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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. Division by zero is undefined. Each of the expressions 6
˜
Multiplication
A number is divisible by 3
Division by Zero
2. Aka The Osculating Circle - a way to measure the curvature of a line.
a - c = b - c
The Kissing Circle
Division is not Commutative
a
3. 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.
Bijection
Solve the Equation
The Same
Least Common Multiple (LCM)
4. This result says that the symmetries of geometric objects can be expressed as groups of permutations.
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5. The process of taking a complicated signal and breaking it into sine and cosine components.
repeated addition
Multiplying both Sides of an Equation by the Same Quantity
Fourier Analysis
Rarefactior
6. ____________ 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
Principal Curvatures
Normal Distribution
Probability
Amplitude
7. 4 more than a certain number is 12
4 + x = 12
A number is divisible by 3
B - 125 = 1200
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.
8. (a · b) · c = a · (b · c)
evaluate the expression in the innermost pair of grouping symbols first.
Associative Property of Multiplication:
Box Diagram
Equation
9. 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.
Tone
perimeter
The BML Traffic Model
Additive Identity:
10. If a = b then
left to right
a · c = b · c for c does not equal 0
Topology
Modular Arithmetic
11. A + (-a) = (-a) + a = 0
Permutation
variable
Additive Inverse:
Euclid's Postulates
12. 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).
Euclid's Postulates
Multiplicative Inverse:
Associative Property of Addition:
A number is divisible by 3
13. 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).
Line Land
Euler Characteristic
Discrete
A number is divisible by 9
14. An algebraic 'sentence' containing an unknown quantity.
Irrational
Polynomial
Aleph-Null
Topology
15. 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
Figurate Numbers
Division is not Commutative
General Relativity
16. A + b = b + a
Commutative Property of Multiplication
Commutative Property of Addition:
The Set of Whole Numbers
Periodic Function
17. If a represents any whole number - then a
Aleph-Null
Wave Equation
Multiplication by Zero
Exponents
18. A · 1/a = 1/a · a = 1
Non-Euclidian Geometry
Multiplicative Inverse:
Hypersphere
Answer the Question
19. The system that Euclid used in The Elements
Axiomatic Systems
In Euclidean four-space
a + c = b + c
Factor Trees
20. If a = b then a + c = b + c If a = b then a - c = b - c If a = b then a
Discrete
Properties of Equality
Primes
Group
21. A way to extrinsically measure the curvature of a surface by looking at a given point and finding the contour line with the greatest curvature and the contour line with the least curvature.
Modular Arithmetic
Denominator
Galton Board
Principal Curvatures
22. The fundamental theorem of arithmetic says that
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
Transfinite
Prime Number
each whole number can be uniquely decomposed into products of primes.
23. A '___________' infinite set is one that can be put into one-to-one correspondence with the set of natural numbers.
A number is divisible by 9
Tone
Countable
Noether's Theorem
24. 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
Pigeonhole Principle
Set up a Variable Dictionary.
Ramsey Theory
In Euclidean four-space
25. All integers are thus divided into three classes:
A number is divisible by 10
Probability
Division by Zero
1. The unit 2. Prime numbers 3. Composite numbers
26. An important part of problem solving is identifying
A number is divisible by 3
perimeter
variable
Order of Operations - PEMDAS 'Please Excuse My Dear Aunt Sally'
27. This famous - as yet unproven - result relates to the distribution of prime numbers on the number line.
Greatest Common Factor (GCF)
Multiplication
The Riemann Hypothesis
inline
28. 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
Ramsey Theory
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.
Hypercube
The Multiplicative Identity Property
29. This method can create a flat map from a curved surface while preserving all angles in any features present.
The Multiplicative Identity Property
per line
Stereographic Projection
Factor Trees
30. 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).
Factor Trees
Multiplying both Sides of an Equation by the Same Quantity
The BML Traffic Model
Prime Number
31. When writing mathematical statements - follow the mantra:
The Prime Number Theorem
One equal sign per line
Markov Chains
Transfinite
32. Let a and b represent two whole numbers. Then - a + b = b + a.
The Commutative Property of Addition
General Relativity
Rational
Hamilton Cycle
33. The solutions to this gambling dilemma is traditionally held to be the start of modern probability theory.
˜
Problem of the Points
Overtone
a divided by b
34. Is the shortest string that contains all possible permutations of a particular length from a given set.
Composite Numbers
does not change the solution set.
De Bruijn Sequence
Equation
35. Some numbers make geometric shapes when arranged as a collection of dots - for example - 16 makes a square - and 10 makes a triangle.
Figurate Numbers
Commutative Property of Multiplication
Greatest Common Factor (GCF)
Solve the Equation
36. If a and b are any whole numbers - then a
Commutative Property of Multiplication
1. The unit 2. Prime numbers 3. Composite numbers
Overtone
The Commutative Property of Addition
37. You must let your readers know what each variable in your problem represents. This can be accomplished in a number of ways: Statements such as 'Let P represent the perimeter of the rectangle.' - Labeling unknown values with variables in a table - Lab
Order of Operations - PEMDAS 'Please Excuse My Dear Aunt Sally'
Overtone
Set up a Variable Dictionary.
Associate Property of Addition
38. Topological objects are categorized by their _______ (number of holes). The genus of a surface is a feature of its global topology.
Genus
The BML Traffic Model
Wave Equation
Products and Factors
39. If a whole number is not a prime number - then it is called a...
The Associative Property of Multiplication
Composite Numbers
The Additive Identity Property
Fourier Analysis
40. Objects are topologically equivalent if they can be continuously deformed into one another. Properties that are preserved during this process are called topological invariants.
A number is divisible by 9
Denominator
variable
Irrational
41. Is a symbol (usually a letter) that stands for a value that may vary.
A number is divisible by 5
Variable
Exponents
Complete Graph
42. 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.'
Hyperland
Transfinite
Solution
The Prime Number Theorem
43. A number is divisible by 2
One equal sign per line
Countable
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
Tone
44. 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 -
Answer the Question
The inverse of subtraction is addition
Normal Distribution
Rarefactior
45. A · b = b · a
Commutative Property of Multiplication:
evaluate the expression in the innermost pair of grouping symbols first.
Expected Value
Additive Identity:
46. 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
Expected Value
Pigeonhole Principle
47. Collection of objects. list all the objects in the set and enclosing the list in curly braces.
Tone
set
Multiplying both Sides of an Equation by the Same Quantity
does not change the solution set.
48. Every solution to a word problem must include a carefully crafted equation that accurately describes the constraints in the problem statement.
Set up an Equation
A number is divisible by 5
Euclid's Postulates
Distributive Property:
49. If a = b then
a + c = b + c
Discrete
The Kissing Circle
division
50. Whether or not we hear waves as sound has everything to do with their _____________ - or how many times every second the molecules switch from compression to rarefaction and back to compression again - and their intensity - or how much the air is com
each whole number can be uniquely decomposed into products of primes.
Galton Board
Frequency
Topology