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Test your basic knowledge |
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. A topological invariant that relates a surface's vertices - edges - and faces.
per line
Expected Value
Non-Orientability
Euler Characteristic
2. Points in two-dimensional space require two numbers to specify them completely. The Cartesian plane is a good way to envision two-dimensional space.
Set up an Equation
Flat Land
The BML Traffic Model
Problem of the Points
3. A topological object that can be used to study the allowable states of a given system.
Group
Solve the Equation
Configuration Space
Galois Theory
4. This area of mathematics relates symmetry to whether or not an equation has a 'simple' solution.
Galois Theory
repeated addition
Rational
1. The unit 2. Prime numbers 3. Composite numbers
5. Multiplication is equivalent to
repeated addition
The Associative Property of Multiplication
Euler Characteristic
Wave Equation
6. (a + b) + c = a + (b + c)
Variable
General Relativity
Solution
Associative Property of Addition:
7. Solving Equations
Dividing both Sides of an Equation by the Same Quantity
Unique Factorization Theorem
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
Box Diagram
8. 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
Factor Trees
perimeter
Look Back
Cayley's Theorem
9. An instrument's _____ - the sound it produces - is a complex mixture of waves of different frequencies.
Geometry
Rarefactior
variable
Tone
10. The answer to the question of why the primes occur where they do on the number line has eluded mathematicians for centuries. Gauss's Prime Number Theorem is perhaps one of the most famous attempts to find the 'pattern behind the primes.'
The Prime Number Theorem
a + c = b + c
Factor Trees
Spherical Geometry
11. We can think of the space between primes as 'prime deserts -' strings of consecutive numbers - none of which are prime.
Prime Deserts
Division is not Commutative
Markov Chains
Flat Land
12. Has no factors other than 1 and itself
Euler Characteristic
Dividing both Sides of an Equation by the Same Quantity
Commutative Property of Addition:
A prime number
13. Is a symbol (usually a letter) that stands for a value that may vary.
Sign Rules for Division
Galton Board
Symmetry
Variable
14. This result relates conserved physical quantities - like conservation of energy - to continuous symmetries of spacetime.
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15. When writing mathematical statements - follow the mantra:
The Commutative Property of Addition
One equal sign per line
Comparison Property
Ramsey Theory
16. 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
Hypersphere
Flat Land
Dividing both Sides of an Equation by the Same Quantity
Geometry
17. The process of taking a complicated signal and breaking it into sine and cosine components.
Hyperland
Fourier Analysis
Expected Value
Prime Deserts
18. Let a - b - and c represent whole numbers. Then - (a + b) + c = a + (b + c).
left to right
Associate Property of Addition
repeated addition
Factor Tree Alternate Approach
19. × - ( )( ) - · - 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
Multiplication
left to right
Additive Identity:
Stereographic Projection
20. Says that when a random process - such as dropping marbles through a Galton board - is repeated many times - the frequencies of the observed outcomes get increasingly closer to the theoretical probabilities.
Cardinality
Continuous Symmetry
4 + x = 12
Law of Large Numbers
21. Rules for Rounding - To round a number to a particular place - follow these steps:
The Same
Topology
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
Hyperland
22. Einstein's famous theory - relates gravity to the curvature of spacetime.
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 Riemann Hypothesis
General Relativity
Modular Arithmetic
23. Two equations if they have the same solution set.
Equivalent Equations
Equation
Frequency
The Distributive Property (Subtraction)
24. Dimension is how mathematicians express the idea of degrees of freedom
Set up an Equation
a · c = b · c for c does not equal 0
Probability
Dimension
25. 4 more than a certain number is 12
Complete Graph
inline
4 + x = 12
Denominator
26. Every solution to a word problem must include a carefully crafted equation that accurately describes the constraints in the problem statement.
bar graph
Set up an Equation
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
Hypersphere
27. An algebraic 'sentence' containing an unknown quantity.
Polynomial
Pigeonhole Principle
Division is not Associative
Set up an Equation
28. Add and subtract
Countable
Bijection
Transfinite
inline
29. The expression a/b means
Extrinsic View
Euclid's Postulates
set
a divided by b
30. The whole number zero is called the additive identity. If a is any whole number - then a + 0 = a.
Expected Value
Look Back
Commutative Property of Addition:
The Additive Identity Property
31. A factor tree is a way to visualize a number's
Non-Orientability
Aleph-Null
Tone
prime factors
32. This method can create a flat map from a curved surface while preserving all angles in any features present.
Stereographic Projection
Least Common Multiple (LCM)
Prime Deserts
Overtone
33. 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.
Public Key Encryption
Least Common Multiple (LCM)
One equal sign per line
The BML Traffic Model
34. If a represents any whole number - then a
Flat Land
Line Land
Intrinsic View
Multiplication by Zero
35. 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.
counting numbers
Denominator
Division is not Associative
Spherical Geometry
36. 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).
Sign Rules for Division
A number is divisible by 9
Normal Distribution
Multiplication by Zero
37. Cannot be written as a ratio of natural numbers.
Spaceland
Irrational
Division is not Commutative
repeated addition
38. 1. Any two points can be joined by a straight line. 2. Any straight line segment can be extended indefinitely in a straight line. 3. Given any straight line segment - a circle can be drawn having the segment as radius and one endpoint as center. 4. A
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39. 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
Rarefactior
Multiplication
Commensurability
Divisible
40. You must always solve the equation set up in the previous step.
Topology
Solve the Equation
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
B - 125 = 1200
41. Codifies the 'average behavior' of a random event and is a key concept in the application of probability.
Figurate Numbers
Expected Value
The inverse of subtraction is addition
The Multiplicative Identity Property
42. This result says that the symmetries of geometric objects can be expressed as groups of permutations.
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43. 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.
Grouping Symbols
Solution
The Commutative Property of Addition
A prime number
44. Public key encryption allows two parties to communicate securely over an un-secured computer network using the properties of prime numbers and modular arithmetic. RSA is the modern standard for public key encryption.
The Additive Identity Property
Invarient
Commutative Property of Multiplication
Public Key Encryption
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
The Distributive Property (Subtraction)
perimeter
Irrational
Non-Orientability
46. If a = b then
a + c = b + c
division
Hyperbolic Geometry
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
47. 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
Exponents
Standard Deviation
The BML Traffic Model
48. 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.
The Kissing Circle
Associative Property of Addition:
Box Diagram
Bijection
49. Original Balance minus River Tam's Withdrawal is Current Balance
Sign Rules for Division
Geometry
B - 125 = 1200
Topology
50. An important part of problem solving is identifying
Symmetry
Associate Property of Addition
variable
The Prime Number Theorem