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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. When comparing two whole numbers a and b - only one of three possibilities is true: a < b or a = b or a > b.
Rarefactior
Comparison Property
Genus
Tone
2. Use parentheses - brackets - or curly braces to delimit the part of an expression you want evaluated first.
Euler Characteristic
Commensurability
Dimension
Grouping Symbols
3. The fundamental theorem of arithmetic says that
Symmetry
De Bruijn Sequence
Figurate Numbers
each whole number can be uniquely decomposed into products of primes.
4. 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
Commutative Property of Multiplication
prime factors
Group
a · c = b · c for c does not equal 0
5. An instrument's _____ - the sound it produces - is a complex mixture of waves of different frequencies.
Irrational
Multiplicative Inverse:
Division by Zero
Tone
6. A · 1/a = 1/a · a = 1
Multiplicative Inverse:
Hypersphere
a + c = b + c
The inverse of subtraction is addition
7. 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.'
Cayley's Theorem
The BML Traffic Model
The Prime Number Theorem
Dimension
8. In any ratio of two whole numbers - expressed as a fraction - we can interpret the first (top) number to be the 'counter -' or numerator
variable
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
Denominator
Products and Factors
9. All integers are thus divided into three classes:
Figurate Numbers
Overtone
a - c = b - c
1. The unit 2. Prime numbers 3. Composite numbers
10. 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.
Cardinality
bar graph
Additive Identity:
Expected Value
11. ____________ 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
Probability
The inverse of addition is subtraction
In Euclidean four-space
Rational
12. Also known as gluing diagrams - are a convenient way to examine intrinsic topology.
4 + x = 12
The Commutative Property of Addition
Prime Deserts
Box Diagram
13. This important result says that every natural number greater than one can be expressed as a product of primes in exactly one way.
Commensurability
Composite Numbers
Fundamental Theorem of Arithmetic
Division is not Commutative
14. Has no factors other than 1 and itself
Intrinsic View
Look Back
A prime number
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
15. The process of taking a complicated signal and breaking it into sine and cosine components.
repeated addition
Fourier Analysis
Division is not Commutative
a · c = b · c for c does not equal 0
16. 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
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
Probability
Topology
Multiplying both Sides of an Equation by the Same Quantity
17. 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
Products and Factors
Rational
Factor Tree Alternate Approach
Set up an Equation
18. This area of mathematics relates symmetry to whether or not an equation has a 'simple' solution.
Galois Theory
Hyperland
Periodic Function
Commutative Property of Multiplication
19. Breaks a complicated signal into a combination of simple sine waves. Fourier synthesis does the opposite - constructing a complicated signal from simple sine waves.
A number is divisible by 10
Non-Euclidian Geometry
Fourier Analysis and Synthesis
Factor Trees
20. A topological object that can be used to study the allowable states of a given system.
Bijection
Configuration Space
The Kissing Circle
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
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).
Factor Tree Alternate Approach
Multiplication
A number is divisible by 9
Hypercube
22. The amount of displacement - as measured from the still surface line.
Irrational
Expected Value
Amplitude
Multiplication by Zero
23. 1. Parentheses (or any grouping symbol {braces} - [square brackets] - |absolute value|)
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24. 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
Grouping Symbols
Variable
Figurate Numbers
25. 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.
Spherical Geometry
Multiplying both Sides of an Equation by the Same Quantity
Bijection
Normal Distribution
26. A point in three-dimensional space requires three numbers to fix its location.
The Set of Whole Numbers
Spaceland
bar graph
Non-Orientability
27. Let a and b represent two whole numbers. Then - a + b = b + a.
One equal sign per line
A number is divisible by 9
Topology
The Commutative Property of Addition
28. 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.
Continuous Symmetry
Poincare Disk
perimeter
Commutative Property of Addition:
29. A flat map of hyperbolic space.
Countable
set
Poincare Disk
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
30. If a is any whole number - then a
B - 125 = 1200
The Multiplicative Identity Property
Geometry
A number is divisible by 9
31. 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.
Stereographic Projection
Galton Board
The Multiplicative Identity Property
Non-Euclidian Geometry
32. (a · b) · c = a · (b · c)
Solution
a · c = b · c for c does not equal 0
Associative Property of Multiplication:
Cardinality
33. 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.
Law of Large Numbers
a divided by b
The Multiplicative Identity Property
Hamilton Cycle
34. 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
Stereographic Projection
Symmetry
Non-Euclidian Geometry
Galton Board
35. 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
Genus
Frequency
Torus
Multiplicative Identity:
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
A number is divisible by 10
The Additive Identity Property
Hamilton Cycle
Set up a Variable Dictionary.
37. 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.
Unique Factorization Theorem
Periodic Function
Genus
Geometry
38. Rules for Rounding - To round a number to a particular place - follow these steps:
The Multiplicative Identity Property
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
Products and Factors
Transfinite
39. If a = b then
Factor Tree Alternate Approach
a
Commutative Property of Multiplication:
Modular Arithmetic
40. Objects are topologically equivalent if they can be continuously deformed into one another. Properties that are preserved during this process are called topological invariants.
Multiplicative Identity:
a + c = b + c
Standard Deviation
Irrational
41. If a = b then a + c = b + c If a = b then a - c = b - c If a = b then a
Fundamental Theorem of Arithmetic
Multiplication by Zero
Properties of Equality
Frequency
42. 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.
Bijection
Solution
Additive Identity:
a divided by b
43. Collection of objects. list all the objects in the set and enclosing the list in curly braces.
Least Common Multiple (LCM)
set
Symmetry
Continuous
44. A '___________' infinite set is one that can be put into one-to-one correspondence with the set of natural numbers.
Wave Equation
Additive Identity:
the set of natural numbers
Countable
45. Points in two-dimensional space require two numbers to specify them completely. The Cartesian plane is a good way to envision two-dimensional space.
The Riemann Hypothesis
Irrational
Multiplicative Identity:
Flat Land
46. The multitude concept presented numbers as collections of discrete units - rather like indivisible atoms.
B - 125 = 1200
Discrete
General Relativity
Modular Arithmetic
47. 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.
Products and Factors
Hyperbolic Geometry
Topology
Hyperland
48. A number is divisible by 2
Solution
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
Box Diagram
variable
49. 1. Find the prime factorizations of each number.
Genus
The Set of Whole Numbers
Line Land
Greatest Common Factor (GCF)
50. Is the shortest string that contains all possible permutations of a particular length from a given set.
De Bruijn Sequence
Invarient
Factor Tree Alternate Approach
Additive Identity: