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CLEP General Math: Number Sense - Patterns - Algebraic Thinking
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Subjects
:
clep
,
math
,
algebra
Instructions:
Answer 50 questions in 15 minutes.
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study here
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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. This result says that the symmetries of geometric objects can be expressed as groups of permutations.
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2. Is the shortest string that contains all possible permutations of a particular length from a given set.
Transfinite
De Bruijn Sequence
Sign Rules for Division
4 + x = 12
3. Topological objects are categorized by their _______ (number of holes). The genus of a surface is a feature of its global topology.
Intrinsic View
Exponents
Genus
Amplitude
4. 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
Rational
Multiplicative Inverse:
Group
Dimension
5. A topological object that can be used to study the allowable states of a given system.
repeated addition
a · c = b · c for c does not equal 0
Configuration Space
A number is divisible by 3
6. This famous - as yet unproven - result relates to the distribution of prime numbers on the number line.
A number is divisible by 5
The Riemann Hypothesis
Topology
counting numbers
7. Some numbers make geometric shapes when arranged as a collection of dots - for example - 16 makes a square - and 10 makes a triangle.
Solve the Equation
The inverse of subtraction is addition
Figurate Numbers
Dividing both Sides of an Equation by the Same Quantity
8. Let a - b - and c be any whole numbers. Then - a
Amplitude
The Distributive Property (Subtraction)
Flat Land
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
9. Cantor called the cardinality of all the sets that can be put into one-to-one correspondence with the counting numbers - or 'Aleph Null.'
Multiplication by Zero
does not change the solution set.
Aleph-Null
Commutative Property of Addition:
10. (a · b) · c = a · (b · c)
Associate Property of Addition
Multiplicative Inverse:
Associative Property of Multiplication:
Hypersphere
11. If the sum of its digits is divisible by 3 (ex: 3591 is divisible by 3 since 3 + 5 + 9 + 1 = 18 is divisible by 3).
A number is divisible by 3
The Associative Property of Multiplication
Solve the Equation
Least Common Multiple (LCM)
12. A number is divisible by 2
Galton Board
left to right
Set up an Equation
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
13. A way to analyze sequences of events where the outcomes of prior events affect the probability of outcomes of subsequent events.
Geometry
Markov Chains
Group
prime factors
14. All integers are thus divided into three classes:
Irrational
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
Associative Property of Addition:
1. The unit 2. Prime numbers 3. Composite numbers
15. Also known as gluing diagrams - are a convenient way to examine intrinsic topology.
Irrational
Torus
Box Diagram
Fourier Analysis and Synthesis
16. The identification of a 'one-to-one' correspondence--enables us to enumerate a set that may be difficult to count in terms of another set that is more easily counted.
Axiomatic Systems
Aleph-Null
A number is divisible by 3
Bijection
17. A whole number (other than 1) is a _____________ if its only factors (divisors) are 1 and itself. Equivalently - a number is prime if and only if it has exactly two factors (divisors).
Prime Number
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
Euclid's Postulates
Commensurability
18. The study of shape from the perspective of being on the surface of the shape.
The BML Traffic Model
division
Continuous
Intrinsic View
19. A point in one dimension requires only one number to define it. The number line is a good example of a one-dimensional space.
Public Key Encryption
a - c = b - c
A number is divisible by 10
Line Land
20. 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.'
counting numbers
Additive Inverse:
left to right
Hyperland
21. If its final digit is a 0 or 5.
The Multiplicative Identity Property
Hypercube
A prime number
A number is divisible by 5
22. 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
Figurate Numbers
Answer the Question
Multiplying both Sides of an Equation by the Same Quantity
A number is divisible by 5
23. The system that Euclid used in The Elements
Division is not Associative
Rarefactior
Axiomatic Systems
Multiplication
24. Non-Euclidean geometries abide by some - but not all of Euclid's five postulates.
The Commutative Property of Addition
Public Key Encryption
Multiplicative Identity:
Non-Euclidian Geometry
25. 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.
