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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. Let a - b - and c be any whole numbers. Then - a
Non-Euclidian Geometry
Rational
The Distributive Property (Subtraction)
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
2. Positive integers are
counting numbers
a + c = b + c
Probability
The Distributive Property (Subtraction)
3. When writing mathematical statements - follow the mantra:
The BML Traffic Model
One equal sign per line
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
repeated addition
4. The cardinality of sets that cannot be put into one-to-one correspondence with the counting numbers - such as the set of real numbers - is referred to as c. The designations A_0 and c are known as 'transfinite' cardinalities.
Rarefactior
Transfinite
Torus
variable
5. A + (-a) = (-a) + a = 0
The Associative Property of Multiplication
Commutative Property of Addition:
Additive Inverse:
Order of Operations - PEMDAS 'Please Excuse My Dear Aunt Sally'
6. This famous - as yet unproven - result relates to the distribution of prime numbers on the number line.
left to right
Fundamental Theorem of Arithmetic
The Distributive Property (Subtraction)
The Riemann Hypothesis
7. If a = b then a + c = b + c If a = b then a - c = b - c If a = b then a
Properties of Equality
a · c = b · c for c does not equal 0
The inverse of subtraction is addition
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.
8. Every solution to a word problem must include a carefully crafted equation that accurately describes the constraints in the problem statement.
The Distributive Property (Subtraction)
Equivalent Equations
Set up an Equation
Conditional Probability
9. 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
Hypercube
set
Galois Theory
Expected Value
10. 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
Discrete
B - 125 = 1200
Pigeonhole Principle
Products and Factors
11. Arise from the attempt to measure all quantities with a common unit of measure.
bar graph
Solve the Equation
Rational
Overtone
12. 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.
Hyperland
a + c = b + c
The BML Traffic Model
Hamilton Cycle
13. Cantor called the cardinality of all the sets that can be put into one-to-one correspondence with the counting numbers - or 'Aleph Null.'
The Prime Number Theorem
Central Limit Theorem
Aleph-Null
Countable
14. 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
Aleph-Null
Complete Graph
The Same
Commensurability
15. Cannot be written as a ratio of natural numbers.
4 + x = 12
Principal Curvatures
Transfinite
Irrational
16. Objects are topologically equivalent if they can be continuously deformed into one another. Properties that are preserved during this process are called topological invariants.
The Additive Identity Property
Irrational
Commensurability
Solution
17. 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.
Flat Land
Continuous Symmetry
Public Key Encryption
a divided by b
18. If a = b then
a - c = b - c
evaluate the expression in the innermost pair of grouping symbols first.
Public Key Encryption
Additive Identity:
19. 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.
4 + x = 12
The Riemann Hypothesis
Commensurability
Cardinality
20. Points in two-dimensional space require two numbers to specify them completely. The Cartesian plane is a good way to envision two-dimensional space.
Flat Land
Additive Inverse:
Periodic Function
the set of natural numbers
21. 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
Multiplication by Zero
Divisible
Non-Euclidian Geometry
Answer the Question
22. Let a and b represent two whole numbers. Then - a + b = b + a.
Solution
Standard Deviation
Factor Tree Alternate Approach
The Commutative Property of Addition
23. A factor tree is a way to visualize a number's
Grouping Symbols
left to right
prime factors
The inverse of addition is subtraction
24. 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
Torus
Products and Factors
Multiplying both Sides of an Equation by the Same Quantity
Euclid's Postulates
25. When comparing two whole numbers a and b - only one of three possibilities is true: a < b or a = b or a > b.
Fundamental Theorem of Arithmetic
The Prime Number Theorem
Distributive Property:
Comparison Property
26. ____________ 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
Multiplication by Zero
Flat Land
Cardinality
Probability
27. (a + b) + c = a + (b + c)
Order of Operations - PEMDAS 'Please Excuse My Dear Aunt Sally'
Associative Property of Addition:
Exponents
Look Back
28. A '___________' infinite set is one that can be put into one-to-one correspondence with the set of natural numbers.
1. The unit 2. Prime numbers 3. Composite numbers
Countable
set
4 + x = 12
29. 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 Same
left to right
Spherical Geometry
30. 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.
Prime Deserts
Distributive Property:
Normal Distribution
The Prime Number Theorem
31. In some ways - the opposite of a multitude is a magnitude - which is ___________. In other words - there are no well defined partitions.
Figurate Numbers
Continuous
the set of natural numbers
Euclid's Postulates
32. The amount of displacement - as measured from the still surface line.
Frequency
Amplitude
Continuous
a · c = b · c for c does not equal 0
33. A way to measure how far away a given individual result is from the average result.
Wave Equation
Variable
Standard Deviation
Topology
34. Dimension is how mathematicians express the idea of degrees of freedom
repeated addition
Dimension
The Same
counting numbers
35. If a = b then
a + c = b + c
Continuous
Discrete
Products and Factors
36. You must let your readers know what each variable in your problem represents. This can be accomplished in a number of ways: Statements such as 'Let P represent the perimeter of the rectangle.' - Labeling unknown values with variables in a table - Lab
Set up a Variable Dictionary.
Division by Zero
Cardinality
Probability
37. This area of mathematics relates symmetry to whether or not an equation has a 'simple' solution.
Box Diagram
Galois Theory
Extrinsic View
Hyperland
38. Negative
A number is divisible by 3
The Kissing Circle
Spherical Geometry
Sign Rules for Division
39. An arrangement where order matters.
Variable
Permutation
4 + x = 12
Hamilton Cycle
40. At each level of the tree - break the current number into a product of two factors. The process is complete when all of the 'circled leaves' at the bottom of the tree are prime numbers. Arranging the factors in the 'circled leaves' in order. The fina
The index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.
Factor Trees
Group
Countable
41. 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.'
Multiplication by Zero
Divisible
Prime Number
inline
42. Let a - b - and c represent whole numbers. Then - (a + b) + c = a + (b + c).
Frequency
Associate Property of Addition
Dividing both Sides of an Equation by the Same Quantity
Hypercube
43. A point in one dimension requires only one number to define it. The number line is a good example of a one-dimensional space.
Dividing both Sides of an Equation by the Same Quantity
left to right
Irrational
Line Land
44. A(b + c) = a · b + a · c a(b - c) = a · b - a · c
Equation
In Euclidean four-space
Distributive Property:
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.
45. 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)
Commensurability
The Prime Number Theorem
Set up a Variable Dictionary.
Greatest Common Factor (GCF)
46. A way to analyze sequences of events where the outcomes of prior events affect the probability of outcomes of subsequent events.
The inverse of multiplication is division
Flat Land
Markov Chains
The Same
47. The process of taking a complicated signal and breaking it into sine and cosine components.
A prime number
Fourier Analysis
Expected Value
Stereographic Projection
48. Writing Mathematical equations - arrange your work one equation
set
repeated addition
Divisible
per line
49. 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.
Additive Inverse:
A number is divisible by 5
Fourier Analysis and Synthesis
Exponents
50. Non-Euclidean geometries abide by some - but not all of Euclid's five postulates.
Complete Graph
Fourier Analysis
Tone
Non-Euclidian Geometry