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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.
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. Two equations if they have the same solution set.
Conditional Probability
Fourier Analysis and Synthesis
Equivalent Equations
Extrinsic View
2. Is a path that visits every node in a graph and ends where it began.
Fundamental Theorem of Arithmetic
Multiplicative Inverse:
Commensurability
Hamilton Cycle
3. This method can create a flat map from a curved surface while preserving all angles in any features present.
Continuous
Fourier Analysis
a divided by b
Stereographic Projection
4. The expression a/b means
Irrational
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
Conditional Probability
a divided by b
5. Means approximately equal.
˜
Equivalent Equations
Denominator
inline
6. 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.
the set of natural numbers
Transfinite
Topology
inline
7. Our standard notions of Pythagorean distance and angle via the inner product extend quite nicely from three-space.
Solve the Equation
Poincare Disk
One equal sign per line
In Euclidean four-space
8. The distribution of averages of many trials is always normal - even if the distribution of each trial is not.
B - 125 = 1200
Public Key Encryption
Central Limit Theorem
Transfinite
9. If on a surface there is no meaningful way to tell an object's orientation (left or right handedness) - the surface is said to be non-orientable.
Symmetry
Non-Orientability
The Prime Number Theorem
Multiplicative Identity:
10. This result says that the symmetries of geometric objects can be expressed as groups of permutations.
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11. A · b = b · a
Frequency
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
Commutative Property of Multiplication:
The Associative Property of Multiplication
12. Writing Mathematical equations - arrange your work one equation
Multiplying both Sides of an Equation by the Same Quantity
Sign Rules for Division
per line
Solve the Equation
13. The process of taking a complicated signal and breaking it into sine and cosine components.
Fourier Analysis
Multiplicative Inverse:
Spaceland
Divisible
14. The inverse of multiplication
set
Set up a Variable Dictionary.
division
Associative Property of Multiplication:
15. 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.
Polynomial
The inverse of multiplication is division
Ramsey Theory
The Multiplicative Identity Property
16. A way to measure how far away a given individual result is from the average result.
Standard Deviation
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
Euler Characteristic
Sign Rules for Division
17. The state of appearing unchanged.
Invarient
Noether's Theorem
Properties of Equality
Associative Property of Multiplication:
18. Has no factors other than 1 and itself
A number is divisible by 9
A prime number
1. The unit 2. Prime numbers 3. Composite numbers
Modular Arithmetic
19. Let a and b represent two whole numbers. Then - a + b = b + a.
Exponents
the set of natural numbers
Ramsey Theory
The Commutative Property of Addition
20. 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
Dividing both Sides of an Equation by the Same Quantity
left to right
Least Common Multiple (LCM)
Non-Euclidian Geometry
21. An equation is a numerical value that satisfies the equation. That is - when the variable in the equation is replaced by the solution - a true statement results.
Euler Characteristic
Ramsey Theory
Fourier Analysis and Synthesis
Solution
22. 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.'
General Relativity
Divisible
A number is divisible by 5
Line Land
23. Negative
a + c = b + c
Divisible
Sign Rules for Division
Countable
24. If its final digit is a 0 or 5.
Multiplication by Zero
A number is divisible by 5
Discrete
Rarefactior
25. You must always solve the equation set up in the previous step.
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
Solve the Equation
Frequency
Central Limit Theorem
26. If its final digit is a 0.
Problem of the Points
A number is divisible by 10
Complete Graph
˜
27. Positive integers are
variable
counting numbers
The inverse of addition is subtraction
Discrete
28. Perform all additions and subtractions in the order presented
Genus
Stereographic Projection
Transfinite
left to right
29. 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
Sign Rules for Division
Dividing both Sides of an Equation by the Same Quantity
Noether's Theorem
30. If a = b then a + c = b + c If a = b then a - c = b - c If a = b then a
The inverse of addition is subtraction
Properties of Equality
Non-Euclidian Geometry
The Riemann Hypothesis
31. This important result says that every natural number greater than one can be expressed as a product of primes in exactly one way.
Fundamental Theorem of Arithmetic
Axiomatic Systems
Transfinite
Periodic Function
32. An algebraic 'sentence' containing an unknown quantity.
Hypersphere
Associative Property of Addition:
Answer the Question
Polynomial
33. Mathematical statement that equates two mathematical expressions.
Galton Board
Non-Orientability
Prime Number
Equation
34. Topological objects are categorized by their _______ (number of holes). The genus of a surface is a feature of its global topology.
Set up a Variable Dictionary.
General Relativity
Division is not Associative
Genus
35. When comparing two whole numbers a and b - only one of three possibilities is true: a < b or a = b or a > b.
counting numbers
The inverse of subtraction is addition
Comparison Property
Multiplication
36. 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.
General Relativity
A number is divisible by 5
Geometry
Denominator
37. Solving Equations
Problem of the Points
Prime Number
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
Commutative Property of Multiplication:
38. A flat map of hyperbolic space.
Intrinsic View
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.
Poincare Disk
Division is not Commutative
39. 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.
A prime number
Permutation
Bijection
Answer the Question
40. We can think of the space between primes as 'prime deserts -' strings of consecutive numbers - none of which are prime.
Division is not Associative
Commutative Property of Multiplication:
Prime Deserts
Dividing both Sides of an Equation by the Same Quantity
41. Is the length around an object. Used to calculate such things as fencing around a yard - trimming a piece of material - and the amount of baseboard needed for a room.It is not necessary to have a formula since it is always just calculated by adding t
Fourier Analysis and Synthesis
perimeter
Periodic Function
De Bruijn Sequence
42. The surface of a standard 'donut shape'.
Poincare Disk
Torus
Unique Factorization Theorem
Galton Board
43. Codifies the 'average behavior' of a random event and is a key concept in the application of probability.
Expected Value
Torus
Answer the Question
Group
44. 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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45. 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.
Amplitude
Normal Distribution
Discrete
The Kissing Circle
46. When writing mathematical statements - follow the mantra:
The Additive Identity Property
Conditional Probability
Associate Property of Addition
One equal sign per line
47. 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.
One equal sign per line
Multiplicative Identity:
Law of Large Numbers
1. The unit 2. Prime numbers 3. Composite numbers
48. A point in one dimension requires only one number to define it. The number line is a good example of a one-dimensional space.
variable
Irrational
Line Land
The Multiplicative Identity Property
49. Also known as gluing diagrams - are a convenient way to examine intrinsic topology.
Greatest Common Factor (GCF)
Box Diagram
Divisible
Polynomial
50. 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
Associative Property of Multiplication:
Rarefactior
perimeter
Galois Theory