Solution
Transfinite
The inverse of multiplication is division
Sign Rules for Division
26. 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
Rational
left to right
Markov Chains
Look Back
27. The multitude concept presented numbers as collections of discrete units - rather like indivisible atoms.
Non-Orientability
each whole number can be uniquely decomposed into products of primes.
Discrete
division
28. This area of mathematics relates symmetry to whether or not an equation has a 'simple' solution.
Probability
Galois Theory
Line Land
Standard Deviation
29. You must always solve the equation set up in the previous step.
Solve the Equation
Division is not Associative
Factor Tree Alternate Approach
each whole number can be uniquely decomposed into products of primes.
30. 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.
Comparison Property
The Riemann Hypothesis
Galton Board
Rarefactior
31. Arise from the attempt to measure all quantities with a common unit of measure.
Set up an Equation
Bijection
Rational
Continuous Symmetry
32. 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 -
Geometry
Additive Identity:
The inverse of addition is subtraction
Division is not Commutative
33. Original Balance minus River Tam's Withdrawal is Current Balance
Solve the Equation
B - 125 = 1200
Prime Deserts
Central Limit Theorem
34. This method can create a flat map from a curved surface while preserving all angles in any features present.
Central Limit Theorem
Flat Land
each whole number can be uniquely decomposed into products of primes.
Stereographic Projection
35. Every solution to a word problem must include a carefully crafted equation that accurately describes the constraints in the problem statement.
Set up an Equation
Spaceland
Public Key Encryption
evaluate the expression in the innermost pair of grouping symbols first.
36. If a and b are any whole numbers - then a
Multiplication
The inverse of addition is subtraction
Commutative Property of Multiplication
Multiplicative Identity:
37. The process of taking a complicated signal and breaking it into sine and cosine components.
Spaceland
Order of Operations - PEMDAS 'Please Excuse My Dear Aunt Sally'
Fourier Analysis
Division by Zero
38. If a is any whole number - then a
De Bruijn Sequence
Dimension
The Additive Identity Property
The Multiplicative Identity Property
39. Our standard notions of Pythagorean distance and angle via the inner product extend quite nicely from three-space.
The inverse of addition is subtraction
In Euclidean four-space
Normal Distribution
Irrational
40. Used to display measurements. The measurement was taken is placed on the horizontal axis - and the height of each bar equals the amount during that year.
bar graph
The Commutative Property of Addition
Hyperbolic Geometry
Commutative Property of Addition:
41. 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.
Continuous Symmetry
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
Composite Numbers
Discrete
42. Use parentheses - brackets - or curly braces to delimit the part of an expression you want evaluated first.
Denominator
Periodic Function
Fundamental Theorem of Arithmetic
Grouping Symbols
43. Uses second derivatives to relate acceleration in space to acceleration in time.
Problem of the Points
Division by Zero
In Euclidean four-space
Wave Equation
44. 4 more than a certain number is 12
the set of natural numbers
The BML Traffic Model
4 + x = 12
Periodic Function
45. Is the length around an object. Used to calculate such things as fencing around a yard - trimming a piece of material - and the amount of baseboard needed for a room.It is not necessary to have a formula since it is always just calculated by adding t
Ramsey Theory
perimeter
Euclid's Postulates
Primes
46. 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
prime factors
Factor Trees
The Kissing Circle
The Riemann Hypothesis
47. A graph in which every node is connected to every other node is called a complete graph.
Look Back
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
Complete Graph
Irrational
48. Points in two-dimensional space require two numbers to specify them completely. The Cartesian plane is a good way to envision two-dimensional space.
The Distributive Property (Subtraction)
Line Land
Multiplying both Sides of an Equation by the Same Quantity
Flat Land
49. 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
Products and Factors
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
Multiplying both Sides of an Equation by the Same Quantity
Frequency
50. Also known as 'clock math -' incorporates 'wrap around' effects by having some number other than zero play the role of zero in addition - subtraction - multiplication - and division.
Noether's Theorem
Hamilton Cycle
Euler Characteristic
Modular Arithmetic
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