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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. If the sum of its digits is divisible by 3 (ex: 3591 is divisible by 3 since 3 + 5 + 9 + 1 = 18 is divisible by 3).
the set of natural numbers
each whole number can be uniquely decomposed into products of primes.
A number is divisible by 3
Equivalent Equations
2. A topological object that can be used to study the allowable states of a given system.
Configuration Space
Group
Continuous Symmetry
The BML Traffic Model
3. The state of appearing unchanged.
Invarient
A prime number
Euclid's Postulates
perimeter
4. A + (-a) = (-a) + a = 0
inline
Additive Inverse:
Continuous
Grouping Symbols
5. 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.
Countable
The Associative Property of Multiplication
a + c = b + c
Geometry
6. Does not change the solution set. That is - if a = b - then dividing both sides of the equation by c produces the equivalent equation a/c = b/c - provided c = 0.
Distributive Property:
Dividing both Sides of an Equation by the Same Quantity
Galois Theory
General Relativity
7. Multiplication is equivalent to
left to right
Solve the Equation
repeated addition
division
8. When writing mathematical statements - follow the mantra:
Markov Chains
Line Land
One equal sign per line
perimeter
9. 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.
Additive Inverse:
Problem of the Points
Complete Graph
Solution
10. In some ways - the opposite of a multitude is a magnitude - which is ___________. In other words - there are no well defined partitions.
Continuous
Commensurability
Figurate Numbers
In Euclidean four-space
11. (a · b) · c = a · (b · c)
The Set of Whole Numbers
Configuration Space
Associative Property of Multiplication:
Standard Deviation
12. The fundamental theorem of arithmetic says that
Modular Arithmetic
each whole number can be uniquely decomposed into products of primes.
Factor Tree Alternate Approach
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
13. Originally known as analysis situs
Invarient
Topology
Fundamental Theorem of Arithmetic
Central Limit Theorem
14. 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
Principal Curvatures
Euclid's Postulates
Frequency
Non-Euclidian Geometry
15. Writing Mathematical equations - arrange your work one equation
Probability
set
Hypersphere
per line
16. A · b = b · a
Genus
Figurate Numbers
Discrete
Commutative Property of Multiplication:
17. 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.
Sign Rules for Division
Hyperbolic Geometry
The Multiplicative Identity Property
Equation
18. In the expression 3
Countable
Products and Factors
Divisible
Division is not Associative
19. N = {1 - 2 - 3 - 4 - 5 - . . .}.
bar graph
the set of natural numbers
Standard Deviation
Associate Property of Addition
20. Let a - b - and c represent whole numbers. Then - (a + b) + c = a + (b + c).
counting numbers
Galton Board
Associate Property of Addition
Configuration Space
21. 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.'
Divisible
Poincare Disk
Genus
Look Back
22. If its final digit is a 0.
Multiplication by Zero
Cayley's Theorem
Equation
A number is divisible by 10
23. This result relates conserved physical quantities - like conservation of energy - to continuous symmetries of spacetime.
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24. Also known as gluing diagrams - are a convenient way to examine intrinsic topology.
each whole number can be uniquely decomposed into products of primes.
Box Diagram
a divided by b
4 + x = 12
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.
a + c = b + c
B - 125 = 1200
Axiomatic Systems
Irrational
26. 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
Composite Numbers
Hypersphere
prime factors
Least Common Multiple (LCM)
27. (a
Probability
Division is not Associative
Dividing both Sides of an Equation by the Same Quantity
Frequency
28. 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
Flat Land
each whole number can be uniquely decomposed into products of primes.
Modular Arithmetic
29. Perform all additions and subtractions in the order presented
The BML Traffic Model
A number is divisible by 5
left to right
One equal sign per line
30. To describe and extend a numerical pattern
Commutative Property of Addition:
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.
Galois Theory
prime factors
31. Are the fundamental building blocks of arithmetic.
Primes
Genus
Markov Chains
The Additive Identity Property
32. 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
Discrete
a - c = b - c
Galton Board
33. A + 0 = 0 + a = a
Set up a Variable Dictionary.
bar graph
Additive Identity:
Frequency
34. 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.
Equivalent Equations
Hyperbolic Geometry
The BML Traffic Model
per line
35. Collection of objects. list all the objects in the set and enclosing the list in curly braces.
set
Cayley's Theorem
perimeter
prime factors
36. The solutions to this gambling dilemma is traditionally held to be the start of modern probability theory.
One equal sign per line
Multiplicative Inverse:
Hyperbolic Geometry
Problem of the Points
37. Some numbers make geometric shapes when arranged as a collection of dots - for example - 16 makes a square - and 10 makes a triangle.
Central Limit Theorem
The Distributive Property (Subtraction)
Figurate Numbers
Multiplying both Sides of an Equation by the Same Quantity
38. The system that Euclid used in The Elements
Axiomatic Systems
Aleph-Null
Hyperbolic Geometry
Intrinsic View
39. 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 Multiplicative Identity Property
The inverse of subtraction is addition
per line
Hypercube
40. The whole number zero is called the additive identity. If a is any whole number - then a + 0 = a.
The Additive Identity Property
Multiplication
The Set of Whole Numbers
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.
41. In any ratio of two whole numbers - expressed as a fraction - we can interpret the first (top) number to be the 'counter -' or numerator
Rarefactior
set
Fourier Analysis
Denominator
42. Topological objects are categorized by their _______ (number of holes). The genus of a surface is a feature of its global topology.
Rational
Genus
Solve the Equation
left to right
43. 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
Hamilton Cycle
Division by Zero
Look Back
Denominator
44. A point in three-dimensional space requires three numbers to fix its location.
Spaceland
Sign Rules for Division
variable
Least Common Multiple (LCM)
45. If a is any whole number - then a
Galois Theory
Invarient
Conditional Probability
The Multiplicative Identity Property
46. A(b + c) = a · b + a · c a(b - c) = a · b - a · c
Law of Large Numbers
Non-Orientability
Distributive Property:
inline
47. The multitude concept presented numbers as collections of discrete units - rather like indivisible atoms.
Fourier Analysis
Products and Factors
Discrete
Prime Number
48. A '___________' infinite set is one that can be put into one-to-one correspondence with the set of natural numbers.
bar graph
Permutation
Countable
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
49. Let a and b represent two whole numbers. Then - a + b = b + a.
The Commutative Property of Addition
Division is not Associative
perimeter
Rational
50. You must always solve the equation set up in the previous step.
Solve the Equation
Divisible
left to right
The index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.