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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. If a is any whole number - then a
Tone
The Multiplicative Identity Property
The Same
Commutative Property of Multiplication:
2. Determines the likelihood of events that are not independent of one another.
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
Conditional Probability
perimeter
Configuration Space
3. In some ways - the opposite of a multitude is a magnitude - which is ___________. In other words - there are no well defined partitions.
Associate Property of Addition
Amplitude
Continuous
Composite Numbers
4. If a = b then
a - c = b - c
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
Euler Characteristic
Dividing both Sides of an Equation by the Same Quantity
5. You must always solve the equation set up in the previous step.
Solve the Equation
Euclid's Postulates
The index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.
Sign Rules for Division
6. This famous - as yet unproven - result relates to the distribution of prime numbers on the number line.
Fourier Analysis and Synthesis
a + c = b + c
Least Common Multiple (LCM)
The Riemann Hypothesis
7. Requirements for Word Problem Solutions.
Polynomial
Configuration Space
Fourier Analysis
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
8. 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
set
The inverse of multiplication is division
Fourier Analysis and Synthesis
Additive Inverse:
9. 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
Associate Property of Addition
Prime Deserts
Answer the Question
Spaceland
10. The system that Euclid used in The Elements
Multiplication
The Commutative Property of Addition
Axiomatic Systems
Irrational
11. A graph in which every node is connected to every other node is called a complete graph.
Grouping Symbols
Complete Graph
The Set of Whole Numbers
counting numbers
12. × - ( )( ) - · - 1. Multiply the numbers (ignoring the signs)2. The answer is positive if they have the same signs. 3. The answer is negative if they have different signs. 4. Alternatively - count the amount of negative numbers. If there are an even
counting numbers
Symmetry
Multiplication
Genus
13. This area of mathematics relates symmetry to whether or not an equation has a 'simple' solution.
Public Key Encryption
Galois Theory
Polynomial
Commutative Property of Addition:
14. Is the shortest string that contains all possible permutations of a particular length from a given set.
Galton Board
Sign Rules for Division
Additive Identity:
De Bruijn Sequence
15. Writing Mathematical equations - arrange your work one equation
Extrinsic View
Stereographic Projection
Variable
per line
16. The fundamental theorem of arithmetic says that
Prime Deserts
per line
each whole number can be uniquely decomposed into products of primes.
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
17. Let a - b - and c represent whole numbers. Then - (a + b) + c = a + (b + c).
Associative Property of Multiplication:
Flat Land
Associate Property of Addition
Complete Graph
18. 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.
The Associative Property of Multiplication
Law of Large Numbers
Configuration Space
Geometry
19. 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.
Stereographic Projection
per line
Dividing both Sides of an Equation by the Same Quantity
variable
20. A + b = b + a
The Set of Whole Numbers
Commutative Property of Addition:
Variable
Irrational
21. A topological invariant that relates a surface's vertices - edges - and faces.
Euler Characteristic
Topology
Symmetry
Spherical Geometry
22. 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
Composite Numbers
Euler Characteristic
Stereographic Projection
23. This result relates conserved physical quantities - like conservation of energy - to continuous symmetries of spacetime.
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24. A · 1 = 1 · a = a
Multiplicative Identity:
Genus
Composite Numbers
Spherical Geometry
25. 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.
The Kissing Circle
Polynomial
The Commutative Property of Addition
Spherical Geometry
26. 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.
does not change the solution set.
Complete Graph
Dimension
A prime number
27. This important result says that every natural number greater than one can be expressed as a product of primes in exactly one way.
The Prime Number Theorem
Multiplication
Fundamental Theorem of Arithmetic
Central Limit Theorem
28. Is a symbol (usually a letter) that stands for a value that may vary.
bar graph
The Same
Aleph-Null
Variable
29. A topological object that can be used to study the allowable states of a given system.
Probability
Law of Large Numbers
Commutative Property of Addition:
Configuration Space
30. The study of shape from the perspective of being on the surface of the shape.
perimeter
Additive Identity:
Intrinsic View
Principal Curvatures
31. A way to measure how far away a given individual result is from the average result.
Standard Deviation
Galois Theory
Group
1. The unit 2. Prime numbers 3. Composite numbers
32. 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
a + c = b + c
division
Multiplying both Sides of an Equation by the Same Quantity
Distributive Property:
33. 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.
Axiomatic Systems
Transfinite
Commensurability
4 + x = 12
34. Einstein's famous theory - relates gravity to the curvature of spacetime.
General Relativity
Solution
A prime number
Prime Number
35. It is important to note that this step does not imply that you should simply check your solution in your equation. After all - it's possible that your equation incorrectly models the problem's situation - so you could have a valid solution to an inco
Invarient
inline
Principal Curvatures
Look Back
36. Let a and b represent two whole numbers. Then - a + b = b + a.
Line Land
Unique Factorization Theorem
The Commutative Property of Addition
Division by Zero
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
Associative Property of Addition:
prime factors
Standard Deviation
Set up a Variable Dictionary.
38. An arrangement where order matters.
Permutation
Galton Board
a - c = b - c
set
39. The study of shape from an external perspective.
Extrinsic View
Primes
Spaceland
The index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.
40. Points in two-dimensional space require two numbers to specify them completely. The Cartesian plane is a good way to envision two-dimensional space.
counting numbers
Flat Land
Euler Characteristic
Primes
41. 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 -
Commutative Property of Addition:
The inverse of subtraction is addition
Continuous Symmetry
Dividing both Sides of an Equation by the Same Quantity
42. When comparing two whole numbers a and b - only one of three possibilities is true: a < b or a = b or a > b.
Periodic Function
Multiplication by Zero
Principal Curvatures
Comparison Property
43. Means approximately equal.
˜
Answer the Question
One equal sign per line
Wave Equation
44. Is a path that visits every node in a graph and ends where it began.
Equivalent Equations
Hamilton Cycle
Associative Property of Addition:
Rational
45. 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
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
Equivalent Equations
The Commutative Property of Addition
Least Common Multiple (LCM)
46. Two equations if they have the same solution set.
Equivalent Equations
bar graph
Unique Factorization Theorem
Divisible
47. When writing mathematical statements - follow the mantra:
One equal sign per line
Tone
Greatest Common Factor (GCF)
per line
48. Aka The Osculating Circle - a way to measure the curvature of a line.
Set up an Equation
Ramsey Theory
The inverse of multiplication is division
The Kissing Circle
49. Original Balance minus River Tam's Withdrawal is Current Balance
Continuous
B - 125 = 1200
Probability
Figurate Numbers
50. 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
Group
Pigeonhole Principle
a · c = b · c for c does not equal 0
Fundamental Theorem of Arithmetic