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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. A way to measure how far away a given individual result is from the average result.
De Bruijn Sequence
Standard Deviation
Spaceland
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.
The Multiplicative Identity Property
Rarefactior
Transfinite
Cayley's Theorem
3. The fundamental theorem of arithmetic says that
Normal Distribution
each whole number can be uniquely decomposed into products of primes.
prime factors
A number is divisible by 10
4. This result says that the symmetries of geometric objects can be expressed as groups of permutations.
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5. If a = b then
Tone
Flat Land
a · c = b · c for c does not equal 0
One equal sign per line
6. A topological invariant that relates a surface's vertices - edges - and faces.
each whole number can be uniquely decomposed into products of primes.
Euler Characteristic
per line
Grouping Symbols
7. A + b = b + a
Cayley's Theorem
Commutative Property of Addition:
Dividing both Sides of an Equation by the Same Quantity
Markov Chains
8. 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.
A number is divisible by 10
Solution
each whole number can be uniquely decomposed into products of primes.
Markov Chains
9. × - ( )( ) - · - 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
Pigeonhole Principle
Multiplication
Division by Zero
Multiplicative Identity:
10. 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 -
The inverse of subtraction is addition
Hypersphere
Markov Chains
The Same
11. 1. Find the prime factorizations of each number.
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
The Multiplicative Identity Property
variable
Greatest Common Factor (GCF)
12. Is a symbol (usually a letter) that stands for a value that may vary.
Multiplicative Inverse:
Ramsey Theory
Expected Value
Variable
13. 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.
Multiplication by Zero
Modular Arithmetic
Properties of Equality
Group
14. Uses second derivatives to relate acceleration in space to acceleration in time.
Set up a Variable Dictionary.
Wave Equation
Dividing both Sides of an Equation by the Same Quantity
Greatest Common Factor (GCF)
15. Determines the likelihood of events that are not independent of one another.
Ramsey Theory
Conditional Probability
The Distributive Property (Subtraction)
Modular Arithmetic
16. Is a path that visits every node in a graph and ends where it began.
prime factors
Division is not Commutative
Hamilton Cycle
a + c = b + c
17. 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 -
Permutation
The inverse of addition is subtraction
Multiplicative Identity:
Galois Theory
18. If a - b - and c are any whole numbers - then a
Central Limit Theorem
The Associative Property of Multiplication
Intrinsic View
The BML Traffic Model
19. This important result says that every natural number greater than one can be expressed as a product of primes in exactly one way.
Associative Property of Multiplication:
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.
Fundamental Theorem of Arithmetic
Euler Characteristic
20. If a represents any whole number - then a
Multiplication by Zero
Commutative Property of Multiplication
Non-Euclidian Geometry
A number is divisible by 5
21. Topological objects are categorized by their _______ (number of holes). The genus of a surface is a feature of its global topology.
a
Multiplicative Inverse:
Genus
per line
22. 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.
Exponents
Noether's Theorem
Principal Curvatures
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
23. The amount of displacement - as measured from the still surface line.
Principal Curvatures
The Set of Whole Numbers
evaluate the expression in the innermost pair of grouping symbols first.
Amplitude
24. 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.
Hypersphere
Non-Orientability
Set up an Equation
Transfinite
25. 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
Invarient
Spaceland
Tone
perimeter
26. 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.'
Polynomial
Hyperland
Topology
A number is divisible by 9
27. 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
The Distributive Property (Subtraction)
The Associative Property of Multiplication
Overtone
Factor Tree Alternate Approach
28. Add and subtract
evaluate the expression in the innermost pair of grouping symbols first.
One equal sign per line
Bijection
inline
29. If a is any whole number - then a
The Distributive Property (Subtraction)
Markov Chains
The Multiplicative Identity Property
Periodic Function
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
Permutation
Denominator
Genus
Comparison Property
31. Aka The Osculating Circle - a way to measure the curvature of a line.
Least Common Multiple (LCM)
Topology
The Kissing Circle
Modular Arithmetic
32. A flat map of hyperbolic space.
Poincare Disk
Properties of Equality
The inverse of addition is subtraction
Hamilton Cycle
33. The process of taking a complicated signal and breaking it into sine and cosine components.
Multiplication by Zero
Fourier Analysis
Irrational
Ramsey Theory
34. 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.
Group
Cardinality
Normal Distribution
Wave Equation
35. Non-Euclidean geometries abide by some - but not all of Euclid's five postulates.
Irrational
Properties of Equality
Non-Euclidian Geometry
Sign Rules for Division
36. Cannot be written as a ratio of natural numbers.
Invarient
Variable
The Multiplicative Identity Property
Irrational
37. Dimension is how mathematicians express the idea of degrees of freedom
Frequency
Dimension
The Set of Whole Numbers
Hyperbolic Geometry
38. 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.'
Fundamental Theorem of Arithmetic
The Prime Number Theorem
Irrational
Periodic Function
39. The expression a/b means
a divided by b
Least Common Multiple (LCM)
Grouping Symbols
variable
40. Positive integers are
Noether's Theorem
Poincare Disk
counting numbers
Fourier Analysis and Synthesis
41. If a and b are any whole numbers - then a
Commutative Property of Multiplication
Additive Identity:
˜
Genus
42. Two equations if they have the same solution set.
Multiplying both Sides of an Equation by the Same Quantity
A number is divisible by 9
Markov Chains
Equivalent Equations
43. Writing Mathematical equations - arrange your work one equation
Multiplying both Sides of an Equation by the Same Quantity
Periodic Function
per line
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.
44. A point in one dimension requires only one number to define it. The number line is a good example of a one-dimensional space.
Line Land
left to right
Aleph-Null
counting numbers
45. If a = b then a + c = b + c If a = b then a - c = b - c If a = b then a
Hamilton Cycle
Commutative Property of Multiplication:
Properties of Equality
A number is divisible by 3
46. 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
Hypersphere
Modular Arithmetic
Noether's Theorem
Least Common Multiple (LCM)
47. A + 0 = 0 + a = a
Multiplicative Inverse:
Principal Curvatures
Additive Identity:
counting numbers
48. Collection of objects. list all the objects in the set and enclosing the list in curly braces.
Principal Curvatures
Fourier Analysis and Synthesis
Division by Zero
set
49. Instruments produce notes that have a fundamental frequency in combination with multiples of that frequency known as partials or overtones
1. The unit 2. Prime numbers 3. Composite numbers
Amplitude
Tone
Overtone
50. 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.
Pigeonhole Principle
Genus
Public Key Encryption
The Additive Identity Property