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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.
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. 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.
Cardinality
Stereographic Projection
a - c = b - c
Division is not Commutative
2. Some numbers make geometric shapes when arranged as a collection of dots - for example - 16 makes a square - and 10 makes a triangle.
counting numbers
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
Figurate Numbers
Discrete
3. 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.
a + c = b + c
De Bruijn Sequence
Non-Orientability
Rational
4. (a + b) + c = a + (b + c)
Galton Board
Associative Property of Addition:
Commensurability
Figurate Numbers
5. Of central importance in Ramsey Theory - and in combinatorics in general - is the 'pigeonhole principle -' also known as Dirichlet's box. This principle simply states that we cannot fit n+1 pigeons into n pigeonholes in such a way that only one pigeo
Additive Inverse:
Unique Factorization Theorem
Irrational
Pigeonhole Principle
6. Uses second derivatives to relate acceleration in space to acceleration in time.
Flat Land
Wave Equation
Tone
Polynomial
7. 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
Solve the Equation
Divisible
Variable
8. If a = b then
Poincare Disk
Conditional Probability
a - c = b - c
Polynomial
9. 1. Find the prime factorizations of each number.
Galois Theory
Greatest Common Factor (GCF)
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
Least Common Multiple (LCM)
10. Cannot be written as a ratio of natural numbers.
The index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.
Irrational
B - 125 = 1200
Overtone
11. 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.
A number is divisible by 9
Divisible
Hyperland
Solution
12. Two equations if they have the same solution set.
A number is divisible by 10
Denominator
Equivalent Equations
Commensurability
13. 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.
Geometry
Products and Factors
Spaceland
Distributive Property:
14. Instruments produce notes that have a fundamental frequency in combination with multiples of that frequency known as partials or overtones
Bijection
Division is not Commutative
a · c = b · c for c does not equal 0
Overtone
15. Aka The Osculating Circle - a way to measure the curvature of a line.
The Kissing Circle
Multiplicative Inverse:
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
Bijection
16. The system that Euclid used in The Elements
Axiomatic Systems
Continuous
Division by Zero
Additive Inverse:
17. Codifies the 'average behavior' of a random event and is a key concept in the application of probability.
Expected Value
Additive Identity:
Hypersphere
Dimension
18. Does not change the solution set. That is - if a = b - then multiplying both sides of the equation by c produces the equivalent equation a
The Kissing Circle
˜
Multiplication by Zero
Multiplying both Sides of an Equation by the Same Quantity
19. An instrument's _____ - the sound it produces - is a complex mixture of waves of different frequencies.
Dimension
Prime Deserts
per line
Tone
20. 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.
The Associative Property of Multiplication
Stereographic Projection
Law of Large Numbers
Torus
21. An object possessing continuous symmetries can remain invariant while one symmetry is turned into another. A circle is an example of an object with continuous symmetries.
left to right
The Commutative Property of Addition
Set up a Variable Dictionary.
Continuous Symmetry
22. A
Probability
prime factors
Intrinsic View
Division is not Commutative
23. Objects are topologically equivalent if they can be continuously deformed into one another. Properties that are preserved during this process are called topological invariants.
Irrational
Fourier Analysis
Dividing both Sides of an Equation by the Same Quantity
Continuous
24. A + 0 = 0 + a = a
Line Land
Symmetry
The inverse of multiplication is division
Additive Identity:
25. Trigonometric functions - such as sine and cosine - are useful for modeling sound waves - because they oscillate between values
The Riemann Hypothesis
Hamilton Cycle
Greatest Common Factor (GCF)
Periodic Function
26. 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.
Set up an Equation
Axiomatic Systems
Noether's Theorem
27. 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.
Hamilton Cycle
Division by Zero
Associative Property of Addition:
does not change the solution set.
28. The multitude concept presented numbers as collections of discrete units - rather like indivisible atoms.
Discrete
Hypersphere
Overtone
Tone
29. The process of taking a complicated signal and breaking it into sine and cosine components.
Division is not Commutative
Transfinite
Fourier Analysis
The Distributive Property (Subtraction)
30. We can think of the space between primes as 'prime deserts -' strings of consecutive numbers - none of which are prime.
Prime Deserts
Modular Arithmetic
Poincare Disk
Additive Inverse:
31. Positive integers are
Rarefactior
Composite Numbers
Torus
counting numbers
32. 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.
In Euclidean four-space
Axiomatic Systems
Flat Land
Public Key Encryption
33. Is a path that visits every node in a graph and ends where it began.
Equivalent Equations
Spaceland
Primes
Hamilton Cycle
34. If a and b are any whole numbers - then a
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.
bar graph
The Associative Property of Multiplication
Commutative Property of Multiplication
35. If a = b then
a · c = b · c for c does not equal 0
Division is not Associative
˜
Fundamental Theorem of Arithmetic
36. This famous - as yet unproven - result relates to the distribution of prime numbers on the number line.
Principal Curvatures
Prime Number
Commutative Property of Addition:
The Riemann Hypothesis
37. Means approximately equal.
˜
each whole number can be uniquely decomposed into products of primes.
Set up a Variable Dictionary.
Equation
38. A factor tree is a way to visualize a number's
counting numbers
prime factors
Commensurability
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.
39. 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.
Group
Configuration Space
Spherical Geometry
Central Limit Theorem
40. A graph in which every node is connected to every other node is called a complete graph.
Standard Deviation
Irrational
Complete Graph
Multiplying both Sides of an Equation by the Same Quantity
41. This area of mathematics relates symmetry to whether or not an equation has a 'simple' solution.
Galois Theory
Solve the Equation
Set up a Variable Dictionary.
Commutative Property of Addition:
42. Non-Euclidean geometries abide by some - but not all of Euclid's five postulates.
Set up a Variable Dictionary.
Non-Euclidian Geometry
Irrational
Principal Curvatures
43. A + (-a) = (-a) + a = 0
Geometry
Fourier Analysis
variable
Additive Inverse:
44. The amount of displacement - as measured from the still surface line.
Composite Numbers
bar graph
The Kissing Circle
Amplitude
45. Has no factors other than 1 and itself
The BML Traffic Model
A prime number
The Set of Whole Numbers
Commutative Property of Multiplication:
46. A flat map of hyperbolic space.
prime factors
Multiplication by Zero
Poincare Disk
Prime Number
47. 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
Permutation
Distributive Property:
Central Limit Theorem
The Same
48. If its final digit is a 0 or 5.
Rarefactior
The Commutative Property of Addition
A number is divisible by 5
Associative Property of Multiplication:
49. 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 BML Traffic Model
The inverse of addition is subtraction
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
The Prime Number Theorem
50. Dimension is how mathematicians express the idea of degrees of freedom
Dimension
Multiplication by Zero
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.
perimeter
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