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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. Is the shortest string that contains all possible permutations of a particular length from a given set.
De Bruijn Sequence
Fundamental Theorem of Arithmetic
Division by Zero
Public Key Encryption
2. If a = b then
Answer the Question
Sign Rules for Division
a - c = b - c
Flat Land
3. 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
inline
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
The Additive Identity Property
4. × - ( )( ) - · - 1. Multiply the numbers (ignoring the signs)2. The answer is positive if they have the same signs. 3. The answer is negative if they have different signs. 4. Alternatively - count the amount of negative numbers. If there are an even
repeated addition
The Commutative Property of Addition
Multiplication
Box Diagram
5. A factor tree is a way to visualize a number's
Solution
Prime Number
Continuous
prime factors
6. 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
inline
Multiplicative Inverse:
Rarefactior
Solution
7. Aka The Osculating Circle - a way to measure the curvature of a line.
The inverse of multiplication is division
division
Comparison Property
The Kissing Circle
8. Original Balance minus River Tam's Withdrawal is Current Balance
Amplitude
B - 125 = 1200
Additive Inverse:
The Multiplicative Identity Property
9. 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
Central Limit Theorem
Multiplication by Zero
Rarefactior
Group
10. 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
11. 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
Equation
repeated addition
Non-Orientability
12. It is important to note that this step does not imply that you should simply check your solution in your equation. After all - it's possible that your equation incorrectly models the problem's situation - so you could have a valid solution to an inco
does not change the solution set.
Commensurability
Associate Property of Addition
Look Back
13. Mathematical statement that equates two mathematical expressions.
Additive Identity:
Equation
Equivalent Equations
Flat Land
14. 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.
Public Key Encryption
the set of natural numbers
Division by Zero
Transfinite
15. The distribution of averages of many trials is always normal - even if the distribution of each trial is not.
Divisible
Look Back
Central Limit Theorem
The Additive Identity Property
16. 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.
prime factors
Amplitude
counting numbers
Galton Board
17. A(b + c) = a · b + a · c a(b - c) = a · b - a · c
Bijection
Solution
Distributive Property:
Primes
18. This result relates conserved physical quantities - like conservation of energy - to continuous symmetries of spacetime.
19. 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
Bijection
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
4 + x = 12
20. 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.
Fundamental Theorem of Arithmetic
per line
Continuous Symmetry
Division is not Commutative
21. The solutions to this gambling dilemma is traditionally held to be the start of modern probability theory.
Problem of the Points
Figurate Numbers
Denominator
Expected Value
22. 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
Line Land
Multiplying both Sides of an Equation by the Same Quantity
Hypercube
Equation
23. W = {0 - 1 - 2 - 3 - 4 - 5 - . . .} is called
Complete Graph
Division is not Commutative
The Set of Whole Numbers
Prime Deserts
24. An important part of problem solving is identifying
The index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.
The Kissing Circle
Rarefactior
variable
25. Multiplication is equivalent to
Hypercube
each whole number can be uniquely decomposed into products of primes.
repeated addition
Box Diagram
26. A flat map of hyperbolic space.
Box Diagram
Poincare Disk
prime factors
Irrational
27. The amount of displacement - as measured from the still surface line.
Countable
Solution
left to right
Amplitude
28. If a = b then a + c = b + c If a = b then a - c = b - c If a = b then a
Properties of Equality
The index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.
Axiomatic Systems
Polynomial
29. A topological invariant that relates a surface's vertices - edges - and faces.
set
Hypercube
Noether's Theorem
Euler Characteristic
30. In any ratio of two whole numbers - expressed as a fraction - we can interpret the first (top) number to be the 'counter -' or numerator
Denominator
Divisible
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 Commutative Property of Addition
31. If a = b then
Invarient
Factor Trees
a
Euclid's Postulates
32. A graph in which every node is connected to every other node is called a complete graph.
The BML Traffic Model
Axiomatic Systems
Figurate Numbers
Complete Graph
33. Requirements for Word Problem Solutions.
A prime number
Configuration Space
Conditional Probability
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
34. The study of shape from the perspective of being on the surface of the shape.
Intrinsic View
Division by Zero
Additive Inverse:
Look Back
35. Add and subtract
Poincare Disk
Countable
inline
Wave Equation
36. When writing mathematical statements - follow the mantra:
Properties of Equality
Pigeonhole Principle
One equal sign per line
perimeter
37. 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.
Stereographic Projection
does not change the solution set.
Fourier Analysis
Tone
38. A way to extrinsically measure the curvature of a surface by looking at a given point and finding the contour line with the greatest curvature and the contour line with the least curvature.
Principal Curvatures
Poincare Disk
Cayley's Theorem
Pigeonhole Principle
39. 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.
Unique Factorization Theorem
the set of natural numbers
Normal Distribution
Associative Property of Addition:
40. Instruments produce notes that have a fundamental frequency in combination with multiples of that frequency known as partials or overtones
Overtone
In Euclidean four-space
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
Countable
41. Index p radicand
prime factors
Central Limit Theorem
The index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.
Bijection
42. This result says that the symmetries of geometric objects can be expressed as groups of permutations.
43. A whole number (other than 1) is a _____________ if its only factors (divisors) are 1 and itself. Equivalently - a number is prime if and only if it has exactly two factors (divisors).
A number is divisible by 5
Amplitude
Flat Land
Prime Number
44. The multitude concept presented numbers as collections of discrete units - rather like indivisible atoms.
Discrete
Symmetry
Continuous
Variable
45. Collection of objects. list all the objects in the set and enclosing the list in curly braces.
Commutative Property of Multiplication:
set
Markov Chains
Products and Factors
46. 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.
Factor Tree Alternate Approach
Line Land
counting numbers
Exponents
47. If its final digit is a 0.
A number is divisible by 10
The Commutative Property of Addition
each whole number can be uniquely decomposed into products of primes.
does not change the solution set.
48. 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.
Factor Trees
Commutative Property of Multiplication
Pigeonhole Principle
Geometry
49. A + (-a) = (-a) + a = 0
Periodic Function
Galton Board
Additive Inverse:
Commutative Property of Addition:
50. 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
The Commutative Property of Addition
Set up a Variable Dictionary.
Intrinsic View
Grouping Symbols