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Test your basic knowledge |
CLEP General Math: Number Sense - Patterns - Algebraic Thinking
Start Test
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. Aka The Osculating Circle - a way to measure the curvature of a line.
The Kissing Circle
Rational
Additive Identity:
The BML Traffic Model
2. This area of mathematics relates symmetry to whether or not an equation has a 'simple' solution.
Aleph-Null
Galois Theory
Continuous Symmetry
Unique Factorization Theorem
3. 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
Frequency
Hypersphere
Bijection
Equivalent Equations
4. If a is any whole number - then a
The Multiplicative Identity Property
General Relativity
A number is divisible by 3
Line Land
5. A point in three-dimensional space requires three numbers to fix its location.
A number is divisible by 5
Additive Inverse:
Spaceland
Hamilton Cycle
6. If its final digit is a 0.
The inverse of subtraction is addition
A number is divisible by 10
prime factors
Primes
7. Rules for Rounding - To round a number to a particular place - follow these steps:
Intrinsic View
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
Grouping Symbols
Solution
8. An algebraic 'sentence' containing an unknown quantity.
The Associative Property of Multiplication
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
Polynomial
Dimension
9. 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
Poincare Disk
A prime number
The inverse of subtraction is addition
Rarefactior
10. A(b + c) = a · b + a · c a(b - c) = a · b - a · c
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.
left to right
Unique Factorization Theorem
Distributive Property:
11. An important part of problem solving is identifying
variable
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
Rational
Figurate Numbers
12. A way to analyze sequences of events where the outcomes of prior events affect the probability of outcomes of subsequent events.
˜
Markov Chains
Rarefactior
Associate Property of Addition
13. Is the shortest string that contains all possible permutations of a particular length from a given set.
Permutation
division
De Bruijn Sequence
Additive Identity:
14. 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.
Multiplicative Identity:
Countable
Set up a Variable Dictionary.
Dividing both Sides of an Equation by the Same Quantity
15. If its final digit is a 0 or 5.
division
The Set of Whole Numbers
a
A number is divisible by 5
16. The fundamental theorem of arithmetic says that
The Commutative Property of Addition
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
each whole number can be uniquely decomposed into products of primes.
The Prime Number Theorem
17. We can think of the space between primes as 'prime deserts -' strings of consecutive numbers - none of which are prime.
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
Primes
Prime Deserts
Additive Identity:
18. 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 Riemann Hypothesis
Cayley's Theorem
Hyperbolic Geometry
Multiplication
19. A '___________' infinite set is one that can be put into one-to-one correspondence with the set of natural numbers.
Hyperland
Exponents
prime factors
Countable
20. 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
˜
Hypercube
set
Additive Inverse:
21. Originally known as analysis situs
Associative Property of Addition:
Topology
Prime Number
Division is not Commutative
22. The surface of a standard 'donut shape'.
Non-Orientability
Torus
Periodic Function
left to right
23. Let a and b represent two whole numbers. Then - a + b = b + a.
The Commutative Property of Addition
Fourier Analysis
Prime Number
Torus
24. Collection of objects. list all the objects in the set and enclosing the list in curly braces.
Ramsey Theory
Normal Distribution
Prime Number
set
25. The study of shape from an external perspective.
Distributive Property:
Composite Numbers
Extrinsic View
The Commutative Property of Addition
26. GThe mathematical study of space. The geometry of a space goes hand in hand with how one defines the shortest distance between two points in that space.
Wave Equation
Equivalent Equations
The inverse of subtraction is addition
Geometry
27. 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 addition is subtraction
Euler Characteristic
A prime number
Factor Trees
28. Every solution to a word problem must include a carefully crafted equation that accurately describes the constraints in the problem statement.
Complete Graph
Set up an Equation
Commutative Property of Addition:
Sign Rules for Division
29. When comparing two whole numbers a and b - only one of three possibilities is true: a < b or a = b or a > b.
Comparison Property
The Riemann Hypothesis
a + c = b + c
Spherical Geometry
30. 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 -
Topology
Distributive Property:
The inverse of addition is subtraction
Solution
31. All integers are thus divided into three classes:
Stereographic Projection
variable
Comparison Property
1. The unit 2. Prime numbers 3. Composite numbers
32. If a = b then
Equivalent Equations
Exponents
a
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
33. The amount of displacement - as measured from the still surface line.
General Relativity
Amplitude
The Kissing Circle
Hamilton Cycle
34. Non-Euclidean geometries abide by some - but not all of Euclid's five postulates.
Non-Euclidian Geometry
Aleph-Null
Multiplication by Zero
Markov Chains
35. ____________ 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
Factor Trees
Probability
Set up an Equation
repeated addition
36. Also known as gluing diagrams - are a convenient way to examine intrinsic topology.
Central Limit Theorem
Box Diagram
Tone
Commensurability
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
Overtone
Non-Orientability
Set up a Variable Dictionary.
Answer the Question
38. A number is divisible by 2
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
counting numbers
Factor Trees
Multiplication
39. 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.
Continuous Symmetry
division
Exponents
Euler Characteristic
40. 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.
Law of Large Numbers
Transfinite
Additive Identity:
Associative Property of Addition:
41. This famous - as yet unproven - result relates to the distribution of prime numbers on the number line.
The Riemann Hypothesis
a
Rarefactior
Aleph-Null
42. Codifies the 'average behavior' of a random event and is a key concept in the application of probability.
Expected Value
B - 125 = 1200
The Kissing Circle
Transfinite
43. You must always solve the equation set up in the previous step.
Solve the Equation
Division is not Commutative
Commensurability
each whole number can be uniquely decomposed into products of primes.
44. 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.'
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
prime factors
The Prime Number Theorem
a
45. A graph in which every node is connected to every other node is called a complete graph.
B - 125 = 1200
Wave Equation
Complete Graph
Commutative Property of Multiplication:
46. Requirements for Word Problem Solutions.
Permutation
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
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
Factor Tree Alternate Approach
47. A topological invariant that relates a surface's vertices - edges - and faces.
Sign Rules for Division
Distributive Property:
Euler Characteristic
In Euclidean four-space
48. The multitude concept presented numbers as collections of discrete units - rather like indivisible atoms.
Bijection
Discrete
repeated addition
Unique Factorization Theorem
49. The solutions to this gambling dilemma is traditionally held to be the start of modern probability theory.
Tone
Comparison Property
Hypercube
Problem of the Points
50. 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
the set of natural numbers
The Additive Identity Property
A prime number