
Commensurability
Public Key Encryption
42. The distribution of averages of many trials is always normal - even if the distribution of each trial is not.
Figurate Numbers
Tone
The Kissing Circle
Central Limit Theorem
43. If a represents any whole number - then a
Multiplication by Zero
Irrational
Public Key Encryption
Central Limit Theorem
44. A way to measure how far away a given individual result is from the average result.
Markov Chains
Conditional Probability
A number is divisible by 3
Standard Deviation
45. 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).
A number is divisible by 9
Unique Factorization Theorem
The Kissing Circle
Division is not Commutative
46. The state of appearing unchanged.
Equation
Probability
Irrational
Invarient
47. × - ( )( ) - · - 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
Hyperbolic Geometry
Look Back
Multiplication
a · c = b · c for c does not equal 0
48. Division by zero is undefined. Each of the expressions 6
Factor Tree Alternate Approach
Division by Zero
Poincare Disk
The inverse of subtraction is addition
49. 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
Markov Chains
Noether's Theorem
Hyperbolic Geometry
50. 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
Associative Property of Addition:
Genus
Hypercube
Fourier Analysis
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