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Test your basic knowledge |
CLEP General Math: Number Sense - Patterns - Algebraic Thinking
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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. All integers are thus divided into three classes:
The inverse of multiplication is division
A number is divisible by 9
1. The unit 2. Prime numbers 3. Composite numbers
Discrete
2. The inverse of multiplication
division
Distributive Property:
Multiplicative Inverse:
Solve the Equation
3. ____________ theory enables us to use mathematics to characterize and predict the behavior of random events. By 'random' we mean 'unpredictable' in the sense that in a given specific situation - our knowledge of current conditions gives us no way to
Conditional Probability
Continuous
Probability
Rational
4. 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.
Euler Characteristic
bar graph
Box Diagram
Unique Factorization Theorem
5. 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
division
Cardinality
Rarefactior
a · c = b · c for c does not equal 0
6. If a = b then
a + c = b + c
repeated addition
Factor Tree Alternate Approach
Central Limit Theorem
7. 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.
Set up an Equation
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
counting numbers
Dividing both Sides of an Equation by the Same Quantity
8. This result says that the symmetries of geometric objects can be expressed as groups of permutations.
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9. A(b + c) = a · b + a · c a(b - c) = a · b - a · c
Distributive Property:
Euclid's Postulates
Fundamental Theorem of Arithmetic
Least Common Multiple (LCM)
10. A flat map of hyperbolic space.
Poincare Disk
Box Diagram
a - c = b - c
A prime number
11. If a represents any whole number - then a
Multiplication by Zero
Comparison Property
A prime number
Principal Curvatures
12. 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.
Primes
Symmetry
Public Key Encryption
perimeter
13. 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 -
The inverse of subtraction is addition
a
The inverse of addition is subtraction
each whole number can be uniquely decomposed into products of primes.
14. 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 Same
Multiplication
4 + x = 12
Group
15. Some numbers make geometric shapes when arranged as a collection of dots - for example - 16 makes a square - and 10 makes a triangle.
variable
The Kissing Circle
each whole number can be uniquely decomposed into products of primes.
Figurate Numbers
16. 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.
Equivalent Equations
Spherical Geometry
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.
Associate Property of Addition
17. If its final digit is a 0 or 5.
Division is not Associative
Public Key Encryption
A number is divisible by 5
The Same
18. Positive integers are
set
Aleph-Null
Division is not Associative
counting numbers
19. N = {1 - 2 - 3 - 4 - 5 - . . .}.
the set of natural numbers
Products and Factors
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
evaluate the expression in the innermost pair of grouping symbols first.
20. 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.
Denominator
Wave Equation
Poincare Disk
Exponents
21. 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
Group
Extrinsic View
Continuous Symmetry
22. Cantor called the cardinality of all the sets that can be put into one-to-one correspondence with the counting numbers - or 'Aleph Null.'
Ramsey Theory
evaluate the expression in the innermost pair of grouping symbols first.
The inverse of addition is subtraction
Aleph-Null
23. Is a path that visits every node in a graph and ends where it began.
Distributive Property:
Additive Identity:
Hamilton Cycle
Associative Property of Multiplication:
24. An object possessing continuous symmetries can remain invariant while one symmetry is turned into another. A circle is an example of an object with continuous symmetries.
Unique Factorization Theorem
Equivalent Equations
Continuous Symmetry
a + c = b + c
25. The multitude concept presented numbers as collections of discrete units - rather like indivisible atoms.
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
Discrete
Principal Curvatures
variable
26. 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
Fundamental Theorem of Arithmetic
Multiplying both Sides of an Equation by the Same Quantity
Solution
Noether's Theorem
27. If a = b then
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.
Topology
Transfinite
a
28. Negative
Sign Rules for Division
Fourier Analysis
Multiplication by Zero
Primes
29. Of central importance in Ramsey Theory - and in combinatorics in general - is the 'pigeonhole principle -' also known as Dirichlet's box. This principle simply states that we cannot fit n+1 pigeons into n pigeonholes in such a way that only one pigeo
Fourier Analysis and Synthesis
Pigeonhole Principle
Irrational
Problem of the Points
30. Are the fundamental building blocks of arithmetic.
Primes
A prime number
Associate Property of Addition
1. The unit 2. Prime numbers 3. Composite numbers
31. If a = b then a + c = b + c If a = b then a - c = b - c If a = b then a
Set up a Variable Dictionary.
The Same
Properties of Equality
a - c = b - c
32. 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).
Dividing both Sides of an Equation by the Same Quantity
A number is divisible by 9
Complete Graph
Galton Board
33. 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:
The inverse of subtraction is addition
Genus
The Prime Number Theorem
34. Solving Equations
Box Diagram
General Relativity
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
Hypercube
35. If grouping symbols are nested
evaluate the expression in the innermost pair of grouping symbols first.
Products and Factors
Pigeonhole Principle
inline
36. Uses second derivatives to relate acceleration in space to acceleration in time.
Figurate Numbers
Tone
Wave Equation
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
37. The state of appearing unchanged.
A prime number
Box Diagram
Invarient
Stereographic Projection
38. 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
Spaceland
does not change the solution set.
A number is divisible by 3
39. In some ways - the opposite of a multitude is a magnitude - which is ___________. In other words - there are no well defined partitions.
Continuous
Configuration Space
Hamilton Cycle
Periodic Function
40. An algebraic 'sentence' containing an unknown quantity.
Polynomial
variable
Non-Euclidian Geometry
Axiomatic Systems
41. We can think of the space between primes as 'prime deserts -' strings of consecutive numbers - none of which are prime.
Prime Deserts
Properties of Equality
Line Land
Unique Factorization Theorem
42. In a mathematical sense - it is a transformation that leaves an object invariant. Symmetry is perhaps most familiar as an artistic or aesthetic concept. Designs are said to be symmetric if they exhibit specific kinds of balance - repetition - and/or
Symmetry
Principal Curvatures
Equivalent Equations
The Set of Whole Numbers
43. This famous - as yet unproven - result relates to the distribution of prime numbers on the number line.
Sign Rules for Division
Dividing both Sides of an Equation by the Same Quantity
The Riemann Hypothesis
Hyperland
44. The four-dimensional analog of the cube - square - and line segment. A hypercube is formed by taking a 3-D cube - pushing a copy of it into the fourth dimension - and connecting it with cubes. Envisioning this object in lower dimensions requires that
the set of natural numbers
Hypercube
Multiplication by Zero
Amplitude
45. The system that Euclid used in The Elements
Group
The index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.
Exponents
Axiomatic Systems
46. Aka The Osculating Circle - a way to measure the curvature of a line.
Problem of the Points
Composite Numbers
Properties of Equality
The Kissing Circle
47. You must always solve the equation set up in the previous step.
Euclid's Postulates
Solve the Equation
Commutative Property of Multiplication:
A prime number
48. A '___________' infinite set is one that can be put into one-to-one correspondence with the set of natural numbers.
Equivalent Equations
Countable
Division by Zero
Look Back
49. (a · b) · c = a · (b · c)
Comparison Property
Commutative Property of Addition:
Associative Property of Multiplication:
The Riemann Hypothesis
50. An arrangement where order matters.
Public Key Encryption
repeated addition
Permutation
Prime Number