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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. If a and b are any whole numbers - then a
Rarefactior
Galton Board
Associative Property of Addition:
Commutative Property of Multiplication
2. A topological invariant that relates a surface's vertices - edges - and faces.
a divided by b
Fourier Analysis
A number is divisible by 3
Euler Characteristic
3. (a
Division is not Associative
The Same
Exponents
a + c = b + c
4. The distribution of averages of many trials is always normal - even if the distribution of each trial is not.
Flat Land
Central Limit Theorem
Denominator
Geometry
5. A point in one dimension requires only one number to define it. The number line is a good example of a one-dimensional space.
Wave Equation
Line Land
General Relativity
Multiplication by Zero
6. 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
Multiplication
Line Land
Group
Invarient
7. In some ways - the opposite of a multitude is a magnitude - which is ___________. In other words - there are no well defined partitions.
Galois Theory
Continuous
perimeter
the set of natural numbers
8. 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
Standard Deviation
Multiplication
repeated addition
Multiplying both Sides of an Equation by the Same Quantity
9. We can think of the space between primes as 'prime deserts -' strings of consecutive numbers - none of which are prime.
Prime Deserts
Principal Curvatures
Figurate Numbers
The Commutative Property of Addition
10. Writing Mathematical equations - arrange your work one equation
De Bruijn Sequence
Cayley's Theorem
Overtone
per line
11. If a - b - and c are any whole numbers - then a
a divided by b
The Associative Property of Multiplication
a - c = b - c
Torus
12. In this type of geometry the angles of a triangle add up to less than 180 degrees. In such a system - one has to replace the parallel postulate with a version that admits many parallel lines.
Properties of Equality
Hyperbolic Geometry
The Multiplicative Identity Property
Solve the Equation
13. 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 index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.
Law of Large Numbers
repeated addition
Intrinsic View
14. 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.
Dividing both Sides of an Equation by the Same Quantity
Divisible
Multiplicative Inverse:
bar graph
15. The process of taking a complicated signal and breaking it into sine and cosine components.
1. The unit 2. Prime numbers 3. Composite numbers
A prime number
a + c = b + c
Fourier Analysis
16. Some numbers make geometric shapes when arranged as a collection of dots - for example - 16 makes a square - and 10 makes a triangle.
prime factors
Wave Equation
Figurate Numbers
Permutation
17. An arrangement where order matters.
a divided by b
Products and Factors
Permutation
The BML Traffic Model
18. Is the shortest string that contains all possible permutations of a particular length from a given set.
Commensurability
De Bruijn Sequence
Prime Number
Extrinsic View
19. 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.
Least Common Multiple (LCM)
The BML Traffic Model
Invarient
Grouping Symbols
20. 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
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
In Euclidean four-space
Factor Tree Alternate Approach
Primes
21. 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
Factor Tree Alternate Approach
Set up a Variable Dictionary.
Polynomial
22. An important part of problem solving is identifying
variable
Multiplicative Inverse:
Sign Rules for Division
evaluate the expression in the innermost pair of grouping symbols first.
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
The Distributive Property (Subtraction)
prime factors
Discrete
24. A way to measure how far away a given individual result is from the average result.
each whole number can be uniquely decomposed into products of primes.
Properties of Equality
Standard Deviation
Central Limit Theorem
25. This area of mathematics relates symmetry to whether or not an equation has a 'simple' solution.
Galois Theory
Exponents
Configuration Space
a - c = b - c
26. 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).
the set of natural numbers
Multiplicative Inverse:
Prime Number
The Riemann Hypothesis
27. 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
Division is not Commutative
Commutative Property of Addition:
Hypercube
Non-Orientability
28. A sphere can be thought of as a stack of circular discs of increasing - then decreasing - radii. The process of slicing is one way to visualize higher-dimensional objects via level curves and surfaces. A hypersphere can be thought of as a 'stack' of
Divisible
Prime Number
Hypersphere
Aleph-Null
29. The system that Euclid used in The Elements
Distributive Property:
Divisible
Axiomatic Systems
One equal sign per line
30. (a + b) + c = a + (b + c)
Associative Property of Addition:
Non-Orientability
Standard Deviation
each whole number can be uniquely decomposed into products of primes.
31. 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
Spaceland
Ramsey Theory
Rarefactior
Geometry
32. All integers are thus divided into three classes:
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
Pigeonhole Principle
1. The unit 2. Prime numbers 3. Composite numbers
Division by Zero
33. 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 inverse of multiplication is division
Commensurability
A number is divisible by 3
Standard Deviation
34. 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).
prime factors
Division by Zero
Permutation
A number is divisible by 3
35. 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 Set of Whole Numbers
The inverse of multiplication is division
Galois Theory
does not change the solution set.
36. 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)
Topology
Commensurability
Products and Factors
a - c = b - c
37. This method can create a flat map from a curved surface while preserving all angles in any features present.
Polynomial
Stereographic Projection
Probability
Spaceland
38. 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.
Amplitude
prime factors
Public Key Encryption
Probability
39. A
Division is not Commutative
Multiplying both Sides of an Equation by the Same Quantity
Tone
Expected Value
40. Requirements for Word Problem Solutions.
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
Figurate Numbers
Problem of the Points
Least Common Multiple (LCM)
41. A(b + c) = a · b + a · c a(b - c) = a · b - a · c
Associative Property of Addition:
Amplitude
Distributive Property:
Hyperland
42. A + b = b + a
Dimension
The Associative Property of Multiplication
Commutative Property of Addition:
Axiomatic Systems
43. Breaks a complicated signal into a combination of simple sine waves. Fourier synthesis does the opposite - constructing a complicated signal from simple sine waves.
Fourier Analysis and Synthesis
Transfinite
The inverse of subtraction is addition
1. The unit 2. Prime numbers 3. Composite numbers
44. The study of shape from the perspective of being on the surface of the shape.
B - 125 = 1200
a - c = b - c
Intrinsic View
Rational
45. W = {0 - 1 - 2 - 3 - 4 - 5 - . . .} is called
The index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.
Multiplying both Sides of an Equation by the Same Quantity
The Set of Whole Numbers
Pigeonhole Principle
46. 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
One equal sign per line
The Set of Whole Numbers
the set of natural numbers
47. An instrument's _____ - the sound it produces - is a complex mixture of waves of different frequencies.
Tone
Rarefactior
Torus
˜
48. The surface of a standard 'donut shape'.
Primes
Hypercube
Fundamental Theorem of Arithmetic
Torus
49. Rules for Rounding - To round a number to a particular place - follow these steps:
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
Composite Numbers
Transfinite
Multiplication
50. 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
General Relativity
The Kissing Circle
perimeter