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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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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. Trigonometric functions - such as sine and cosine - are useful for modeling sound waves - because they oscillate between values
each whole number can be uniquely decomposed into products of primes.
Periodic Function
Continuous
Commensurability
2. In the expression 3
Tone
Products and Factors
evaluate the expression in the innermost pair of grouping symbols first.
In Euclidean four-space
3. 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.
Dimension
Poincare Disk
Normal Distribution
Conditional Probability
4. Use parentheses - brackets - or curly braces to delimit the part of an expression you want evaluated first.
Grouping Symbols
The Multiplicative Identity Property
Properties of Equality
General Relativity
5. A · 1/a = 1/a · a = 1
Hamilton Cycle
Fundamental Theorem of Arithmetic
Irrational
Multiplicative Inverse:
6. Every solution to a word problem must include a carefully crafted equation that accurately describes the constraints in the problem statement.
Discrete
Symmetry
Set up an Equation
does not change the solution set.
7. Are the fundamental building blocks of arithmetic.
Axiomatic Systems
Primes
Cayley's Theorem
Modular Arithmetic
8. 1. Parentheses (or any grouping symbol {braces} - [square brackets] - |absolute value|)
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9. 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.
Unique Factorization Theorem
Spherical Geometry
Standard Deviation
Hypersphere
10. 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
Group
Factor Trees
a
11. Writing Mathematical equations - arrange your work one equation
division
per line
General Relativity
Overtone
12. 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.
Dimension
Pigeonhole Principle
Products and Factors
Solution
13. 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
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 10
Problem of the Points
Hypersphere
14. If a - b - and c are any whole numbers - then a
General Relativity
Look Back
Torus
The Associative Property of Multiplication
15. Aka The Osculating Circle - a way to measure the curvature of a line.
a · c = b · c for c does not equal 0
Division is not Associative
The Kissing Circle
Configuration Space
16. Cannot be written as a ratio of natural numbers.
Sign Rules for Division
Modular Arithmetic
Cayley's Theorem
Irrational
17. If a and b are any whole numbers - then a
Variable
Polynomial
Markov Chains
Commutative Property of Multiplication
18. The amount of displacement - as measured from the still surface line.
Amplitude
Factor Tree Alternate Approach
Commutative Property of Multiplication
Variable
19. 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.
Properties of Equality
Exponents
Fundamental Theorem of Arithmetic
Permutation
20. The state of appearing unchanged.
Invarient
Distributive Property:
Products and Factors
A number is divisible by 5
21. Solving Equations
Discrete
The 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
Associative Property of Addition:
22. Whether or not we hear waves as sound has everything to do with their _____________ - or how many times every second the molecules switch from compression to rarefaction and back to compression again - and their intensity - or how much the air is com
Look Back
Frequency
The inverse of addition is subtraction
Multiplicative Inverse:
23. Is a path that visits every node in a graph and ends where it began.
Normal Distribution
Problem of the Points
Fundamental Theorem of Arithmetic
Hamilton Cycle
24. Non-Euclidean geometries abide by some - but not all of Euclid's five postulates.
Non-Euclidian Geometry
The Multiplicative Identity Property
Products and Factors
Aleph-Null
25. 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 -
The inverse of subtraction is addition
Continuous
Euler Characteristic
Prime Number
26. The multitude concept presented numbers as collections of discrete units - rather like indivisible atoms.
does not change the solution set.
Figurate Numbers
Discrete
A prime number
27. 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
The inverse of subtraction is addition
The Same
B - 125 = 1200
Factor Trees
28. Cantor called the cardinality of all the sets that can be put into one-to-one correspondence with the counting numbers - or 'Aleph Null.'
Aleph-Null
Continuous Symmetry
Geometry
each whole number can be uniquely decomposed into products of primes.
29. Our standard notions of Pythagorean distance and angle via the inner product extend quite nicely from three-space.
Division is not Associative
Axiomatic Systems
In Euclidean four-space
Additive Identity:
30. The study of shape from an external perspective.
Group
The inverse of subtraction is addition
Extrinsic View
Irrational
31. Objects are topologically equivalent if they can be continuously deformed into one another. Properties that are preserved during this process are called topological invariants.
Intrinsic View
Irrational
1. The unit 2. Prime numbers 3. Composite numbers
Fourier Analysis
32. Division by zero is undefined. Each of the expressions 6
General Relativity
Division by Zero
Composite Numbers
Associative Property of Multiplication:
33. A · b = b · a
Tone
Commutative Property of Multiplication:
inline
Cayley's Theorem
34. Mathematical statement that equates two mathematical expressions.
Equation
The Commutative Property of Addition
Division is not Commutative
perimeter
35. This famous - as yet unproven - result relates to the distribution of prime numbers on the number line.
Continuous
The Riemann Hypothesis
The Prime Number Theorem
Noether's Theorem
36. A topological object that can be used to study the allowable states of a given system.
Probability
Set up a Variable Dictionary.
Configuration Space
Division by Zero
37. A(b + c) = a · b + a · c a(b - c) = a · b - a · c
Dimension
Wave Equation
Stereographic Projection
Distributive Property:
38. 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
The Commutative Property of Addition
Least Common Multiple (LCM)
The inverse of multiplication is division
Continuous Symmetry
39. Topological objects are categorized by their _______ (number of holes). The genus of a surface is a feature of its global topology.
Division is not Associative
a - c = b - c
Genus
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.
40. To describe and extend a numerical pattern
A prime number
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.
Bijection
Markov Chains
41. The process of taking a complicated signal and breaking it into sine and cosine components.
Look Back
Fourier Analysis
Dividing both Sides of an Equation by the Same Quantity
Cardinality
42. 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.
Spherical Geometry
Principal Curvatures
B - 125 = 1200
Aleph-Null
43. N = {1 - 2 - 3 - 4 - 5 - . . .}.
Dimension
The inverse of addition is subtraction
the set of natural numbers
a + c = b + c
44. If a = b then a + c = b + c If a = b then a - c = b - c If a = b then a
The Riemann Hypothesis
Properties of Equality
Overtone
Normal Distribution
45. If a = b then
Noether's Theorem
Bijection
a + c = b + c
Pigeonhole Principle
46. Is the shortest string that contains all possible permutations of a particular length from a given set.
B - 125 = 1200
Hamilton Cycle
a · c = b · c for c does not equal 0
De Bruijn Sequence
47. 4 more than a certain number is 12
Comparison Property
Noether's Theorem
4 + x = 12
Multiplication
48. 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
Division is not Associative
Intrinsic View
The inverse of multiplication is division
Answer the Question
49. The solutions to this gambling dilemma is traditionally held to be the start of modern probability theory.
One equal sign per line
Multiplication by Zero
Problem of the Points
Polynomial
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.
Division is not Commutative
Extrinsic View
Look Back
Modular Arithmetic
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