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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. 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.
Associative Property of Addition:
Periodic Function
Non-Orientability
Public Key Encryption
2. We can think of the space between primes as 'prime deserts -' strings of consecutive numbers - none of which are prime.
Properties of Equality
Prime Deserts
Transfinite
Equivalent Equations
3. The study of shape from the perspective of being on the surface of the shape.
Sign Rules for Division
Intrinsic View
Hyperland
Amplitude
4. The fundamental theorem of arithmetic says that
Order of Operations - PEMDAS 'Please Excuse My Dear Aunt Sally'
Geometry
each whole number can be uniquely decomposed into products of primes.
Dividing both Sides of an Equation by the Same Quantity
5. If its final digit is a 0 or 5.
Hyperland
a · c = b · c for c does not equal 0
A number is divisible by 5
Galois Theory
6. Originally known as analysis situs
Topology
Set up a Variable Dictionary.
Distributive Property:
Answer the Question
7. A way to measure how far away a given individual result is from the average result.
repeated addition
The Riemann Hypothesis
Multiplicative Identity:
Standard Deviation
8. Is a path that visits every node in a graph and ends where it began.
Tone
1. The unit 2. Prime numbers 3. Composite numbers
Periodic Function
Hamilton Cycle
9. Let a - b - and c represent whole numbers. Then - (a + b) + c = a + (b + c).
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Associate Property of Addition
A number is divisible by 5
Discrete
10. 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).
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.
A number is divisible by 9
The Prime Number Theorem
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
11. An instrument's _____ - the sound it produces - is a complex mixture of waves of different frequencies.
The Associative Property of Multiplication
Galois Theory
Tone
Multiplying both Sides of an Equation by the Same Quantity
12. Original Balance minus River Tam's Withdrawal is Current Balance
the set of natural numbers
Extrinsic View
B - 125 = 1200
The Commutative Property of Addition
13. 4 more than a certain number is 12
Tone
4 + x = 12
The BML Traffic Model
Commutative Property of Multiplication:
14. Writing Mathematical equations - arrange your work one equation
Comparison Property
per line
A number is divisible by 3
variable
15. Three is the common property of the group of sets containing three members. This idea is called '__________ -' which is a synonym for 'size.' The set {a -b -c} is a representative set of the cardinal number 3.
does not change the solution set.
Cardinality
Hypercube
Irrational
16. 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
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
Multiplying both Sides of an Equation by the Same Quantity
set
Torus
17. An arrangement where order matters.
Principal Curvatures
Associative Property of Addition:
Permutation
1. The unit 2. Prime numbers 3. Composite numbers
18. Requirements for Word Problem Solutions.
Multiplicative Inverse:
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
Euler Characteristic
Commutative Property of Multiplication:
19. If its final digit is a 0.
Standard Deviation
A number is divisible by 3
Irrational
A number is divisible by 10
20. Solving Equations
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
Associate Property of Addition
Multiplication by Zero
Composite Numbers
21. Determines the likelihood of events that are not independent of one another.
Grouping Symbols
Conditional Probability
Markov Chains
The BML Traffic Model
22. Has no factors other than 1 and itself
Galois Theory
A prime number
Divisible
a divided by b
23. If a - b - and c are any whole numbers - then a
Equivalent Equations
The inverse of addition is subtraction
The Associative Property of Multiplication
Dimension
24. Negative
One equal sign per line
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
Products and Factors
Sign Rules for Division
25. A topological object that can be used to study the allowable states of a given system.
4 + x = 12
Composite Numbers
Configuration Space
Primes
26. The expression a/b means
a divided by b
Associative Property of Addition:
Conditional Probability
Poincare Disk
27. 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
Order of Operations - PEMDAS 'Please Excuse My Dear Aunt Sally'
Grouping Symbols
Commensurability
Look Back
28. The system that Euclid used in The Elements
Intrinsic View
does not change the solution set.
Multiplicative Identity:
Axiomatic Systems
29. (a + b) + c = a + (b + c)
Exponents
Associative Property of Addition:
Continuous
Non-Orientability
30. A + (-a) = (-a) + a = 0
Hyperbolic Geometry
Additive Inverse:
Tone
The index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.
31. If grouping symbols are nested
a · c = b · c for c does not equal 0
Associative Property of Addition:
evaluate the expression in the innermost pair of grouping symbols first.
Modular Arithmetic
32. Let a and b be whole numbers. Then a is _______________ by b if and only if the remainder is zero when a is divided by b. In this case - we say that 'b is a divisor of a.'
Geometry
Spaceland
Divisible
Hyperland
33. Positive integers are
Dimension
counting numbers
Products and Factors
Principal Curvatures
34. 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
Grouping Symbols
Set up a Variable Dictionary.
Answer the Question
35. 1. Any two points can be joined by a straight line. 2. Any straight line segment can be extended indefinitely in a straight line. 3. Given any straight line segment - a circle can be drawn having the segment as radius and one endpoint as center. 4. A
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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
Rational
Additive Inverse:
Answer the Question
counting numbers
37. 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.
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The Commutative Property of Addition
Complete Graph
Transfinite
38. 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.
Central Limit Theorem
Dividing both Sides of an Equation by the Same Quantity
Dimension
set
39. All integers are thus divided into three classes:
counting numbers
1. The unit 2. Prime numbers 3. Composite numbers
Prime Number
Hypersphere
40. 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.
De Bruijn Sequence
Geometry
Hyperland
Solution
41. 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
Least Common Multiple (LCM)
The index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.
Greatest Common Factor (GCF)
Factor Trees
42. This important result says that every natural number greater than one can be expressed as a product of primes in exactly one way.
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
Multiplying both Sides of an Equation by the Same Quantity
Fundamental Theorem of Arithmetic
does not change the solution set.
43. Multiplication is equivalent to
Invarient
Spherical Geometry
repeated addition
Division by Zero
44. ____________ 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
Solution
Probability
Hyperland
Extrinsic View
45. Our standard notions of Pythagorean distance and angle via the inner product extend quite nicely from three-space.
variable
In Euclidean four-space
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.
General Relativity
46. In a mathematical sense - it is a transformation that leaves an object invariant. Symmetry is perhaps most familiar as an artistic or aesthetic concept. Designs are said to be symmetric if they exhibit specific kinds of balance - repetition - and/or
The inverse of subtraction is addition
Symmetry
Configuration Space
Division is not Associative
47. The surface of a standard 'donut shape'.
Torus
Associate Property of Addition
repeated addition
bar graph
48. Objects are topologically equivalent if they can be continuously deformed into one another. Properties that are preserved during this process are called topological invariants.
The Additive Identity Property
evaluate the expression in the innermost pair of grouping symbols first.
Irrational
Division is not Commutative
49. 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
A number is divisible by 9
Multiplication
Cardinality
Set up a Variable Dictionary.
50. If a = b then
a · c = b · c for c does not equal 0
Poincare Disk
Comparison Property
a + c = b + c