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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. Assuming that the air is of uniform density and pressure to begin with - a region of high pressure will be balanced by a region of low pressure - called rarefaction - immediately following the compression
Equivalent Equations
Rarefactior
Commutative Property of Addition:
Overtone
2. A · 1 = 1 · a = a
Multiplicative Identity:
Euler Characteristic
Poincare Disk
Dimension
3. A + b = b + a
The Commutative Property of Addition
Variable
Commutative Property of Addition:
4 + x = 12
4. 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.
Galton Board
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
Division is not Associative
Equation
5. If a = b then
a
Periodic Function
Prime Number
Law of Large Numbers
6. If a = b then
Additive Identity:
Tone
a · c = b · c for c does not equal 0
A number is divisible by 10
7. Breaks a complicated signal into a combination of simple sine waves. Fourier synthesis does the opposite - constructing a complicated signal from simple sine waves.
Associate Property of Addition
Fourier Analysis and Synthesis
the set of natural numbers
Commutative Property of Multiplication
8. A way to extrinsically measure the curvature of a surface by looking at a given point and finding the contour line with the greatest curvature and the contour line with the least curvature.
Galton Board
Tone
prime factors
Principal Curvatures
9. A flat map of hyperbolic space.
Central Limit Theorem
Euler Characteristic
Poincare Disk
per line
10. The multitude concept presented numbers as collections of discrete units - rather like indivisible atoms.
perimeter
Primes
Multiplicative Identity:
Discrete
11. If a = b then
Rational
per line
The Riemann Hypothesis
a - c = b - c
12. Solving Equations
a
set
Variable
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
13. A + (-a) = (-a) + a = 0
Continuous Symmetry
Additive Inverse:
Symmetry
a
14. Non-Euclidean geometries abide by some - but not all of Euclid's five postulates.
Look Back
Non-Euclidian Geometry
Axiomatic Systems
Irrational
15. If a is any whole number - then a
Line Land
Cayley's Theorem
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
The Multiplicative Identity Property
16. Objects are topologically equivalent if they can be continuously deformed into one another. Properties that are preserved during this process are called topological invariants.
a · c = b · c for c does not equal 0
Irrational
Box Diagram
Conditional Probability
17. Our standard notions of Pythagorean distance and angle via the inner product extend quite nicely from three-space.
In Euclidean four-space
Least Common Multiple (LCM)
perimeter
Transfinite
18. A
Line Land
Unique Factorization Theorem
Associative Property of Multiplication:
Division is not Commutative
19. Use parentheses - brackets - or curly braces to delimit the part of an expression you want evaluated first.
variable
evaluate the expression in the innermost pair of grouping symbols first.
The inverse of subtraction is addition
Grouping Symbols
20. A + 0 = 0 + a = a
Greatest Common Factor (GCF)
Commutative Property of Addition:
Additive Identity:
Group
21. 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.
Line Land
Permutation
Figurate Numbers
Spherical Geometry
22. 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
Least Common Multiple (LCM)
Markov Chains
Fundamental Theorem of Arithmetic
Public Key Encryption
23. Aka The Osculating Circle - a way to measure the curvature of a line.
a
Fourier Analysis and Synthesis
The Kissing Circle
Division is not Commutative
24. The study of shape from the perspective of being on the surface of the shape.
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
Factor Trees
Exponents
Intrinsic View
25. 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.
Continuous Symmetry
Distributive Property:
Multiplicative Identity:
Unique Factorization Theorem
26. This area of mathematics relates symmetry to whether or not an equation has a 'simple' solution.
Products and Factors
Amplitude
Equivalent Equations
Galois Theory
27. The whole number zero is called the additive identity. If a is any whole number - then a + 0 = a.
Hypersphere
per line
The Additive Identity Property
Polynomial
28. A '___________' infinite set is one that can be put into one-to-one correspondence with the set of natural numbers.
Additive Inverse:
Sign Rules for Division
Commutative Property of Multiplication
Countable
29. An important part of problem solving is identifying
Hypercube
Look Back
Commutative Property of Multiplication
variable
30. Original Balance minus River Tam's Withdrawal is Current Balance
Tone
B - 125 = 1200
Products and Factors
Associative Property of Addition:
31. This result says that the symmetries of geometric objects can be expressed as groups of permutations.
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32. If its final digit is a 0 or 5.
Set up an Equation
Fourier Analysis and Synthesis
A number is divisible by 5
Permutation
33. Rules for Rounding - To round a number to a particular place - follow these steps:
Geometry
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.
Grouping Symbols
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
34. Perform all additions and subtractions in the order presented
Dimension
left to right
Hamilton Cycle
Standard Deviation
35. If a and b are any whole numbers - then a
prime factors
Markov Chains
The inverse of subtraction is addition
Commutative Property of Multiplication
36. 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
Hypersphere
Standard Deviation
Distributive Property:
37. 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
Law of Large Numbers
Commensurability
Multiplication by Zero
Frequency
38. Cannot be written as a ratio of natural numbers.
Markov Chains
Composite Numbers
Normal Distribution
Irrational
39. A point in one dimension requires only one number to define it. The number line is a good example of a one-dimensional space.
Hypersphere
The index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.
The Additive Identity Property
Line Land
40. (a
Overtone
Flat Land
Normal Distribution
Division is not Associative
41. Einstein's famous theory - relates gravity to the curvature of spacetime.
General Relativity
A prime number
Torus
a
42. 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.
Solution
The Associative Property of Multiplication
Problem of the Points
Galois Theory
43. 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
Spherical Geometry
per line
Factor Trees
The inverse of subtraction is addition
44. All integers are thus divided into three classes:
A number is divisible by 5
Hypersphere
1. The unit 2. Prime numbers 3. Composite numbers
Group
45. Points in two-dimensional space require two numbers to specify them completely. The Cartesian plane is a good way to envision two-dimensional space.
Fourier Analysis and Synthesis
Flat Land
Factor Trees
Galois Theory
46. Uses second derivatives to relate acceleration in space to acceleration in time.
Wave Equation
each whole number can be uniquely decomposed into products of primes.
Equivalent Equations
Dividing both Sides of an Equation by the Same Quantity
47. An instrument's _____ - the sound it produces - is a complex mixture of waves of different frequencies.
Tone
The Same
Irrational
Figurate Numbers
48. Trigonometric functions - such as sine and cosine - are useful for modeling sound waves - because they oscillate between values
Properties of Equality
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
Periodic Function
a divided by b
49. A topological invariant that relates a surface's vertices - edges - and faces.
Euler Characteristic
Aleph-Null
The Riemann Hypothesis
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
50. 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
Least Common Multiple (LCM)
De Bruijn Sequence
does not change the solution set.
Multiplying both Sides of an Equation by the Same Quantity
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