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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.
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. If a - b - and c are any whole numbers - then a
Line Land
The Associative Property of Multiplication
Solution
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.
2. If its final digit is a 0.
A number is divisible by 10
Division is not Commutative
The Prime Number Theorem
Non-Orientability
3. All integers are thus divided into three classes:
1. The unit 2. Prime numbers 3. Composite numbers
Denominator
Prime Number
Line Land
4. × - ( )( ) - · - 1. Multiply the numbers (ignoring the signs)2. The answer is positive if they have the same signs. 3. The answer is negative if they have different signs. 4. Alternatively - count the amount of negative numbers. If there are an even
Line Land
division
One equal sign per line
Multiplication
5. A way to measure how far away a given individual result is from the average result.
Standard Deviation
per line
The Riemann Hypothesis
Associative Property of Addition:
6. A + b = b + a
Commutative Property of Addition:
Greatest Common Factor (GCF)
a divided by b
perimeter
7. 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
Divisible
perimeter
Geometry
Normal Distribution
8. The fundamental theorem of arithmetic says that
Galton Board
Flat Land
Cayley's Theorem
each whole number can be uniquely decomposed into products of primes.
9. Codifies the 'average behavior' of a random event and is a key concept in the application of probability.
Expected Value
prime factors
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
Fourier Analysis
10. Original Balance minus River Tam's Withdrawal is Current Balance
The Kissing Circle
Axiomatic Systems
set
B - 125 = 1200
11. Originally known as analysis situs
Irrational
The inverse of addition is subtraction
Topology
Transfinite
12. 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.
Normal Distribution
bar graph
Hyperbolic Geometry
The Riemann Hypothesis
13. 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
The Same
Flat Land
Answer the Question
General Relativity
14. An algebraic 'sentence' containing an unknown quantity.
Intrinsic View
a · c = b · c for c does not equal 0
Polynomial
Set up an Equation
15. If a and b are any whole numbers - then a
Probability
Principal Curvatures
evaluate the expression in the innermost pair of grouping symbols first.
Commutative Property of Multiplication
16. Are the fundamental building blocks of arithmetic.
Ramsey Theory
Complete Graph
Primes
Look Back
17. 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.
Principal Curvatures
Central Limit Theorem
Symmetry
Distributive Property:
18. If a = b then a + c = b + c If a = b then a - c = b - c If a = b then a
Properties of Equality
Comparison Property
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
Solution
19. This model is at the forefront of probability research. Mathematicians use it to model traffic patterns in an attempt to understand flow rates and gridlock - among other things.
Hypersphere
Fourier Analysis and Synthesis
Denominator
The BML Traffic Model
20. 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.
Line Land
The Multiplicative Identity Property
Fundamental Theorem of Arithmetic
Continuous Symmetry
21. If a is any whole number - then a
Spaceland
Composite Numbers
Prime Number
The Multiplicative Identity Property
22. Our standard notions of Pythagorean distance and angle via the inner product extend quite nicely from three-space.
A prime number
In Euclidean four-space
Denominator
Variable
23. Determines the likelihood of events that are not independent of one another.
Wave Equation
Principal Curvatures
Aleph-Null
Conditional Probability
24. 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
Dividing both Sides of an Equation by the Same Quantity
Multiplication by Zero
Division is not Associative
Group
25. 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.'
Variable
Spaceland
Hamilton Cycle
Hyperland
26. This result relates conserved physical quantities - like conservation of energy - to continuous symmetries of spacetime.
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183
27. Topological objects are categorized by their _______ (number of holes). The genus of a surface is a feature of its global topology.
left to right
Least Common Multiple (LCM)
Overtone
Genus
28. W = {0 - 1 - 2 - 3 - 4 - 5 - . . .} is called
Equation
does not change the solution set.
The inverse of subtraction is addition
The Set of Whole Numbers
29. 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).
left to right
In Euclidean four-space
A number is divisible by 9
Denominator
30. The study of shape from the perspective of being on the surface of the shape.
Intrinsic View
Flat Land
per line
In Euclidean four-space
31. Instruments produce notes that have a fundamental frequency in combination with multiples of that frequency known as partials or overtones
Overtone
Solution
Hyperbolic Geometry
Order of Operations - PEMDAS 'Please Excuse My Dear Aunt Sally'
32. 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)
Commutative Property of Addition:
Law of Large Numbers
Irrational
33. 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
Sign Rules for Division
Galton Board
The Associative Property of Multiplication
Answer the Question
34. 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
Products and Factors
Hypersphere
De Bruijn Sequence
Cardinality
35. The whole number zero is called the additive identity. If a is any whole number - then a + 0 = a.
a
a + c = b + c
The Additive Identity Property
The Distributive Property (Subtraction)
36. GThe mathematical study of space. The geometry of a space goes hand in hand with how one defines the shortest distance between two points in that space.
Geometry
the set of natural numbers
Unique Factorization Theorem
counting numbers
37. A · 1 = 1 · a = a
Aleph-Null
Multiplicative Identity:
division
Rational
38. 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.
Cayley's Theorem
left to right
Bijection
Continuous Symmetry
39. This method can create a flat map from a curved surface while preserving all angles in any features present.
Polynomial
Noether's Theorem
Stereographic Projection
The Multiplicative Identity Property
40. A + 0 = 0 + a = a
Variable
Additive Identity:
Torus
Set up an Equation
41. You must always solve the equation set up in the previous step.
Cayley's Theorem
Solve the Equation
repeated addition
Dimension
42. In some ways - the opposite of a multitude is a magnitude - which is ___________. In other words - there are no well defined partitions.
Products and Factors
The inverse of subtraction is addition
Sign Rules for Division
Continuous
43. The multitude concept presented numbers as collections of discrete units - rather like indivisible atoms.
Discrete
Group
Conditional Probability
The BML Traffic Model
44. If a whole number is not a prime number - then it is called a...
Composite Numbers
Irrational
Rational
Polynomial
45. Einstein's famous theory - relates gravity to the curvature of spacetime.
Symmetry
Irrational
Commutative Property of Multiplication:
General Relativity
46. 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.'
a - c = b - c
Frequency
Cardinality
Divisible
47. 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
Multiplying both Sides of an Equation by the Same Quantity
Law of Large Numbers
Markov Chains
variable
48. Cannot be written as a ratio of natural numbers.
Additive Inverse:
Irrational
Hyperbolic Geometry
a + c = b + c
49. 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
Geometry
Commensurability
Look Back
The Same
50. (a · b) · c = a · (b · c)
Associative Property of Multiplication:
Invarient
The Set of Whole Numbers
Torus
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