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Test your basic knowledge |
CLEP General Math: Number Sense - Patterns - Algebraic Thinking
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Study First
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. This area of mathematics relates symmetry to whether or not an equation has a 'simple' solution.
Galois Theory
Least Common Multiple (LCM)
Associative Property of Multiplication:
Euclid's Postulates
2. The four-dimensional analog of the cube - square - and line segment. A hypercube is formed by taking a 3-D cube - pushing a copy of it into the fourth dimension - and connecting it with cubes. Envisioning this object in lower dimensions requires that
Invarient
Multiplication by Zero
Least Common Multiple (LCM)
Hypercube
3. A way to analyze sequences of events where the outcomes of prior events affect the probability of outcomes of subsequent events.
Normal Distribution
˜
Group
Markov Chains
4. A point in three-dimensional space requires three numbers to fix its location.
a - c = b - c
Distributive Property:
Spaceland
Answer the Question
5. Requirements for Word Problem Solutions.
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
Geometry
The Kissing Circle
Galois Theory
6. 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
Euler Characteristic
Greatest Common Factor (GCF)
Set up an Equation
Frequency
7. You must always solve the equation set up in the previous step.
Division is not Commutative
Answer the Question
Solve the Equation
The Prime Number Theorem
8. In this type of geometry the angles of a triangle add up to less than 180 degrees. In such a system - one has to replace the parallel postulate with a version that admits many parallel lines.
prime factors
The inverse of subtraction is addition
Noether's Theorem
Hyperbolic Geometry
9. Solving Equations
Pigeonhole Principle
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
Conditional Probability
Euclid's Postulates
10. If its final digit is a 0.
Multiplication by Zero
bar graph
A number is divisible by 10
Principal Curvatures
11. 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.
Modular Arithmetic
Prime Number
Properties of Equality
Euclid's Postulates
12. 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
Fourier Analysis
A number is divisible by 3
Cardinality
13. Division by zero is undefined. Each of the expressions 6
General Relativity
Normal Distribution
Amplitude
Division by Zero
14. Aka The Osculating Circle - a way to measure the curvature of a line.
The Kissing Circle
Periodic Function
Markov Chains
Discrete
15. 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.
counting numbers
Commutative Property of Addition:
Additive Inverse:
The BML Traffic Model
16. 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
Ramsey Theory
Set up a Variable Dictionary.
Additive Inverse:
Group
17. Positive integers are
Law of Large Numbers
Associate Property of Addition
counting numbers
division
18. Adding the same quantity to both sides of an equation - if a = b - then adding c to both sides of the equation produces the equivalent equation a + c = b + c.
Associate Property of Addition
does not change the solution set.
Multiplying both Sides of an Equation by the Same Quantity
Division by Zero
19. 1. Parentheses (or any grouping symbol {braces} - [square brackets] - |absolute value|)
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20. Has no factors other than 1 and itself
A prime number
Fundamental Theorem of Arithmetic
a divided by b
B - 125 = 1200
21. A point in one dimension requires only one number to define it. The number line is a good example of a one-dimensional space.
Solve the Equation
Line Land
perimeter
A number is divisible by 10
22. This result relates conserved physical quantities - like conservation of energy - to continuous symmetries of spacetime.
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23. This means that for any two magnitudes - one should always be able to find a fundamental unit that fits some whole number of times into each of them (i.e. - a unit whose magnitude is a whole number factor of each of the original magnitudes)
Commensurability
The Distributive Property (Subtraction)
Properties of Equality
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.
24. × - ( )( ) - · - 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
a - c = b - c
Fourier Analysis and Synthesis
Multiplication
Order of Operations - PEMDAS 'Please Excuse My Dear Aunt Sally'
25. Objects are topologically equivalent if they can be continuously deformed into one another. Properties that are preserved during this process are called topological invariants.
Ramsey Theory
Look Back
Commutative Property of Addition:
Irrational
26. The expression a/b means
prime factors
Normal Distribution
a divided by b
Sign Rules for Division
27. 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.'
bar graph
Order of Operations - PEMDAS 'Please Excuse My Dear Aunt Sally'
Hyperland
Fourier Analysis
28. 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
Figurate Numbers
Hypersphere
Invarient
Equation
29. A number is divisible by 2
In Euclidean four-space
One equal sign per line
Hypersphere
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
30. Negative
Sign Rules for Division
Equation
Genus
In Euclidean four-space
31. Einstein's famous theory - relates gravity to the curvature of spacetime.
General Relativity
a · c = b · c for c does not equal 0
A number is divisible by 9
Commensurability
32. (a
Cayley's Theorem
Division is not Associative
Group
4 + x = 12
33. Use parentheses - brackets - or curly braces to delimit the part of an expression you want evaluated first.
Tone
The Kissing Circle
Grouping Symbols
Flat Land
34. The inverse of multiplication
Equivalent Equations
Geometry
division
Grouping Symbols
35. Originally known as analysis situs
Comparison Property
Topology
Equivalent Equations
Fourier Analysis and Synthesis
36. 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.
Associative Property of Multiplication:
The BML Traffic Model
Transfinite
Euclid's Postulates
37. 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.
In Euclidean four-space
Answer the Question
Principal Curvatures
Discrete
38. Dimension is how mathematicians express the idea of degrees of freedom
Commutative Property of Multiplication:
Tone
The index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.
Dimension
39. Also known as gluing diagrams - are a convenient way to examine intrinsic topology.
Box Diagram
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
Order of Operations - PEMDAS 'Please Excuse My Dear Aunt Sally'
Sign Rules for Division
40. Are the fundamental building blocks of arithmetic.
Line Land
Primes
a · c = b · c for c does not equal 0
Principal Curvatures
41. If a = b then
Box Diagram
Hamilton Cycle
a - c = b - c
Look Back
42. A factor tree is a way to visualize a number's
Principal Curvatures
Noether's Theorem
Markov Chains
prime factors
43. Codifies the 'average behavior' of a random event and is a key concept in the application of probability.
Pigeonhole Principle
Countable
Commutative Property of Multiplication:
Expected Value
44. Let a and b represent two whole numbers. Then - a + b = b + a.
Euler Characteristic
Commutative Property of Multiplication
Ramsey Theory
The Commutative Property of Addition
45. Mathematical statement that equates two mathematical expressions.
Symmetry
Least Common Multiple (LCM)
Equation
Axiomatic Systems
46. 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.
Commutative Property of Multiplication:
counting numbers
Bijection
Solution
47. We can think of the space between primes as 'prime deserts -' strings of consecutive numbers - none of which are prime.
Conditional Probability
Set up a Variable Dictionary.
Commensurability
Prime Deserts
48. Of central importance in Ramsey Theory - and in combinatorics in general - is the 'pigeonhole principle -' also known as Dirichlet's box. This principle simply states that we cannot fit n+1 pigeons into n pigeonholes in such a way that only one pigeo
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
Hypercube
Pigeonhole Principle
Prime Number
49. The state of appearing unchanged.
Invarient
repeated addition
Group
˜
50. 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
variable
Multiplication
Additive Identity: