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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. The expression a/b means
a divided by b
Axiomatic Systems
The inverse of addition is subtraction
set
2. A point in three-dimensional space requires three numbers to fix its location.
prime factors
Spaceland
division
The inverse of addition is subtraction
3. Rules for Rounding - To round a number to a particular place - follow these steps:
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
Periodic Function
Hypercube
The inverse of multiplication is division
4. This ubiquitous result describes the outcomes of many trials of events from a wide array of contexts. It says that most results cluster around the average with few results far above or far below average.
Pigeonhole Principle
Normal Distribution
bar graph
The Same
5. If a represents any whole number - then a
Amplitude
Multiplication by Zero
variable
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
6. An algebraic 'sentence' containing an unknown quantity.
Principal Curvatures
Conditional Probability
Cardinality
Polynomial
7. The solutions to this gambling dilemma is traditionally held to be the start of modern probability theory.
Order of Operations - PEMDAS 'Please Excuse My Dear Aunt Sally'
Markov Chains
Problem of the Points
The Set of Whole Numbers
8. Einstein's famous theory - relates gravity to the curvature of spacetime.
A prime number
General Relativity
Associative Property of Addition:
Fourier Analysis
9. A factor tree is a way to visualize a number's
prime factors
In Euclidean four-space
Problem of the Points
Irrational
10. Adding the same quantity to both sides of an equation - if a = b - then adding c to both sides of the equation produces the equivalent equation a + c = b + c.
perimeter
Commensurability
does not change the solution set.
Extrinsic View
11. 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.'
Box Diagram
Problem of the Points
Geometry
Hyperland
12. 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
Primes
Cayley's Theorem
The Multiplicative Identity Property
13. Dimension is how mathematicians express the idea of degrees of freedom
Dimension
The BML Traffic Model
Set up a Variable Dictionary.
division
14. Breaks a complicated signal into a combination of simple sine waves. Fourier synthesis does the opposite - constructing a complicated signal from simple sine waves.
The BML Traffic Model
Fourier Analysis and Synthesis
Flat Land
a · c = b · c for c does not equal 0
15. 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
Discrete
Multiplying both Sides of an Equation by the Same Quantity
Multiplicative Inverse:
Extrinsic View
16. The distribution of averages of many trials is always normal - even if the distribution of each trial is not.
Least Common Multiple (LCM)
variable
Geometry
Central Limit Theorem
17. 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.
Equation
Public Key Encryption
The inverse of addition is subtraction
Configuration Space
18. 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
division
1. The unit 2. Prime numbers 3. Composite numbers
Probability
Factor Trees
19. A flat map of hyperbolic space.
Division is not Associative
Spherical Geometry
The Prime Number Theorem
Poincare Disk
20. Collection of objects. list all the objects in the set and enclosing the list in curly braces.
set
Standard Deviation
Distributive Property:
Geometry
21. 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 -
A number is divisible by 9
The inverse of subtraction is addition
Sign Rules for Division
The Distributive Property (Subtraction)
22. Trigonometric functions - such as sine and cosine - are useful for modeling sound waves - because they oscillate between values
Solve the Equation
Commutative Property of Addition:
Periodic Function
Exponents
23. Use parentheses - brackets - or curly braces to delimit the part of an expression you want evaluated first.
Grouping Symbols
Division is not Associative
Rational
Equivalent Equations
24. Is the shortest string that contains all possible permutations of a particular length from a given set.
Conditional Probability
per line
Topology
De Bruijn Sequence
25. The system that Euclid used in The Elements
Complete Graph
Law of Large Numbers
a - c = b - c
Axiomatic Systems
26. If its final digit is a 0 or 5.
In Euclidean four-space
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
A number is divisible by 5
The Associative Property of Multiplication
27. 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.
Geometry
Continuous Symmetry
The Kissing Circle
Topology
28. A point in one dimension requires only one number to define it. The number line is a good example of a one-dimensional space.
Line Land
Pigeonhole Principle
Answer the Question
Law of Large Numbers
29. Arise from the attempt to measure all quantities with a common unit of measure.
Non-Orientability
Rational
The Same
Solution
30. 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.
each whole number can be uniquely decomposed into products of primes.
Dividing both Sides of an Equation by the Same Quantity
Hypersphere
Hamilton Cycle
31. 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
Associative Property of Addition:
Group
Non-Orientability
Transfinite
32. An arrangement where order matters.
Irrational
Permutation
Distributive Property:
Geometry
33. 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.
set
Exponents
Continuous Symmetry
Invarient
34. This result relates conserved physical quantities - like conservation of energy - to continuous symmetries of spacetime.
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35. 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.
perimeter
Unique Factorization Theorem
Axiomatic Systems
Comparison Property
36. This step is easily overlooked. For example - the problem might ask for Jane's age - but your equation's solution gives the age of Jane's sister Liz. Make sure you answer the original question asked in the problem. Your solution should be written in
A number is divisible by 9
Configuration Space
Fundamental Theorem of Arithmetic
Answer the Question
37. A · 1 = 1 · a = a
Associative Property of Addition:
Least Common Multiple (LCM)
Multiplicative Identity:
Look Back
38. Index p radicand
inline
Permutation
Denominator
The index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.
39. A · b = b · a
Solve the Equation
Commutative Property of Multiplication:
Non-Euclidian Geometry
Stereographic Projection
40. 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.
Order of Operations - PEMDAS 'Please Excuse My Dear Aunt Sally'
Expected Value
The inverse of subtraction is addition
Continuous Symmetry
41. The study of shape from an external perspective.
Extrinsic View
A number is divisible by 3
Noether's Theorem
Exponents
42. A topological invariant that relates a surface's vertices - edges - and faces.
Euler Characteristic
a + c = b + c
Normal Distribution
Frequency
43. The study of shape from the perspective of being on the surface of the shape.
Intrinsic View
Hamilton Cycle
Complete Graph
Prime Deserts
44. N = {1 - 2 - 3 - 4 - 5 - . . .}.
Complete Graph
the set of natural numbers
Equation
Aleph-Null
45. ____________ 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
Non-Euclidian Geometry
a - c = b - c
Probability
Commutative Property of Multiplication:
46. Codifies the 'average behavior' of a random event and is a key concept in the application of probability.
Expected Value
Commutative Property of Addition:
Order of Operations - PEMDAS 'Please Excuse My Dear Aunt Sally'
Fourier Analysis
47. 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 -
Continuous
Hamilton Cycle
Geometry
The inverse of addition is subtraction
48. Also known as gluing diagrams - are a convenient way to examine intrinsic topology.
does not change the solution set.
Box Diagram
Non-Euclidian Geometry
Multiplicative Identity:
49. If a = b then
The index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.
Topology
a
Associative Property of Addition:
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).
Bijection
A number is divisible by 9
per line
Box Diagram