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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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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. 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.
Hyperbolic Geometry
Rarefactior
left to right
Frequency
2. 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
Dimension
Periodic Function
Line Land
3. TA model of a sequence of random events. Each marble that passes through the system represents a trial consisting of as many random events as there are rows in the system.
Galton Board
Galois Theory
Principal Curvatures
a + c = b + c
4. 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
Discrete
Distributive Property:
Polynomial
Hypersphere
5. If we start with a number x and subtract a number a - then adding a to the result will return us to the original number x. In symbols - x - a + a = x. So -
The inverse of subtraction is addition
Factor Tree Alternate Approach
a + c = b + c
Multiplication
6. 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.
Non-Euclidian Geometry
Torus
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.
Public Key Encryption
7. Let a - b - and c be any whole numbers. Then - a
Non-Orientability
The Distributive Property (Subtraction)
Equation
Associative Property of Multiplication:
8. 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.'
Multiplying both Sides of an Equation by the Same Quantity
repeated addition
Hyperland
prime factors
9. 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.
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
Bijection
The BML Traffic Model
The Same
10. The expression a/b means
A number is divisible by 3
Fourier Analysis
Group
a divided by b
11. 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 BML Traffic Model
Law of Large Numbers
Set up an Equation
Products and Factors
12. The state of appearing unchanged.
Multiplicative Identity:
Invarient
Multiplication
A number is divisible by 9
13. 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.
Equivalent Equations
Normal Distribution
Rarefactior
The Set of Whole Numbers
14. The process of taking a complicated signal and breaking it into sine and cosine components.
Fourier Analysis
A number is divisible by 5
Fundamental Theorem of Arithmetic
General Relativity
15. A flat map of hyperbolic space.
Poincare Disk
Grouping Symbols
Tone
Prime Deserts
16. Uses second derivatives to relate acceleration in space to acceleration in time.
A number is divisible by 9
Group
Wave Equation
Fourier Analysis and Synthesis
17. 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).
left to right
Countable
Prime Number
The Associative Property of Multiplication
18. (a · b) · c = a · (b · c)
Associative Property of Multiplication:
Stereographic Projection
prime factors
Expected Value
19. A topological invariant that relates a surface's vertices - edges - and faces.
Non-Euclidian Geometry
Euler Characteristic
One equal sign per line
1. The unit 2. Prime numbers 3. Composite numbers
20. 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.
Unique Factorization Theorem
˜
Ramsey Theory
Rational
21. 4 more than a certain number is 12
The Associative Property of Multiplication
The Distributive Property (Subtraction)
4 + x = 12
Frequency
22. If a = b then
division
a · c = b · c for c does not equal 0
Overtone
The Prime Number Theorem
23. 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
Hyperbolic Geometry
Least Common Multiple (LCM)
Factor Trees
The inverse of multiplication is division
24. 1. Find the prime factorizations of each number. To find the prime factorization one method is a factor tree where you begin with any two factors and proceed by dividing the numbers until all the ends are prime factors. 2. Star factors which are shar
Multiplying both Sides of an Equation by the Same Quantity
Least Common Multiple (LCM)
Axiomatic Systems
Invarient
25. 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.
Overtone
bar graph
Box Diagram
Multiplication by Zero
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.
A number is divisible by 10
Associative Property of Addition:
Geometry
The BML Traffic Model
27. Let a and b represent two whole numbers. Then - a + b = b + a.
The Commutative Property of Addition
Variable
Sign Rules for Division
Set up a Variable Dictionary.
28. An important part of problem solving is identifying
variable
Euclid's Postulates
Group
Solve the Equation
29. The distribution of averages of many trials is always normal - even if the distribution of each trial is not.
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
Continuous
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
Central Limit Theorem
30. A + (-a) = (-a) + a = 0
Poincare Disk
Additive Inverse:
Multiplication by Zero
Spaceland
31. 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.
Multiplying both Sides of an Equation by the Same Quantity
Geometry
Set up a Variable Dictionary.
Continuous Symmetry
32. 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.
Symmetry
Associate Property of Addition
Non-Orientability
Exponents
33. Means approximately equal.
Greatest Common Factor (GCF)
˜
division
Permutation
34. The amount of displacement - as measured from the still surface line.
A number is divisible by 3
Countable
Poincare Disk
Amplitude
35. 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 inverse of addition is subtraction
Variable
Box Diagram
per line
36. Are the fundamental building blocks of arithmetic.
Pigeonhole Principle
Primes
Multiplicative Inverse:
Prime Deserts
37. If a is any whole number - then a
Exponents
Solve the Equation
Prime Deserts
The Multiplicative Identity Property
38. A point in one dimension requires only one number to define it. The number line is a good example of a one-dimensional space.
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
Transfinite
The BML Traffic Model
Line Land
39. This area of mathematics relates symmetry to whether or not an equation has a 'simple' solution.
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
Galois Theory
Factor Trees
The index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.
40. Is the shortest string that contains all possible permutations of a particular length from a given set.
De Bruijn Sequence
Multiplicative Inverse:
variable
Frequency
41. This result says that the symmetries of geometric objects can be expressed as groups of permutations.
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42. Is a path that visits every node in a graph and ends where it began.
Commensurability
˜
Hamilton Cycle
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
43. Einstein's famous theory - relates gravity to the curvature of spacetime.
Public Key Encryption
Non-Orientability
General Relativity
variable
44. If grouping symbols are nested
evaluate the expression in the innermost pair of grouping symbols first.
Invarient
perimeter
Least Common Multiple (LCM)
45. 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
Group
Answer the Question
counting numbers
Continuous
46. Rules for Rounding - To round a number to a particular place - follow these steps:
Poincare Disk
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
Rarefactior
Normal Distribution
47. Trigonometric functions - such as sine and cosine - are useful for modeling sound waves - because they oscillate between values
a - c = b - c
Periodic Function
Box Diagram
Central Limit Theorem
48. Topological objects are categorized by their _______ (number of holes). The genus of a surface is a feature of its global topology.
Exponents
Genus
Fundamental Theorem of Arithmetic
Invarient
49. A way to analyze sequences of events where the outcomes of prior events affect the probability of outcomes of subsequent events.
Products and Factors
Markov Chains
Galton Board
Set up an Equation
50. Division by zero is undefined. Each of the expressions 6
Least Common Multiple (LCM)
Principal Curvatures
Multiplicative Identity:
Division by Zero
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