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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. Objects are topologically equivalent if they can be continuously deformed into one another. Properties that are preserved during this process are called topological invariants.
Hamilton Cycle
Standard Deviation
Commutative Property of Multiplication
Irrational
2. 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.
Box Diagram
One equal sign per line
Transfinite
Commensurability
3. Also known as 'clock math -' incorporates 'wrap around' effects by having some number other than zero play the role of zero in addition - subtraction - multiplication - and division.
Division is not Commutative
Fourier Analysis and Synthesis
Tone
Modular Arithmetic
4. Solving Equations
The Same
perimeter
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
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
5. 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
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
Commensurability
The Additive Identity Property
Pigeonhole Principle
6. 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).
A number is divisible by 3
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.
variable
Non-Euclidian Geometry
7. 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
Hyperland
Additive Inverse:
Factor Tree Alternate Approach
Torus
8. Also known as gluing diagrams - are a convenient way to examine intrinsic topology.
Box Diagram
Division is not Commutative
Topology
Solution
9. Two equations if they have the same solution set.
Factor Tree Alternate Approach
One equal sign per line
The BML Traffic Model
Equivalent Equations
10. Add and subtract
inline
Hypersphere
The Commutative Property of Addition
Division is not Associative
11. The inverse of multiplication
division
Torus
Polynomial
Periodic Function
12. 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
Division is not Commutative
Spherical Geometry
Central Limit Theorem
13. Originally known as analysis situs
Set up an Equation
Commensurability
Topology
Fourier Analysis
14. A · 1/a = 1/a · a = 1
Multiplicative Inverse:
Prime Number
counting numbers
perimeter
15. Determines the likelihood of events that are not independent of one another.
evaluate the expression in the innermost pair of grouping symbols first.
Conditional Probability
Galton Board
Multiplying both Sides of an Equation by the Same Quantity
16. A · 1 = 1 · a = a
The Same
Multiplicative Identity:
Extrinsic View
does not change the solution set.
17. (a + b) + c = a + (b + c)
Solve the Equation
Associative Property of Addition:
Distributive Property:
Public Key Encryption
18. Instruments produce notes that have a fundamental frequency in combination with multiples of that frequency known as partials or overtones
The Distributive Property (Subtraction)
Transfinite
Overtone
Continuous
19. Original Balance minus River Tam's Withdrawal is Current Balance
Amplitude
The index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.
B - 125 = 1200
Periodic Function
20. This area of mathematics relates symmetry to whether or not an equation has a 'simple' solution.
Euclid's Postulates
Wave Equation
Galois Theory
4 + x = 12
21. When writing mathematical statements - follow the mantra:
Law of Large Numbers
bar graph
Group
One equal sign per line
22. An instrument's _____ - the sound it produces - is a complex mixture of waves of different frequencies.
Irrational
Associate Property of Addition
Tone
Polynomial
23. 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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24. Is a path that visits every node in a graph and ends where it began.
One equal sign per line
Prime Number
Least Common Multiple (LCM)
Hamilton Cycle
25. In any ratio of two whole numbers - expressed as a fraction - we can interpret the first (top) number to be the 'counter -' or numerator
Amplitude
Denominator
Galton Board
prime factors
26. 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.
Aleph-Null
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
Fourier Analysis
Continuous Symmetry
27. Use parentheses - brackets - or curly braces to delimit the part of an expression you want evaluated first.
Hypersphere
Grouping Symbols
Cardinality
General Relativity
28. Uses second derivatives to relate acceleration in space to acceleration in time.
a + c = b + c
Multiplicative Identity:
Wave Equation
Fourier Analysis and Synthesis
29. 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
Euclid's Postulates
Fundamental Theorem of Arithmetic
Group
Fourier Analysis and Synthesis
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
Group
Multiplicative Identity:
Multiplicative Inverse:
Rarefactior
31. If we start with a number x and multiply by a number a - then dividing the result by the number a returns us to the original number x. In symbols - a
The inverse of multiplication is division
Modular Arithmetic
Periodic Function
Sign Rules for Division
32. The multitude concept presented numbers as collections of discrete units - rather like indivisible atoms.
A number is divisible by 3
The Prime Number Theorem
Equivalent Equations
Discrete
33. 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
Polynomial
Continuous Symmetry
34. If a represents any whole number - then a
Multiplication by Zero
Box Diagram
bar graph
Least Common Multiple (LCM)
35. 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).
Multiplying both Sides of an Equation by the Same Quantity
˜
The index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.
Prime Number
36. Multiplication is equivalent to
repeated addition
The Kissing Circle
Properties of Equality
4 + x = 12
37. A
Division is not Commutative
Set up an Equation
Line Land
Stereographic Projection
38. If a is any whole number - then a
Hyperbolic Geometry
The Multiplicative Identity Property
The Associative Property of Multiplication
Symmetry
39. 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 Prime Number Theorem
division
Frequency
Factor Trees
40. 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
Hypersphere
perimeter
per line
Public Key Encryption
41. 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
division
The Same
Properties of Equality
Equivalent Equations
42. Let a - b - and c represent whole numbers. Then - (a + b) + c = a + (b + c).
Associate Property of Addition
Commensurability
Comparison Property
prime factors
43. Means approximately equal.
˜
A number is divisible by 5
Order of Operations - PEMDAS 'Please Excuse My Dear Aunt Sally'
Properties of Equality
44. 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.
4 + x = 12
Multiplication
Bijection
Periodic Function
45. W = {0 - 1 - 2 - 3 - 4 - 5 - . . .} is called
Euler Characteristic
Countable
The Set of Whole Numbers
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
46. A topological invariant that relates a surface's vertices - edges - and faces.
Symmetry
Poincare Disk
Euler Characteristic
In Euclidean four-space
47. 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)
Irrational
Commutative Property of Multiplication
Commensurability
Hyperbolic Geometry
48. 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
Set up an Equation
The Commutative Property of Addition
Topology
49. An important part of problem solving is identifying
Group
Genus
˜
variable
50. If a - b - and c are any whole numbers - then a
Variable
Primes
A prime number
The Associative Property of Multiplication