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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. Cantor called the cardinality of all the sets that can be put into one-to-one correspondence with the counting numbers - or 'Aleph Null.'
Division by Zero
Composite Numbers
Hypercube
Aleph-Null
2. A
Division is not Commutative
The Commutative Property of Addition
Spaceland
Commutative Property of Multiplication
3. A + 0 = 0 + a = a
Additive Identity:
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
Order of Operations - PEMDAS 'Please Excuse My Dear Aunt Sally'
Bijection
4. 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.
Symmetry
Composite Numbers
a + c = b + c
Exponents
5. Has no factors other than 1 and itself
a
A prime number
Discrete
Answer the Question
6. A point in three-dimensional space requires three numbers to fix its location.
Spaceland
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.
Discrete
Galois Theory
7. 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.
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
Poincare Disk
Unique Factorization Theorem
The Multiplicative Identity Property
8. 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
Torus
Law of Large Numbers
Factor Tree Alternate Approach
Prime Deserts
9. 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
Standard Deviation
Bijection
Commutative Property of Addition:
10. 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 Kissing Circle
Equivalent Equations
Poincare Disk
Factor Trees
11. If its final digit is a 0.
A number is divisible by 10
Continuous
the set of natural numbers
Properties of Equality
12. A graph in which every node is connected to every other node is called a complete graph.
The Same
Complete Graph
the set of natural numbers
Division by Zero
13. A point in four-space - also known as 4-D space - requires four numbers to fix its position. Four-space has a fourth independent direction - described by 'ana' and 'kata.'
The Set of Whole Numbers
Hyperland
The inverse of multiplication is division
Continuous
14. The expression a/b means
counting numbers
a divided by b
In Euclidean four-space
Multiplicative Inverse:
15. × - ( )( ) - · - 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
Look Back
Standard Deviation
Multiplication
left to right
16. (a · b) · c = a · (b · c)
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
Associative Property of Multiplication:
A number is divisible by 10
Continuous Symmetry
17. A + b = b + a
Commutative Property of Addition:
counting numbers
Law of Large Numbers
Genus
18. Use parentheses - brackets - or curly braces to delimit the part of an expression you want evaluated first.
Probability
Grouping Symbols
Look Back
Complete Graph
19. Points in two-dimensional space require two numbers to specify them completely. The Cartesian plane is a good way to envision two-dimensional space.
Axiomatic Systems
Flat Land
General Relativity
Fourier Analysis
20. Objects are topologically equivalent if they can be continuously deformed into one another. Properties that are preserved during this process are called topological invariants.
Irrational
The Commutative Property of Addition
Normal Distribution
Configuration Space
21. This area of mathematics relates symmetry to whether or not an equation has a 'simple' solution.
bar graph
Conditional Probability
Galois Theory
Hyperland
22. Cannot be written as a ratio of natural numbers.
Conditional Probability
Grouping Symbols
Products and Factors
Irrational
23. The distribution of averages of many trials is always normal - even if the distribution of each trial is not.
The inverse of multiplication is division
The inverse of subtraction is addition
Central Limit Theorem
Division is not Associative
24. The inverse of multiplication
division
Sign Rules for Division
Amplitude
Configuration Space
25. If a - b - and c are any whole numbers - then a
The Associative Property of Multiplication
Euler Characteristic
Irrational
Fundamental Theorem of Arithmetic
26. Arise from the attempt to measure all quantities with a common unit of measure.
Factor Tree Alternate Approach
Rational
Continuous
Properties of Equality
27. A '___________' infinite set is one that can be put into one-to-one correspondence with the set of natural numbers.
Countable
Amplitude
Principal Curvatures
4 + x = 12
28. This result says that the symmetries of geometric objects can be expressed as groups of permutations.
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29. 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
perimeter
Divisible
Irrational
Torus
30. 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
Hypersphere
perimeter
Hamilton Cycle
Line Land
31. If a represents any whole number - then a
Pigeonhole Principle
inline
Multiplication by Zero
a divided by b
32. 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.
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
Hyperbolic Geometry
Invarient
Box Diagram
33. In this type of geometry the angles of a triangle add up to more than 180 degrees. In such a system - one has to replace the parallel postulate with a version that admits no parallel lines as well as modify Euclid's first two postulates.
a - c = b - c
Spherical Geometry
Distributive Property:
Modular Arithmetic
34. If a = b then a + c = b + c If a = b then a - c = b - c If a = b then a
Tone
Commutative Property of Addition:
Properties of Equality
1. The unit 2. Prime numbers 3. Composite numbers
35. 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
Commutative Property of Multiplication:
Set up a Variable Dictionary.
Answer the Question
Continuous
36. 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)
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
Commensurability
Overtone
Unique Factorization Theorem
37. 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).
Euler Characteristic
Invarient
Cayley's Theorem
A number is divisible by 9
38. The fundamental theorem of arithmetic says that
The Set of Whole Numbers
division
each whole number can be uniquely decomposed into products of primes.
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.
39. 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
Non-Euclidian Geometry
Look Back
4 + x = 12
Order of Operations - PEMDAS 'Please Excuse My Dear Aunt Sally'
40. 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
Associative Property of Multiplication:
A number is divisible by 9
Cayley's Theorem
41. Let a - b - and c represent whole numbers. Then - (a + b) + c = a + (b + c).
Hyperland
Grouping Symbols
B - 125 = 1200
Associate Property of Addition
42. Rules for Rounding - To round a number to a particular place - follow these steps:
Law of Large Numbers
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
Grouping Symbols
Frequency
43. Einstein's famous theory - relates gravity to the curvature of spacetime.
Order of Operations - PEMDAS 'Please Excuse My Dear Aunt Sally'
General Relativity
Galton Board
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
44. 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.
Box Diagram
Pigeonhole Principle
bar graph
Cayley's Theorem
45. Original Balance minus River Tam's Withdrawal is Current Balance
Hypersphere
Exponents
prime factors
B - 125 = 1200
46. The study of shape from an external perspective.
inline
Discrete
Unique Factorization Theorem
Extrinsic View
47. Public key encryption allows two parties to communicate securely over an un-secured computer network using the properties of prime numbers and modular arithmetic. RSA is the modern standard for public key encryption.
The BML Traffic Model
Pigeonhole Principle
One equal sign per line
Public Key Encryption
48. 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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49. 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.'
Divisible
Factor Trees
per line
Euclid's Postulates
50. Negative
Division is not Commutative
Sign Rules for Division
Unique Factorization Theorem
Rational