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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.
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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. 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.
Factor Trees
Modular Arithmetic
The Riemann Hypothesis
Additive Inverse:
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
Multiplying both Sides of an Equation by the Same Quantity
Associative Property of Multiplication:
Principal Curvatures
Continuous
3. Solving Equations
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
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
Order of Operations - PEMDAS 'Please Excuse My Dear Aunt Sally'
Rational
4. 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.'
Bijection
Discrete
The Prime Number Theorem
Conditional Probability
5. Let a and b represent two whole numbers. Then - a + b = b + a.
The Commutative Property of Addition
A number is divisible by 10
Group
Associative Property of Addition:
6. 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
Modular Arithmetic
perimeter
Spherical Geometry
Intrinsic View
7. 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
The Multiplicative Identity Property
Complete Graph
Expected Value
Group
8. The system that Euclid used in The Elements
˜
Markov Chains
Axiomatic Systems
Multiplying both Sides of an Equation by the Same Quantity
9. A point in three-dimensional space requires three numbers to fix its location.
Solution
Stereographic Projection
Distributive Property:
Spaceland
10. Codifies the 'average behavior' of a random event and is a key concept in the application of probability.
Hyperland
The Additive Identity Property
Expected Value
Wave Equation
11. 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.
Irrational
Wave Equation
the set of natural numbers
Transfinite
12. 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.'
Ramsey Theory
Divisible
Configuration Space
Sign Rules for Division
13. If a = b then
a - c = b - c
Distributive Property:
The Additive Identity Property
Prime Deserts
14. This result relates conserved physical quantities - like conservation of energy - to continuous symmetries of spacetime.
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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.
The Additive Identity Property
The inverse of addition is subtraction
Prime Deserts
Bijection
16. The surface of a standard 'donut shape'.
Greatest Common Factor (GCF)
Torus
Noether's Theorem
Commensurability
17. When writing mathematical statements - follow the mantra:
One equal sign per line
Prime Deserts
evaluate the expression in the innermost pair of grouping symbols first.
Equivalent Equations
18. 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.
The inverse of multiplication is division
Factor Tree Alternate Approach
Unique Factorization Theorem
bar graph
19. 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).
A number is divisible by 9
Fundamental Theorem of Arithmetic
Unique Factorization Theorem
Associative Property of Addition:
20. If a - b - and c are any whole numbers - then a
left to right
The Associative Property of Multiplication
Spherical Geometry
perimeter
21. The multitude concept presented numbers as collections of discrete units - rather like indivisible atoms.
The Multiplicative Identity Property
General Relativity
Discrete
a + c = b + c
22. 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)
Associative Property of Multiplication:
Irrational
Commensurability
Probability
23. A · b = b · a
Commutative Property of Multiplication:
Galton Board
Non-Orientability
does not change the solution set.
24. 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.
Pigeonhole Principle
The Associative Property of Multiplication
a divided by b
Law of Large Numbers
25. Means approximately equal.
The index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.
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
Axiomatic Systems
˜
26. This area of mathematics relates symmetry to whether or not an equation has a 'simple' solution.
Hyperbolic Geometry
Principal Curvatures
Set up a Variable Dictionary.
Galois Theory
27. (a · b) · c = a · (b · c)
Torus
A prime number
The Associative Property of Multiplication
Associative Property of Multiplication:
28. A graph in which every node is connected to every other node is called a complete graph.
Complete Graph
each whole number can be uniquely decomposed into products of primes.
The BML Traffic Model
perimeter
29. A '___________' infinite set is one that can be put into one-to-one correspondence with the set of natural numbers.
Normal Distribution
The index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.
Rational
Countable
30. Our standard notions of Pythagorean distance and angle via the inner product extend quite nicely from three-space.
Set up an Equation
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.
In Euclidean four-space
The Distributive Property (Subtraction)
31. The amount of displacement - as measured from the still surface line.
A number is divisible by 10
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
Amplitude
The Same
32. Let a - b - and c represent whole numbers. Then - (a + b) + c = a + (b + c).
Fourier Analysis and Synthesis
The Distributive Property (Subtraction)
Torus
Associate Property of Addition
33. The solutions to this gambling dilemma is traditionally held to be the start of modern probability theory.
Fourier Analysis
The Set of Whole Numbers
Problem of the Points
1. The unit 2. Prime numbers 3. Composite numbers
34. Dimension is how mathematicians express the idea of degrees of freedom
Grouping Symbols
Associative Property of Multiplication:
Dimension
Solve the Equation
35. 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
Hyperland
counting numbers
a - c = b - c
The inverse of multiplication is division
36. Uses second derivatives to relate acceleration in space to acceleration in time.
Intrinsic View
Expected Value
Wave Equation
The Distributive Property (Subtraction)
37. If a represents any whole number - then a
Associative Property of Multiplication:
each whole number can be uniquely decomposed into products of primes.
A number is divisible by 5
Multiplication by Zero
38. If a = b then
4 + x = 12
Multiplicative Identity:
a + c = b + c
inline
39. Non-Euclidean geometries abide by some - but not all of Euclid's five postulates.
Products and Factors
The Set of Whole Numbers
Non-Euclidian Geometry
Extrinsic View
40. 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 -
Associative Property of Addition:
Variable
Box Diagram
The inverse of subtraction is addition
41. 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.
Euler Characteristic
each whole number can be uniquely decomposed into products of primes.
Dividing both Sides of an Equation by the Same Quantity
inline
42. 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
The Same
Tone
Multiplicative Identity:
a - c = b - c
43. A way to analyze sequences of events where the outcomes of prior events affect the probability of outcomes of subsequent events.
Extrinsic View
division
Prime Number
Markov Chains
44. Two equations if they have the same solution set.
Equivalent Equations
Equation
Additive Inverse:
Public Key Encryption
45. Index p radicand
The index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.
Invarient
Permutation
Fourier Analysis
46. A point in one dimension requires only one number to define it. The number line is a good example of a one-dimensional space.
Fourier Analysis and Synthesis
Expected Value
Line Land
Group
47. A flat map of hyperbolic space.
a · c = b · c for c does not equal 0
Hamilton Cycle
Associative Property of Multiplication:
Poincare Disk
48. Is a path that visits every node in a graph and ends where it began.
variable
Hamilton Cycle
Tone
The inverse of addition is subtraction
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.
The inverse of subtraction is addition
Division is not Commutative
Hyperbolic Geometry
Variable
50. Division by zero is undefined. Each of the expressions 6
Answer the Question
A prime number
Division by Zero
Permutation
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