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Test your basic knowledge |
CLEP General Math: Number Sense - Patterns - Algebraic Thinking
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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. 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.
The Distributive Property (Subtraction)
The BML Traffic Model
Grouping Symbols
Primes
2. 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.
Topology
Law of Large Numbers
Axiomatic Systems
The BML Traffic Model
3. 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 Kissing Circle
The inverse of addition is subtraction
Answer the Question
each whole number can be uniquely decomposed into products of primes.
4. Whether or not we hear waves as sound has everything to do with their _____________ - or how many times every second the molecules switch from compression to rarefaction and back to compression again - and their intensity - or how much the air is com
Greatest Common Factor (GCF)
Frequency
Modular Arithmetic
a · c = b · c for c does not equal 0
5. A '___________' infinite set is one that can be put into one-to-one correspondence with the set of natural numbers.
A prime number
Permutation
Central Limit Theorem
Countable
6. A point in one dimension requires only one number to define it. The number line is a good example of a one-dimensional space.
Noether's Theorem
a
Modular Arithmetic
Line Land
7. Aka The Osculating Circle - a way to measure the curvature of a line.
Division is not Commutative
Equivalent Equations
bar graph
The Kissing Circle
8. All integers are thus divided into three classes:
Division is not Commutative
does not change the solution set.
1. The unit 2. Prime numbers 3. Composite numbers
The Associative Property of Multiplication
9. Non-Euclidean geometries abide by some - but not all of Euclid's five postulates.
Conditional Probability
The BML Traffic Model
Galois Theory
Non-Euclidian Geometry
10. Writing Mathematical equations - arrange your work one equation
Denominator
division
repeated addition
per line
11. The expression a/b means
A number is divisible by 10
a divided by b
Probability
Tone
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.
Public Key Encryption
Flat Land
variable
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
13. If its final digit is a 0 or 5.
Fourier Analysis and Synthesis
Grouping Symbols
A number is divisible by 9
A number is divisible by 5
14. A topological object that can be used to study the allowable states of a given system.
Configuration Space
Associate Property of Addition
Factor Trees
counting numbers
15. Is a symbol (usually a letter) that stands for a value that may vary.
Variable
Look Back
Multiplication
General Relativity
16. Collection of objects. list all the objects in the set and enclosing the list in curly braces.
Exponents
Answer the Question
Fundamental Theorem of Arithmetic
set
17. W = {0 - 1 - 2 - 3 - 4 - 5 - . . .} is called
Dimension
Sign Rules for Division
Denominator
The Set of Whole Numbers
18. 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.'
Primes
Composite Numbers
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
The Prime Number Theorem
19. Division by zero is undefined. Each of the expressions 6
Division by Zero
Line Land
Problem of the Points
The inverse of subtraction is addition
20. The surface of a standard 'donut shape'.
Torus
Composite Numbers
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
Box Diagram
21. 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).
Prime Number
Hamilton Cycle
Genus
A number is divisible by 9
22. Are the fundamental building blocks of arithmetic.
Stereographic Projection
counting numbers
Invarient
Primes
23. A topological invariant that relates a surface's vertices - edges - and faces.
Euler Characteristic
Modular Arithmetic
Wave Equation
per line
24. To describe and extend a numerical pattern
Multiplicative Identity:
Non-Orientability
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.
Rational
25. Instruments produce notes that have a fundamental frequency in combination with multiples of that frequency known as partials or overtones
De Bruijn Sequence
Commutative Property of Multiplication
Rational
Overtone
26. 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
The Distributive Property (Subtraction)
Standard Deviation
4 + x = 12
27. 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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28. 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.
Fourier Analysis and Synthesis
does not change the solution set.
The Multiplicative Identity Property
Galton Board
29. 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.
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
Factor Tree Alternate Approach
Hyperbolic Geometry
Denominator
30. N = {1 - 2 - 3 - 4 - 5 - . . .}.
The inverse of addition is subtraction
Associative Property of Multiplication:
repeated addition
the set of natural numbers
31. 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
Tone
Wave Equation
The Same
Polynomial
32. 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.
Comparison Property
Continuous Symmetry
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 Prime Number Theorem
33. Means approximately equal.
Order of Operations - PEMDAS 'Please Excuse My Dear Aunt Sally'
Hamilton Cycle
Prime Number
˜
34. Uses second derivatives to relate acceleration in space to acceleration in time.
Grouping Symbols
Products and Factors
Solve the Equation
Wave Equation
35. In some ways - the opposite of a multitude is a magnitude - which is ___________. In other words - there are no well defined partitions.
Topology
General Relativity
One equal sign per line
Continuous
36. An algebraic 'sentence' containing an unknown quantity.
Group
Standard Deviation
One equal sign per line
Polynomial
37. A(b + c) = a · b + a · c a(b - c) = a · b - a · c
Box Diagram
Standard Deviation
Distributive Property:
Multiplication
38. Index p radicand
Composite Numbers
per line
Geometry
The index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.
39. 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.
Box Diagram
Cardinality
The index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.
Equivalent Equations
40. The fundamental theorem of arithmetic says that
Periodic Function
each whole number can be uniquely decomposed into products of primes.
inline
The Distributive Property (Subtraction)
41. 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
Modular Arithmetic
Hypersphere
Grouping Symbols
42. Two equations if they have the same solution set.
Equivalent Equations
Division is not Commutative
Factor Trees
a + c = b + c
43. Positive integers are
Hamilton Cycle
Set up an Equation
Dimension
counting numbers
44. 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.
The inverse of addition is subtraction
Factor Tree Alternate Approach
The Same
Bijection
45. When writing mathematical statements - follow the mantra:
One equal sign per line
Non-Euclidian Geometry
Multiplicative Inverse:
Associative Property of Multiplication:
46. Some numbers make geometric shapes when arranged as a collection of dots - for example - 16 makes a square - and 10 makes a triangle.
Figurate Numbers
a
De Bruijn Sequence
Non-Euclidian Geometry
47. A graph in which every node is connected to every other node is called a complete graph.
each whole number can be uniquely decomposed into products of primes.
Spherical Geometry
A prime number
Complete Graph
48. This famous - as yet unproven - result relates to the distribution of prime numbers on the number line.
˜
Set up an Equation
Fourier Analysis and Synthesis
The Riemann Hypothesis
49. ____________ 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
Comparison Property
Associative Property of Multiplication:
Probability
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
50. If a = b then
a + c = b + c
Factor Tree Alternate Approach
a
Least Common Multiple (LCM)