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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. (a
Division is not Associative
perimeter
Poincare Disk
Spaceland
2. 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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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
Division by Zero
Non-Orientability
Multiplicative Identity:
4. 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.
Cardinality
Multiplication by Zero
Irrational
Hamilton Cycle
5. 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
Extrinsic View
Torus
Answer the Question
The Additive Identity Property
6. This result says that the symmetries of geometric objects can be expressed as groups of permutations.
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7. The expression a/b means
A number is divisible by 5
a divided by b
Multiplicative Inverse:
bar graph
8. If a is any whole number - then a
The Same
The Multiplicative Identity Property
Amplitude
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
9. A way to measure how far away a given individual result is from the average result.
Tone
Standard Deviation
Intrinsic View
a
10. 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 Riemann Hypothesis
The Additive Identity Property
Multiplicative Identity:
11. Let a - b - and c be any whole numbers. Then - a
B - 125 = 1200
Tone
The Distributive Property (Subtraction)
Commutative Property of Multiplication:
12. If a = b then a + c = b + c If a = b then a - c = b - c If a = b then a
Ramsey Theory
Solve the Equation
A number is divisible by 10
Properties of Equality
13. If a represents any whole number - then a
Multiplication by Zero
Grouping Symbols
left to right
Amplitude
14. All integers are thus divided into three classes:
set
Intrinsic View
1. The unit 2. Prime numbers 3. Composite numbers
A number is divisible by 5
15. The state of appearing unchanged.
Invarient
The Commutative Property of Addition
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
Normal Distribution
16. ____________ 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
Hyperland
Markov Chains
Hyperbolic Geometry
17. When writing mathematical statements - follow the mantra:
One equal sign per line
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
A number is divisible by 10
Topology
18. Perform all additions and subtractions in the order presented
Factor Tree Alternate Approach
left to right
does not change the solution set.
Variable
19. 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).
Poincare Disk
A number is divisible by 3
Normal Distribution
Galois Theory
20. The process of taking a complicated signal and breaking it into sine and cosine components.
Multiplicative Identity:
Distributive Property:
The Multiplicative Identity Property
Fourier Analysis
21. 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
Products and Factors
Multiplying both Sides of an Equation by the Same Quantity
bar graph
Frequency
22. N = {1 - 2 - 3 - 4 - 5 - . . .}.
the set of natural numbers
variable
Division is not Associative
Spherical Geometry
23. Multiplication is equivalent to
repeated addition
Multiplication
Expected Value
division
24. 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
The BML Traffic Model
1. The unit 2. Prime numbers 3. Composite numbers
The Commutative Property of Addition
25. If its final digit is a 0 or 5.
prime factors
Tone
A number is divisible by 5
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
26. Determines the likelihood of events that are not independent of one another.
The Associative Property of Multiplication
a
Conditional Probability
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
27. 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
a · c = b · c for c does not equal 0
4 + x = 12
Pigeonhole Principle
Properties of Equality
28. The distribution of averages of many trials is always normal - even if the distribution of each trial is not.
Central Limit Theorem
Least Common Multiple (LCM)
The BML Traffic Model
Aleph-Null
29. A + (-a) = (-a) + a = 0
Additive Inverse:
per line
repeated addition
1. The unit 2. Prime numbers 3. Composite numbers
30. Assuming that the air is of uniform density and pressure to begin with - a region of high pressure will be balanced by a region of low pressure - called rarefaction - immediately following the compression
Rarefactior
Line Land
Modular Arithmetic
Wave Equation
31. 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.
Conditional Probability
Invarient
The BML Traffic Model
Modular Arithmetic
32. Instruments produce notes that have a fundamental frequency in combination with multiples of that frequency known as partials or overtones
The Commutative Property of Addition
Overtone
Frequency
Figurate Numbers
33. 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
Grouping Symbols
inline
Group
Associate Property of Addition
34. A · 1/a = 1/a · a = 1
The Distributive Property (Subtraction)
Multiplicative Inverse:
The Set of Whole Numbers
The inverse of multiplication is division
35. 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
per line
The Riemann Hypothesis
Ramsey Theory
Hypersphere
36. 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
Hamilton Cycle
Hypercube
Division is not Commutative
Polynomial
37. 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.
Modular Arithmetic
Non-Orientability
Torus
Bijection
38. 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.
Comparison Property
Greatest Common Factor (GCF)
Grouping Symbols
Geometry
39. If a - b - and c are any whole numbers - then a
1. The unit 2. Prime numbers 3. Composite numbers
The Associative Property of Multiplication
A number is divisible by 3
Fourier Analysis
40. A point in one dimension requires only one number to define it. The number line is a good example of a one-dimensional space.
Line Land
The Additive Identity Property
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
Greatest Common Factor (GCF)
41. Einstein's famous theory - relates gravity to the curvature of spacetime.
a divided by b
Extrinsic View
counting numbers
General Relativity
42. Original Balance minus River Tam's Withdrawal is Current Balance
B - 125 = 1200
Set up an Equation
Spaceland
Equation
43. 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
Hyperland
Set up a Variable Dictionary.
Associate Property of Addition
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
44. Every whole number can be uniquely factored as a product of primes. This result guarantees that if the prime factors are ordered from smallest to largest - everyone will get the same result when breaking a number into a product of prime factors.
Fundamental Theorem of Arithmetic
The Commutative Property of Addition
Unique Factorization Theorem
bar graph
45. Cantor called the cardinality of all the sets that can be put into one-to-one correspondence with the counting numbers - or 'Aleph Null.'
Aleph-Null
Expected Value
Discrete
Greatest Common Factor (GCF)
46. 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.
Dividing both Sides of an Equation by the Same Quantity
Continuous Symmetry
Normal Distribution
Problem of the Points
47. If a = b then
Euclid's Postulates
Spherical Geometry
a
The BML Traffic Model
48. This important result says that every natural number greater than one can be expressed as a product of primes in exactly one way.
Intrinsic View
per line
Fundamental Theorem of Arithmetic
Spherical Geometry
49. A flat map of hyperbolic space.
A number is divisible by 3
Division is not Associative
Galton Board
Poincare Disk
50. An instrument's _____ - the sound it produces - is a complex mixture of waves of different frequencies.
A number is divisible by 9
Invarient
Hypercube
Tone