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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. Instruments produce notes that have a fundamental frequency in combination with multiples of that frequency known as partials or overtones
Overtone
Permutation
a · c = b · c for c does not equal 0
Additive Identity:
2. 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
Invarient
Multiplying both Sides of an Equation by the Same Quantity
Tone
Overtone
3. A · b = b · a
Principal Curvatures
Multiplicative Identity:
Associate Property of Addition
Commutative Property of Multiplication:
4. A + (-a) = (-a) + a = 0
Fourier Analysis
The Riemann Hypothesis
counting numbers
Additive Inverse:
5. This famous - as yet unproven - result relates to the distribution of prime numbers on the number line.
per line
Grouping Symbols
The Riemann Hypothesis
Bijection
6. Use parentheses - brackets - or curly braces to delimit the part of an expression you want evaluated first.
Associative Property of Multiplication:
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
a + c = b + c
Grouping Symbols
7. 4 more than a certain number is 12
4 + x = 12
Grouping Symbols
Principal Curvatures
Pigeonhole Principle
8. 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.
4 + x = 12
Figurate Numbers
Equivalent Equations
Transfinite
9. Two equations if they have the same solution set.
Equivalent Equations
Division by Zero
Associative Property of Multiplication:
Grouping Symbols
10. Objects are topologically equivalent if they can be continuously deformed into one another. Properties that are preserved during this process are called topological invariants.
Hyperbolic Geometry
a · c = b · c for c does not equal 0
Irrational
Axiomatic Systems
11. If a = b then
A prime number
The Associative Property of Multiplication
a + c = b + c
Bijection
12. A + 0 = 0 + a = a
Variable
Additive Identity:
A number is divisible by 5
Divisible
13. 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).
Prime Number
Fourier Analysis and Synthesis
Division is not Commutative
Pigeonhole Principle
14. Perform all additions and subtractions in the order presented
Solve the Equation
inline
Standard Deviation
left to right
15. 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
Galois Theory
Set up a Variable Dictionary.
Conditional Probability
Least Common Multiple (LCM)
16. A point in three-dimensional space requires three numbers to fix its location.
The index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.
Polynomial
Axiomatic Systems
Spaceland
17. 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).
Distributive Property:
Associate Property of Addition
Polynomial
A number is divisible by 9
18. 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
Equivalent Equations
Transfinite
Factor Tree Alternate Approach
prime factors
19. A number is divisible by 2
Commensurability
General Relativity
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
Multiplying both Sides of an Equation by the Same Quantity
20. Arise from the attempt to measure all quantities with a common unit of measure.
Invarient
Commensurability
Fourier Analysis
Rational
21. If its final digit is a 0 or 5.
Fourier Analysis and Synthesis
Spherical Geometry
A number is divisible by 5
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
22. If a = b then
a · c = b · c for c does not equal 0
does not change the solution set.
Hypercube
Torus
23. In any ratio of two whole numbers - expressed as a fraction - we can interpret the first (top) number to be the 'counter -' or numerator
Complete Graph
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
The Distributive Property (Subtraction)
Denominator
24. 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
Public Key Encryption
Continuous
prime factors
25. A factor tree is a way to visualize a number's
prime factors
Exponents
The Set of Whole Numbers
Topology
26. When writing mathematical statements - follow the mantra:
One equal sign per line
Central Limit Theorem
The Commutative Property of Addition
Hypersphere
27. If its final digit is a 0.
A number is divisible by 10
Prime Number
Hyperland
Division is not Associative
28. A + b = b + a
Fourier Analysis
Denominator
Commutative Property of Addition:
Solve the Equation
29. Cannot be written as a ratio of natural numbers.
Modular Arithmetic
Order of Operations - PEMDAS 'Please Excuse My Dear Aunt Sally'
Irrational
division
30. The inverse of multiplication
division
Division is not Commutative
Hamilton Cycle
Associative Property of Multiplication:
31. Our standard notions of Pythagorean distance and angle via the inner product extend quite nicely from three-space.
In Euclidean four-space
Continuous Symmetry
The Additive Identity Property
Commutative Property of Multiplication:
32. If we start with a number x and subtract a number a - then adding a to the result will return us to the original number x. In symbols - x - a + a = x. So -
Commutative Property of Multiplication:
Hypersphere
The inverse of subtraction is addition
Configuration Space
33. Rules for Rounding - To round a number to a particular place - follow these steps:
The BML Traffic Model
Continuous
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
Principal Curvatures
34. A topological object that can be used to study the allowable states of a given system.
The Same
Configuration Space
Dividing both Sides of an Equation by the Same Quantity
Look Back
35. The surface of a standard 'donut shape'.
Torus
Problem of the Points
variable
A number is divisible by 10
36. If a = b then
Discrete
Continuous Symmetry
a
A number is divisible by 9
37. Original Balance minus River Tam's Withdrawal is Current Balance
Torus
Hamilton Cycle
B - 125 = 1200
The Set of Whole Numbers
38. Dimension is how mathematicians express the idea of degrees of freedom
Complete Graph
Associative Property of Multiplication:
Additive Inverse:
Dimension
39. A '___________' infinite set is one that can be put into one-to-one correspondence with the set of natural numbers.
Least Common Multiple (LCM)
4 + x = 12
Countable
a
40. 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.
Standard Deviation
Galois Theory
One equal sign per line
Unique Factorization Theorem
41. Negative
Sign Rules for Division
Poincare Disk
Standard Deviation
Geometry
42. The answer to the question of why the primes occur where they do on the number line has eluded mathematicians for centuries. Gauss's Prime Number Theorem is perhaps one of the most famous attempts to find the 'pattern behind the primes.'
The Prime Number Theorem
left to right
Tone
each whole number can be uniquely decomposed into products of primes.
43. 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
Modular Arithmetic
set
Commutative Property of Addition:
44. 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.
Variable
Order of Operations - PEMDAS 'Please Excuse My Dear Aunt Sally'
Law of Large Numbers
Grouping Symbols
45. We can think of the space between primes as 'prime deserts -' strings of consecutive numbers - none of which are prime.
Prime Deserts
Countable
4 + x = 12
Dimension
46. Index p radicand
Frequency
Configuration Space
The index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.
Intrinsic View
47. Means approximately equal.
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
The Riemann Hypothesis
˜
Hyperbolic Geometry
48. Originally known as analysis situs
Unique Factorization Theorem
The Riemann Hypothesis
Topology
Poincare Disk
49. 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.
Hyperbolic Geometry
Spherical Geometry
a · c = b · c for c does not equal 0
each whole number can be uniquely decomposed into products of primes.
50. This area of mathematics relates symmetry to whether or not an equation has a 'simple' solution.
Spaceland
Galois Theory
Polynomial
Group