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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. The whole number zero is called the additive identity. If a is any whole number - then a + 0 = a.
Intrinsic View
The Additive Identity Property
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
set
2. A topological object that can be used to study the allowable states of a given system.
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.
counting numbers
The Set of Whole Numbers
Configuration Space
3. A '___________' infinite set is one that can be put into one-to-one correspondence with the set of natural numbers.
Topology
Primes
Countable
Stereographic Projection
4. Dimension is how mathematicians express the idea of degrees of freedom
Dimension
Non-Euclidian Geometry
a + c = b + c
Non-Orientability
5. The inverse of multiplication
Rational
Unique Factorization Theorem
division
Primes
6. 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
set
Pigeonhole Principle
Principal Curvatures
a + c = b + c
7. Solving Equations
Grouping Symbols
division
Box Diagram
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
8. Our standard notions of Pythagorean distance and angle via the inner product extend quite nicely from three-space.
does not change the solution set.
The Set of Whole Numbers
Hyperbolic Geometry
In Euclidean four-space
9. A topological invariant that relates a surface's vertices - edges - and faces.
Factor Tree Alternate Approach
Euler Characteristic
Multiplying both Sides of an Equation by the Same Quantity
evaluate the expression in the innermost pair of grouping symbols first.
10. Einstein's famous theory - relates gravity to the curvature of spacetime.
Commutative Property of Addition:
Frequency
Cayley's Theorem
General Relativity
11. The system that Euclid used in The Elements
The Kissing Circle
Equation
Axiomatic Systems
The inverse of subtraction is addition
12. 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
The inverse of subtraction is addition
Galton Board
repeated addition
Factor Trees
13. Add and subtract
Irrational
Line Land
Complete Graph
inline
14. 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.
Associative Property of Multiplication:
Bijection
bar graph
Spherical Geometry
15. Aka The Osculating Circle - a way to measure the curvature of a 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.
The Kissing Circle
Unique Factorization Theorem
Properties of Equality
16. Originally known as analysis situs
Topology
Solve the Equation
Additive Identity:
Look Back
17. Two equations if they have the same solution set.
The Associative Property of Multiplication
Bijection
Equivalent Equations
Figurate Numbers
18. If the sum of its digits is divisible by 3 (ex: 3591 is divisible by 3 since 3 + 5 + 9 + 1 = 18 is divisible by 3).
A number is divisible by 3
Greatest Common Factor (GCF)
Division is not Associative
Line Land
19. If a = b then
Standard Deviation
Sign Rules for Division
In Euclidean four-space
a - c = b - c
20. An arrangement where order matters.
Multiplication
Unique Factorization Theorem
Permutation
Continuous Symmetry
21. A point in three-dimensional space requires three numbers to fix its location.
Spaceland
the set of natural numbers
Rarefactior
Look Back
22. Requirements for Word Problem Solutions.
Multiplicative Inverse:
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
Configuration Space
Rarefactior
23. 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
Cayley's Theorem
set
Equation
24. A
Discrete
Group
Division is not Commutative
Normal Distribution
25. If a - b - and c are any whole numbers - then a
Discrete
a · c = b · c for c does not equal 0
The Associative Property of Multiplication
Hyperbolic Geometry
26. The study of shape from an external perspective.
set
Pigeonhole Principle
Topology
Extrinsic View
27. 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
Order of Operations - PEMDAS 'Please Excuse My Dear Aunt Sally'
Aleph-Null
Least Common Multiple (LCM)
Frequency
28. 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
A prime number
Countable
Tone
29. Cantor called the cardinality of all the sets that can be put into one-to-one correspondence with the counting numbers - or 'Aleph Null.'
Hamilton Cycle
Aleph-Null
Solve the Equation
Fundamental Theorem of Arithmetic
30. If a and b are any whole numbers - then a
A number is divisible by 10
Intrinsic View
Cardinality
Commutative Property of Multiplication
31. All integers are thus divided into three classes:
1. The unit 2. Prime numbers 3. Composite numbers
Configuration Space
Amplitude
Composite Numbers
32. ____________ 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
Probability
Hypersphere
Equation
a - c = b - c
33. A + 0 = 0 + a = a
Noether's Theorem
Additive Identity:
Prime Number
The Kissing Circle
34. When comparing two whole numbers a and b - only one of three possibilities is true: a < b or a = b or a > b.
Multiplication
Comparison Property
Law of Large Numbers
The Riemann Hypothesis
35. If its final digit is a 0 or 5.
Non-Euclidian Geometry
A number is divisible by 5
The BML Traffic Model
A number is divisible by 9
36. 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
Group
The inverse of addition is subtraction
The Additive Identity Property
Transfinite
37. Three is the common property of the group of sets containing three members. This idea is called '__________ -' which is a synonym for 'size.' The set {a -b -c} is a representative set of the cardinal number 3.
Primes
Wave Equation
Commutative Property of Addition:
Cardinality
38. Every solution to a word problem must include a carefully crafted equation that accurately describes the constraints in the problem statement.
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
the set of natural numbers
Properties of Equality
Set up an Equation
39. Writing Mathematical equations - arrange your work one equation
per line
The Multiplicative Identity Property
Associative Property of Multiplication:
Composite Numbers
40. 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.'
inline
Euclid's Postulates
Hyperland
The Distributive Property (Subtraction)
41. 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.
Law of Large Numbers
Equivalent Equations
Pigeonhole Principle
Hyperland
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
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
Figurate Numbers
Axiomatic Systems
Symmetry
43. If a = b then
Multiplicative Inverse:
a · c = b · c for c does not equal 0
Division is not Associative
Multiplying both Sides of an Equation by the Same Quantity
44. An instrument's _____ - the sound it produces - is a complex mixture of waves of different frequencies.
Tone
Properties of Equality
Conditional Probability
Polynomial
45. 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.
The BML Traffic Model
4 + x = 12
Non-Euclidian Geometry
Commutative Property of Multiplication:
46. (a + b) + c = a + (b + c)
perimeter
Associative Property of Addition:
the set of natural numbers
a - c = b - c
47. To describe and extend a numerical pattern
The Multiplicative Identity Property
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.
Overtone
Fundamental Theorem of Arithmetic
48. Division by zero is undefined. Each of the expressions 6
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
Euclid's Postulates
Greatest Common Factor (GCF)
Division by Zero
49. Cannot be written as a ratio of natural numbers.
Irrational
Hyperland
Geometry
Periodic Function
50. The distribution of averages of many trials is always normal - even if the distribution of each trial is not.
The Associative Property of Multiplication
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
Central Limit Theorem
Equivalent Equations