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Test your basic knowledge |
CLEP General Math: Number Sense - Patterns - Algebraic Thinking
Start Test
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. 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).
A number is divisible by 9
The Additive Identity Property
The Same
Law of Large Numbers
2. If a whole number is not a prime number - then it is called a...
Associative Property of Addition:
Composite Numbers
Conditional Probability
Multiplication by Zero
3. If a is any whole number - then a
The Kissing Circle
Galois Theory
In Euclidean four-space
The Multiplicative Identity Property
4. A + (-a) = (-a) + a = 0
Central Limit Theorem
left to right
Additive Inverse:
Problem of the Points
5. 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
A prime number
Hypersphere
Countable
One equal sign per line
6. 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
division
per line
Multiplying both Sides of an Equation by the Same Quantity
Associate Property of Addition
7. 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.'
Overtone
The Prime Number Theorem
prime factors
Variable
8. × - ( )( ) - · - 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 by Zero
Multiplication
Spherical Geometry
Additive Identity:
9. Writing Mathematical equations - arrange your work one equation
Non-Orientability
per line
a - c = b - c
left to right
10. A flat map of hyperbolic space.
Grouping Symbols
Poincare Disk
Distributive Property:
Set up an Equation
11. Cannot be written as a ratio of natural numbers.
One equal sign per line
division
Irrational
Bijection
12. 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
variable
Commutative Property of Multiplication:
Set up an Equation
13. A graph in which every node is connected to every other node is called a complete graph.
Non-Euclidian Geometry
Complete Graph
B - 125 = 1200
˜
14. In a mathematical sense - it is a transformation that leaves an object invariant. Symmetry is perhaps most familiar as an artistic or aesthetic concept. Designs are said to be symmetric if they exhibit specific kinds of balance - repetition - and/or
Exponents
Symmetry
Transfinite
In Euclidean four-space
15. Also known as gluing diagrams - are a convenient way to examine intrinsic topology.
Law of Large Numbers
Multiplication by Zero
Box Diagram
Frequency
16. Perform all additions and subtractions in the order presented
Frequency
Set up an Equation
left to right
Wave Equation
17. The fundamental theorem of arithmetic says that
Associative Property of Multiplication:
each whole number can be uniquely decomposed into products of primes.
inline
Solve the Equation
18. Are the fundamental building blocks of arithmetic.
Law of Large Numbers
Normal Distribution
Primes
perimeter
19. This important result says that every natural number greater than one can be expressed as a product of primes in exactly one way.
perimeter
˜
Fundamental Theorem of Arithmetic
Solution
20. The solutions to this gambling dilemma is traditionally held to be the start of modern probability theory.
Additive Inverse:
Probability
Problem of the Points
Tone
21. Collection of objects. list all the objects in the set and enclosing the list in curly braces.
Aleph-Null
Primes
Axiomatic Systems
set
22. Cantor called the cardinality of all the sets that can be put into one-to-one correspondence with the counting numbers - or 'Aleph Null.'
Expected Value
does not change the solution set.
Aleph-Null
The BML Traffic Model
23. 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)
The Commutative Property of Addition
Genus
Conditional Probability
24. We can think of the space between primes as 'prime deserts -' strings of consecutive numbers - none of which are prime.
Prime Deserts
Associate Property of Addition
Wave Equation
Principal Curvatures
25. 1. Find the prime factorizations of each number.
Greatest Common Factor (GCF)
Division is not Associative
left to right
Cayley's Theorem
26. If a = b then a + c = b + c If a = b then a - c = b - c If a = b then a
Variable
set
Public Key Encryption
Properties of Equality
27. The multitude concept presented numbers as collections of discrete units - rather like indivisible atoms.
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
The Commutative Property of Addition
Associative Property of Multiplication:
Discrete
28. 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
Associative Property of Multiplication:
Distributive Property:
Permutation
Hypercube
29. Uses second derivatives to relate acceleration in space to acceleration in time.
Answer the Question
Solve the Equation
Wave Equation
Prime Number
30. In some ways - the opposite of a multitude is a magnitude - which is ___________. In other words - there are no well defined partitions.
The Additive Identity Property
Composite Numbers
Continuous
Comparison Property
31. You must let your readers know what each variable in your problem represents. This can be accomplished in a number of ways: Statements such as 'Let P represent the perimeter of the rectangle.' - Labeling unknown values with variables in a table - Lab
Euler Characteristic
Additive Inverse:
Set up a Variable Dictionary.
Additive Identity:
32. 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
Dimension
Pigeonhole Principle
Set up an Equation
Equation
33. 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.
Irrational
Torus
Rarefactior
Bijection
34. Index p radicand
Set up a Variable Dictionary.
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
The index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.
Additive Inverse:
35. 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
Stereographic Projection
Ramsey Theory
repeated addition
36. If a = b then
De Bruijn Sequence
Set up a Variable Dictionary.
Geometry
a
37. If a = b then
division
a · c = b · c for c does not equal 0
Flat Land
4 + x = 12
38. 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
prime factors
Spherical Geometry
The Same
Hypercube
39. If its final digit is a 0.
A number is divisible by 10
The Distributive Property (Subtraction)
a
inline
40. A way to analyze sequences of events where the outcomes of prior events affect the probability of outcomes of subsequent events.
each whole number can be uniquely decomposed into products of primes.
Markov Chains
Axiomatic Systems
perimeter
41. Means approximately equal.
A prime number
Commutative Property of Multiplication
˜
De Bruijn Sequence
42. If its final digit is a 0 or 5.
Commensurability
Multiplicative Identity:
The Additive Identity Property
A number is divisible by 5
43. N = {1 - 2 - 3 - 4 - 5 - . . .}.
the set of natural numbers
Expected Value
Division is not Commutative
Sign Rules for Division
44. 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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45. Some numbers make geometric shapes when arranged as a collection of dots - for example - 16 makes a square - and 10 makes a triangle.
Prime Deserts
Cayley's Theorem
The Commutative Property of Addition
Figurate Numbers
46. 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
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
Commutative Property of Addition:
Multiplication
47. Non-Euclidean geometries abide by some - but not all of Euclid's five postulates.
The BML Traffic Model
Spherical Geometry
Non-Euclidian Geometry
Division is not Associative
48. Some favor repeatedly dividing by 2 until the result is no longer divisible by 2. Then try repeatedly dividing by the next prime until the result is no longer divisible by that prime. The process terminates when the last resulting quotient is equal t
Transfinite
Public Key Encryption
Factor Tree Alternate Approach
Hyperland
49. (a
Rational
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
Division is not Associative
Euler Characteristic
50. If a = b then
Bijection
The Same
Normal Distribution
a - c = b - c