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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.
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. Add and subtract
General Relativity
inline
Genus
Continuous Symmetry
2. 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
Tone
Problem of the Points
Factor Trees
One equal sign per line
3. 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)
Distributive Property:
Multiplication by Zero
Commensurability
Invarient
4. All integers are thus divided into three classes:
Invarient
1. The unit 2. Prime numbers 3. Composite numbers
inline
Set up an Equation
5. 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
per line
Multiplication
Spaceland
Hypercube
6. A
Division is not Commutative
Intrinsic View
Group
a + c = b + c
7. If a = b then
bar graph
does not change the solution set.
Unique Factorization Theorem
a
8. 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.
Division by Zero
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
Commutative Property of Multiplication:
9. Means approximately equal.
Noether's Theorem
˜
Flat Land
A prime number
10. 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.
The inverse of subtraction is addition
Exponents
B - 125 = 1200
˜
11. Let a - b - and c be any whole numbers. Then - a
The Distributive Property (Subtraction)
Spherical Geometry
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
Unique Factorization Theorem
12. A way to measure how far away a given individual result is from the average result.
Axiomatic Systems
The inverse of addition is subtraction
Set up an Equation
Standard Deviation
13. The system that Euclid used in The Elements
a divided by b
Axiomatic Systems
does not change the solution set.
The Riemann Hypothesis
14. If a = b then a + c = b + c If a = b then a - c = b - c If a = b then a
Properties of Equality
Dimension
The inverse of multiplication is division
Axiomatic Systems
15. Also known as gluing diagrams - are a convenient way to examine intrinsic topology.
Cardinality
a divided by b
Box Diagram
Poincare Disk
16. We can think of the space between primes as 'prime deserts -' strings of consecutive numbers - none of which are prime.
Multiplication by Zero
Prime Deserts
The Associative Property of Multiplication
A number is divisible by 10
17. Einstein's famous theory - relates gravity to the curvature of spacetime.
Intrinsic View
Multiplicative Inverse:
General Relativity
Solve the Equation
18. If a = b then
evaluate the expression in the innermost pair of grouping symbols first.
a · c = b · c for c does not equal 0
Denominator
set
19. The whole number zero is called the additive identity. If a is any whole number - then a + 0 = a.
Non-Euclidian Geometry
set
The Additive Identity Property
In Euclidean four-space
20. 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
Hyperbolic Geometry
repeated addition
a - c = b - c
Frequency
21. An equation is a numerical value that satisfies the equation. That is - when the variable in the equation is replaced by the solution - a true statement results.
Amplitude
prime factors
Solution
B - 125 = 1200
22. If a - b - and c are any whole numbers - then a
Commutative Property of Multiplication
each whole number can be uniquely decomposed into products of primes.
Set up a Variable Dictionary.
The Associative Property of Multiplication
23. A topological invariant that relates a surface's vertices - edges - and faces.
Modular Arithmetic
Line Land
Euler Characteristic
a - c = b - c
24. Original Balance minus River Tam's Withdrawal is Current Balance
Polynomial
Associative Property of Addition:
Fundamental Theorem of Arithmetic
B - 125 = 1200
25. 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
Associative Property of Multiplication:
Continuous Symmetry
bar graph
26. A '___________' infinite set is one that can be put into one-to-one correspondence with the set of natural numbers.
prime factors
repeated addition
Countable
Multiplication by Zero
27. A point in one dimension requires only one number to define it. The number line is a good example of a one-dimensional space.
Central Limit Theorem
Line Land
a divided by b
Problem of the Points
28. 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
4 + x = 12
Exponents
Pigeonhole Principle
Group
29. The amount of displacement - as measured from the still surface line.
Amplitude
Dimension
Stereographic Projection
Torus
30. A way to analyze sequences of events where the outcomes of prior events affect the probability of outcomes of subsequent events.
Symmetry
Markov Chains
bar graph
De Bruijn Sequence
31. This important result says that every natural number greater than one can be expressed as a product of primes in exactly one way.
Fundamental Theorem of Arithmetic
bar graph
Continuous Symmetry
Commutative Property of Multiplication:
32. Is a symbol (usually a letter) that stands for a value that may vary.
Variable
In Euclidean four-space
Discrete
Symmetry
33. If a = b then
Rarefactior
Hyperbolic Geometry
a - c = b - c
Multiplication by Zero
34. 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
Stereographic Projection
Complete Graph
The Distributive Property (Subtraction)
35. Negative
Continuous
Sign Rules for Division
Topology
Rarefactior
36. If on a surface there is no meaningful way to tell an object's orientation (left or right handedness) - the surface is said to be non-orientable.
Spaceland
In Euclidean four-space
The Associative Property of Multiplication
Non-Orientability
37. A number is divisible by 2
counting numbers
Properties of Equality
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
Conditional Probability
38. Arise from the attempt to measure all quantities with a common unit of measure.
Rational
Configuration Space
Factor Trees
The Set of Whole Numbers
39. Multiplication is equivalent to
repeated addition
Products and Factors
˜
Solve the Equation
40. An important part of problem solving is identifying
General Relativity
variable
Sign Rules for Division
Line Land
41. The fundamental theorem of arithmetic says that
Continuous Symmetry
each whole number can be uniquely decomposed into products of primes.
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.
does not change the solution set.
42. 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.'
One equal sign per line
Symmetry
The Prime Number Theorem
Greatest Common Factor (GCF)
43. Collection of objects. list all the objects in the set and enclosing the list in curly braces.
prime factors
˜
Additive Identity:
set
44. The multitude concept presented numbers as collections of discrete units - rather like indivisible atoms.
Discrete
Denominator
Set up an Equation
Fundamental Theorem of Arithmetic
45. To describe and extend a numerical pattern
Associate Property of Addition
Conditional Probability
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.
Line Land
46. 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
Noether's Theorem
Equivalent Equations
The Commutative Property of Addition
The inverse of multiplication is division
47. If a and b are any whole numbers - then a
Solve the Equation
Commutative Property of Multiplication
Prime Number
The Set of Whole Numbers
48. An algebraic 'sentence' containing an unknown quantity.
Geometry
Polynomial
Periodic Function
Non-Euclidian Geometry
49. 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.
Transfinite
Properties of Equality
The BML Traffic Model
Principal Curvatures
50. This method can create a flat map from a curved surface while preserving all angles in any features present.
Stereographic Projection
Comparison Property
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
Principal Curvatures