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Test your basic knowledge |
CLEP General Math: Number Sense - Patterns - Algebraic Thinking
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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. Let a - b - and c be any whole numbers. Then - a
Hamilton Cycle
The Distributive Property (Subtraction)
a
a - c = b - c
2. This model is at the forefront of probability research. Mathematicians use it to model traffic patterns in an attempt to understand flow rates and gridlock - among other things.
set
Fourier Analysis and Synthesis
Cayley's Theorem
The BML Traffic Model
3. If a = b then
a + c = b + c
Expected Value
Markov Chains
Discrete
4. This result says that the symmetries of geometric objects can be expressed as groups of permutations.
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5. 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)
Unique Factorization Theorem
Commensurability
Law of Large Numbers
a
6. 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
Multiplying both Sides of an Equation by the Same Quantity
Probability
The inverse of multiplication is division
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
7. 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
Equivalent Equations
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)
8. 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.
Associative Property of Multiplication:
per line
Frequency
Modular Arithmetic
9. When writing mathematical statements - follow the mantra:
Primes
A prime number
One equal sign per line
De Bruijn Sequence
10. This method can create a flat map from a curved surface while preserving all angles in any features present.
Comparison Property
Stereographic Projection
Discrete
Multiplicative Identity:
11. The process of taking a complicated signal and breaking it into sine and cosine components.
bar graph
Fourier Analysis
prime factors
set
12. Objects are topologically equivalent if they can be continuously deformed into one another. Properties that are preserved during this process are called topological invariants.
Hypercube
Exponents
Hamilton Cycle
Irrational
13. An instrument's _____ - the sound it produces - is a complex mixture of waves of different frequencies.
Tone
Comparison Property
Flat Land
Additive Inverse:
14. 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.'
Comparison Property
Divisible
Solution
bar graph
15. 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.
A prime number
Bijection
Rational
Greatest Common Factor (GCF)
16. 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
Cayley's Theorem
Commutative Property of Multiplication:
per line
Rarefactior
17. If a = b then
Dimension
Multiplication
Expected Value
a
18. (a + b) + c = a + (b + c)
Look Back
Markov Chains
Associative Property of Addition:
A number is divisible by 5
19. 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
Frequency
Tone
Wave Equation
20. Collection of objects. list all the objects in the set and enclosing the list in curly braces.
Multiplicative Inverse:
Overtone
set
De Bruijn Sequence
21. Uses second derivatives to relate acceleration in space to acceleration in time.
set
Genus
Wave Equation
Topology
22. 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.'
Cayley's Theorem
Answer the Question
The Prime Number Theorem
Distributive Property:
23. Trigonometric functions - such as sine and cosine - are useful for modeling sound waves - because they oscillate between values
a · c = b · c for c does not equal 0
Primes
prime factors
Periodic Function
24. W = {0 - 1 - 2 - 3 - 4 - 5 - . . .} is called
The Set of Whole Numbers
Fundamental Theorem of Arithmetic
Intrinsic View
Noether's Theorem
25. 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
Dimension
The Same
Additive Identity:
Genus
26. 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
Least Common Multiple (LCM)
division
Expected Value
Amplitude
27. Two equations if they have the same solution set.
Prime Deserts
Probability
Equivalent Equations
De Bruijn Sequence
28. Cantor called the cardinality of all the sets that can be put into one-to-one correspondence with the counting numbers - or 'Aleph Null.'
a - c = b - c
Aleph-Null
Law of Large Numbers
Equivalent Equations
29. If a = b then a + c = b + c If a = b then a - c = b - c If a = b then a
Flat Land
perimeter
Properties of Equality
Intrinsic View
30. Also known as gluing diagrams - are a convenient way to examine intrinsic topology.
The Associative Property of Multiplication
Box Diagram
Cardinality
A number is divisible by 5
31. N = {1 - 2 - 3 - 4 - 5 - . . .}.
The Set of Whole Numbers
Divisible
Hamilton Cycle
the set of natural numbers
32. 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).
Products and Factors
One equal sign per line
Prime Number
The Additive Identity Property
33. The solutions to this gambling dilemma is traditionally held to be the start of modern probability theory.
Problem of the Points
Multiplicative Inverse:
perimeter
Wave Equation
34. 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.
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
Denominator
Additive Identity:
Spherical Geometry
35. To describe and extend a numerical pattern
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.
Noether's Theorem
a · c = b · c for c does not equal 0
Commutative Property of Multiplication:
36. The fundamental theorem of arithmetic says that
each whole number can be uniquely decomposed into products of primes.
does not change the solution set.
Prime Deserts
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
37. Perform all additions and subtractions in the order presented
Axiomatic Systems
variable
Factor Tree Alternate Approach
left to right
38. 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.
Euclid's Postulates
A number is divisible by 9
Multiplication
Non-Orientability
39. Our standard notions of Pythagorean distance and angle via the inner product extend quite nicely from three-space.
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'
Spherical Geometry
In Euclidean four-space
40. The state of appearing unchanged.
Invarient
Denominator
1. The unit 2. Prime numbers 3. Composite numbers
Axiomatic Systems
41. 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
Factor Trees
Topology
Noether's Theorem
Expected Value
42. Does not change the solution set. That is - if a = b - then dividing both sides of the equation by c produces the equivalent equation a/c = b/c - provided c = 0.
The Distributive Property (Subtraction)
Irrational
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
Dividing both Sides of an Equation by the Same Quantity
43. A · 1/a = 1/a · a = 1
Flat Land
Additive Identity:
Products and Factors
Multiplicative Inverse:
44. Are the fundamental building blocks of arithmetic.
Primes
Public Key Encryption
Comparison Property
Probability
45. (a
Division is not Associative
Multiplication
Associate Property of Addition
Principal Curvatures
46. Einstein's famous theory - relates gravity to the curvature of spacetime.
General Relativity
Least Common Multiple (LCM)
A number is divisible by 9
Problem of the Points
47. 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.
Variable
Commutative Property of Multiplication:
Unique Factorization Theorem
a
48. Negative
A number is divisible by 10
4 + x = 12
a - c = b - c
Sign Rules for Division
49. In the expression 3
Hyperbolic Geometry
Galois Theory
Products and Factors
One equal sign per line
50. We can think of the space between primes as 'prime deserts -' strings of consecutive numbers - none of which are prime.
Commutative Property of Addition:
Spaceland
Prime Deserts
Frequency