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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.
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. Objects are topologically equivalent if they can be continuously deformed into one another. Properties that are preserved during this process are called topological invariants.
Equivalent Equations
Irrational
Complete Graph
Axiomatic Systems
2. A topological object that can be used to study the allowable states of a given system.
Fourier Analysis
Configuration Space
Line Land
Hyperland
3. Breaks a complicated signal into a combination of simple sine waves. Fourier synthesis does the opposite - constructing a complicated signal from simple sine waves.
Permutation
Fourier Analysis and Synthesis
Euler Characteristic
Irrational
4. Requirements for Word Problem Solutions.
Multiplying both Sides of an Equation by the Same Quantity
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
The index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.
The Set of Whole Numbers
5. Positive integers are
Commutative Property of Multiplication:
Hypersphere
Figurate Numbers
counting numbers
6. A · 1 = 1 · a = a
variable
Additive Identity:
Multiplicative Identity:
The Same
7. Non-Euclidean geometries abide by some - but not all of Euclid's five postulates.
Solve the Equation
Non-Euclidian Geometry
1. The unit 2. Prime numbers 3. Composite numbers
Commutative Property of Addition:
8. 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.'
Euler Characteristic
Divisible
Commutative Property of Multiplication
Spaceland
9. Einstein's famous theory - relates gravity to the curvature of spacetime.
General Relativity
Multiplying both Sides of an Equation by the Same Quantity
Associative Property of Multiplication:
Flat Land
10. Is the shortest string that contains all possible permutations of a particular length from a given set.
Invarient
De Bruijn Sequence
Primes
1. The unit 2. Prime numbers 3. Composite numbers
11. If a - b - and c are any whole numbers - then a
The Associative Property of Multiplication
The index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.
4 + x = 12
prime factors
12. 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.'
Overtone
De Bruijn Sequence
Spherical Geometry
Hyperland
13. 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
Properties of Equality
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
Hypercube
Line Land
14. Instruments produce notes that have a fundamental frequency in combination with multiples of that frequency known as partials or overtones
Primes
Grouping Symbols
Normal Distribution
Overtone
15. 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.
Complete Graph
repeated addition
Principal Curvatures
Aleph-Null
16. In a mathematical sense - it is a transformation that leaves an object invariant. Symmetry is perhaps most familiar as an artistic or aesthetic concept. Designs are said to be symmetric if they exhibit specific kinds of balance - repetition - and/or
Periodic Function
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
Symmetry
perimeter
17. If its final digit is a 0.
Periodic Function
The BML Traffic Model
A number is divisible by 10
Division is not Associative
18. Perform all additions and subtractions in the order presented
Comparison Property
The inverse of multiplication is division
left to right
Prime Number
19. Are the fundamental building blocks of arithmetic.
Figurate Numbers
Unique Factorization Theorem
Commutative Property of Multiplication
Primes
20. Our standard notions of Pythagorean distance and angle via the inner product extend quite nicely from three-space.
variable
In Euclidean four-space
Answer the Question
The Kissing Circle
21. 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.
Axiomatic Systems
Hamilton Cycle
Hyperbolic Geometry
One equal sign per line
22. An important part of problem solving is identifying
The Associative Property of Multiplication
A number is divisible by 10
Order of Operations - PEMDAS 'Please Excuse My Dear Aunt Sally'
variable
23. 1. Any two points can be joined by a straight line. 2. Any straight line segment can be extended indefinitely in a straight line. 3. Given any straight line segment - a circle can be drawn having the segment as radius and one endpoint as center. 4. A
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24. Add and subtract
Central Limit Theorem
Tone
Solve the Equation
inline
25. Trigonometric functions - such as sine and cosine - are useful for modeling sound waves - because they oscillate between values
Multiplication
Periodic Function
The Same
Answer the Question
26. Some numbers make geometric shapes when arranged as a collection of dots - for example - 16 makes a square - and 10 makes a triangle.
Axiomatic Systems
Ramsey Theory
Figurate Numbers
Euler Characteristic
27. The fundamental theorem of arithmetic says that
Prime Number
each whole number can be uniquely decomposed into products of primes.
variable
the set of natural numbers
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
Multiplicative Identity:
Multiplication
Probability
A prime number
29. Let a and b represent two whole numbers. Then - a + b = b + a.
Commutative Property of Multiplication:
Variable
Rarefactior
The Commutative Property of Addition
30. Rules for Rounding - To round a number to a particular place - follow these steps:
Continuous Symmetry
Distributive Property:
A number is divisible by 10
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
31. Cannot be written as a ratio of natural numbers.
Equivalent Equations
bar graph
Irrational
Continuous
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).
A number is divisible by 3
A number is divisible by 9
counting numbers
Prime Number
33. This important result says that every natural number greater than one can be expressed as a product of primes in exactly one way.
Fundamental Theorem of Arithmetic
Markov Chains
does not change the solution set.
Standard Deviation
34. This method can create a flat map from a curved surface while preserving all angles in any features present.
Countable
Hypersphere
Stereographic Projection
Dividing both Sides of an Equation by the Same Quantity
35. If a represents any whole number - then a
Pigeonhole Principle
Non-Euclidian Geometry
Multiplication by Zero
The index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.
36. Aka The Osculating Circle - a way to measure the curvature of a line.
variable
Distributive Property:
The Kissing Circle
General Relativity
37. Collection of objects. list all the objects in the set and enclosing the list in curly braces.
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
set
Torus
Fourier Analysis and Synthesis
38. The solutions to this gambling dilemma is traditionally held to be the start of modern probability theory.
Equation
Conditional Probability
Problem of the Points
Galton Board
39. The system that Euclid used in The Elements
Spherical Geometry
counting numbers
A number is divisible by 10
Axiomatic Systems
40. 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
Standard Deviation
Pigeonhole Principle
Prime Number
General Relativity
41. Is a symbol (usually a letter) that stands for a value that may vary.
Public Key Encryption
Commutative Property of Multiplication
Amplitude
Variable
42. This result relates conserved physical quantities - like conservation of energy - to continuous symmetries of spacetime.
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43. Every solution to a word problem must include a carefully crafted equation that accurately describes the constraints in the problem statement.
Variable
Set up an Equation
B - 125 = 1200
Order of Operations - PEMDAS 'Please Excuse My Dear Aunt Sally'
44. The process of taking a complicated signal and breaking it into sine and cosine components.
Unique Factorization Theorem
The Distributive Property (Subtraction)
1. The unit 2. Prime numbers 3. Composite numbers
Fourier Analysis
45. 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).
Denominator
repeated addition
Conditional Probability
A number is divisible by 3
46. When writing mathematical statements - follow the mantra:
Galton Board
Central Limit Theorem
Composite Numbers
One equal sign per line
47. Reveals why we tend to find structure in seemingly random sets. Ramsey numbers indicate how big a set must be to guarantee the existence of certain minimal structures.
Solution
Dimension
variable
Ramsey Theory
48. If a is any whole number - then a
The Multiplicative Identity Property
Amplitude
Fourier Analysis
Primes
49. 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.
Wave Equation
A prime number
repeated addition
Law of Large Numbers
50. A point in three-dimensional space requires three numbers to fix its location.
Prime Deserts
Spaceland
Rarefactior
The Commutative Property of Addition