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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. 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.
The Associative Property of Multiplication
Associative Property of Addition:
Unique Factorization Theorem
Galton Board
2. You must always solve the equation set up in the previous step.
Cardinality
Solve the Equation
The Additive Identity Property
variable
3. We can think of the space between primes as 'prime deserts -' strings of consecutive numbers - none of which are prime.
Factor Trees
Associate Property of Addition
Multiplication by Zero
Prime Deserts
4. A way to analyze sequences of events where the outcomes of prior events affect the probability of outcomes of subsequent events.
Genus
Markov Chains
The inverse of addition is subtraction
Equation
5. This area of mathematics relates symmetry to whether or not an equation has a 'simple' solution.
Equation
Permutation
Galois Theory
per line
6. Objects are topologically equivalent if they can be continuously deformed into one another. Properties that are preserved during this process are called topological invariants.
Irrational
Topology
bar graph
The Set of Whole Numbers
7. Aka The Osculating Circle - a way to measure the curvature of a line.
The Kissing Circle
Solve the Equation
Modular Arithmetic
left to right
8. Originally known as analysis situs
Topology
The Prime Number Theorem
Continuous Symmetry
Probability
9. 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
Periodic Function
Tone
Variable
10. 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.
Sign Rules for Division
The Set of Whole Numbers
1. The unit 2. Prime numbers 3. Composite numbers
Unique Factorization Theorem
11. Topological objects are categorized by their _______ (number of holes). The genus of a surface is a feature of its global topology.
Genus
Order of Operations - PEMDAS 'Please Excuse My Dear Aunt Sally'
Ramsey Theory
Markov Chains
12. If a and b are any whole numbers - then a
The Commutative Property of Addition
Commutative Property of Multiplication
the set of natural numbers
Flat Land
13. When comparing two whole numbers a and b - only one of three possibilities is true: a < b or a = b or a > b.
The Associative Property of Multiplication
Comparison Property
The Riemann Hypothesis
The BML Traffic Model
14. W = {0 - 1 - 2 - 3 - 4 - 5 - . . .} is called
The Set of Whole Numbers
bar graph
Division is not Commutative
The inverse of subtraction is addition
15. A + 0 = 0 + a = a
Hyperland
Factor Trees
Additive Identity:
Flat Land
16. Non-Euclidean geometries abide by some - but not all of Euclid's five postulates.
Discrete
Dimension
inline
Non-Euclidian Geometry
17. A sphere can be thought of as a stack of circular discs of increasing - then decreasing - radii. The process of slicing is one way to visualize higher-dimensional objects via level curves and surfaces. A hypersphere can be thought of as a 'stack' of
each whole number can be uniquely decomposed into products of primes.
Equation
Hypersphere
Standard Deviation
18. The whole number zero is called the additive identity. If a is any whole number - then a + 0 = a.
Associative Property of Multiplication:
The Additive Identity Property
The Set of Whole Numbers
˜
19. Mathematical statement that equates two mathematical expressions.
Equation
A number is divisible by 5
Order of Operations - PEMDAS 'Please Excuse My Dear Aunt Sally'
a + c = b + c
20. An instrument's _____ - the sound it produces - is a complex mixture of waves of different frequencies.
Tone
The inverse of addition is subtraction
The BML Traffic Model
Associate Property of Addition
21. Because of the associate property of addition - when presented with a sum of three numbers - whether you start by adding the first two numbers or the last two numbers - the resulting sum is
inline
The Same
Continuous Symmetry
Periodic Function
22. Perform all additions and subtractions in the order presented
Frequency
Euclid's Postulates
Stereographic Projection
left to right
23. 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.
Hypersphere
Law of Large Numbers
Dividing both Sides of an Equation by the Same Quantity
Irrational
24. The system that Euclid used in The Elements
Solution
The Prime Number Theorem
Tone
Axiomatic Systems
25. 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 -
Properties of Equality
The inverse of addition is subtraction
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
26. The surface of a standard 'donut shape'.
A number is divisible by 9
Torus
Fundamental Theorem of Arithmetic
a - c = b - c
27. Means approximately equal.
Properties of Equality
Irrational
˜
evaluate the expression in the innermost pair of grouping symbols first.
28. 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
per line
Division is not Commutative
Set up a Variable Dictionary.
a - c = b - c
29. 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.
Spherical Geometry
Expected Value
Box Diagram
Continuous Symmetry
30. A · 1/a = 1/a · a = 1
Irrational
Multiplicative Inverse:
Markov Chains
Dividing both Sides of an Equation by the Same Quantity
31. The multitude concept presented numbers as collections of discrete units - rather like indivisible atoms.
A number is divisible by 3
The Associative Property of Multiplication
The inverse of addition is subtraction
Discrete
32. An important part of problem solving is identifying
Pigeonhole Principle
Dividing both Sides of an Equation by the Same Quantity
variable
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
33. The inverse of multiplication
Galois Theory
Multiplying both Sides of an Equation by the Same Quantity
division
Fourier Analysis
34. If a = b then
the set of natural numbers
Permutation
The Additive Identity Property
a · c = b · c for c does not equal 0
35. Use parentheses - brackets - or curly braces to delimit the part of an expression you want evaluated first.
Grouping Symbols
Expected Value
Public Key Encryption
Primes
36. The study of shape from the perspective of being on the surface of the shape.
Irrational
The Set of Whole Numbers
Intrinsic View
Expected Value
37. Some numbers make geometric shapes when arranged as a collection of dots - for example - 16 makes a square - and 10 makes a triangle.
Primes
A prime number
Figurate Numbers
Spherical Geometry
38. ____________ 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
Box Diagram
Periodic Function
The Associative Property of Multiplication
Probability
39. Let a - b - and c represent whole numbers. Then - (a + b) + c = a + (b + c).
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
Associate Property of Addition
Modular Arithmetic
The inverse of addition is subtraction
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.
Denominator
Ramsey Theory
Irrational
Transfinite
41. Writing Mathematical equations - arrange your work one equation
A number is divisible by 10
per line
Multiplication by Zero
Frequency
42. A point in three-dimensional space requires three numbers to fix its location.
Spaceland
Figurate Numbers
Galton Board
Geometry
43. (a + b) + c = a + (b + c)
Factor Tree Alternate Approach
Rational
Non-Euclidian Geometry
Associative Property of Addition:
44. Two equations if they have the same solution set.
left to right
Multiplicative Inverse:
Equivalent Equations
The Additive Identity Property
45. If a = b then
Box Diagram
Associative Property of Multiplication:
a
Pigeonhole Principle
46. A topological object that can be used to study the allowable states of a given system.
Configuration 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.
Dividing both Sides of an Equation by the Same Quantity
a · c = b · c for c does not equal 0
47. 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
Answer the Question
Hypercube
Dimension
Overtone
48. Trigonometric functions - such as sine and cosine - are useful for modeling sound waves - because they oscillate between values
Commensurability
Torus
Hamilton Cycle
Periodic Function
49. (a · b) · c = a · (b · c)
A number is divisible by 9
Aleph-Null
Fundamental Theorem of Arithmetic
Associative Property of Multiplication:
50. Let a - b - and c be any whole numbers. Then - a
Composite Numbers
Hypercube
Commutative Property of Multiplication
The Distributive Property (Subtraction)