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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. Our standard notions of Pythagorean distance and angle via the inner product extend quite nicely from three-space.
Non-Euclidian Geometry
A number is divisible by 10
In Euclidean four-space
division
2. 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
˜
Group
Symmetry
Equation
3. (a + b) + c = a + (b + c)
Hyperbolic Geometry
Associative Property of Addition:
Galton Board
De Bruijn Sequence
4. Einstein's famous theory - relates gravity to the curvature of spacetime.
General Relativity
Rarefactior
The Additive Identity Property
One equal sign per line
5. A graph in which every node is connected to every other node is called a complete graph.
Complete Graph
Division by Zero
Rational
Associate Property of Addition
6. Non-Euclidean geometries abide by some - but not all of Euclid's five postulates.
Denominator
the set of natural numbers
Multiplying both Sides of an Equation by the Same Quantity
Non-Euclidian Geometry
7. Breaks a complicated signal into a combination of simple sine waves. Fourier synthesis does the opposite - constructing a complicated signal from simple sine waves.
Figurate Numbers
The inverse of subtraction is addition
Expected Value
Fourier Analysis and Synthesis
8. Objects are topologically equivalent if they can be continuously deformed into one another. Properties that are preserved during this process are called topological invariants.
Cayley's Theorem
bar graph
a + c = b + c
Irrational
9. 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.
Transfinite
The Commutative Property of Addition
evaluate the expression in the innermost pair of grouping symbols first.
Frequency
10. This important result says that every natural number greater than one can be expressed as a product of primes in exactly one way.
Distributive Property:
Fundamental Theorem of Arithmetic
does not change the solution set.
Hamilton Cycle
11. A · b = b · a
Non-Euclidian Geometry
A number is divisible by 9
Line Land
Commutative Property of Multiplication:
12. A topological invariant that relates a surface's vertices - edges - and faces.
Euler Characteristic
Genus
left to right
Cardinality
13. 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
Poincare Disk
Bijection
Pigeonhole Principle
Rarefactior
14. 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.
Normal Distribution
Probability
Problem of the Points
Hyperbolic Geometry
15. Aka The Osculating Circle - a way to measure the curvature of a line.
Solve the Equation
Axiomatic Systems
Fourier Analysis and Synthesis
The Kissing Circle
16. A + (-a) = (-a) + a = 0
Commutative Property of Addition:
Figurate Numbers
Order of Operations - PEMDAS 'Please Excuse My Dear Aunt Sally'
Additive Inverse:
17. 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.
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.
Products and Factors
Axiomatic Systems
Normal Distribution
18. A point in three-dimensional space requires three numbers to fix its location.
bar graph
Spaceland
Factor Tree Alternate Approach
Discrete
19. 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.
Properties of Equality
Bijection
repeated addition
Grouping Symbols
20. If we start with a number x and add a number a - then subtracting a from the result will return us to the original number x. x + a - a = x. so -
4 + x = 12
The inverse of addition is subtraction
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.
Genus
21. Topological objects are categorized by their _______ (number of holes). The genus of a surface is a feature of its global topology.
Genus
Galton Board
The BML Traffic Model
Division is not Commutative
22. An important part of problem solving is identifying
variable
Rational
Order of Operations - PEMDAS 'Please Excuse My Dear Aunt Sally'
Hyperbolic Geometry
23. Let a and b represent two whole numbers. Then - a + b = b + a.
The Commutative Property of Addition
The Distributive Property (Subtraction)
Hamilton Cycle
Hyperland
24. If its final digit is a 0 or 5.
Multiplicative Inverse:
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.
A number is divisible by 5
Division is not Associative
25. If a is any whole number - then a
does not change the solution set.
Problem of the Points
Central Limit Theorem
The Multiplicative Identity Property
26. The solutions to this gambling dilemma is traditionally held to be the start of modern probability theory.
Problem of the Points
Pigeonhole Principle
The Multiplicative Identity Property
Euclid's Postulates
27. A '___________' infinite set is one that can be put into one-to-one correspondence with the set of natural numbers.
1. The unit 2. Prime numbers 3. Composite numbers
Stereographic Projection
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
Countable
28. The whole number zero is called the additive identity. If a is any whole number - then a + 0 = a.
Non-Orientability
Countable
The Additive Identity Property
Poincare Disk
29. 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
Answer the Question
Tone
Multiplication by Zero
Continuous Symmetry
30. 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
Cardinality
perimeter
Line Land
Least Common Multiple (LCM)
31. This famous - as yet unproven - result relates to the distribution of prime numbers on the number line.
Tone
The Riemann Hypothesis
Ramsey Theory
Modular Arithmetic
32. Collection of objects. list all the objects in the set and enclosing the list in curly braces.
set
Unique Factorization Theorem
Intrinsic View
The Additive Identity Property
33. A number is divisible by 2
Order of Operations - PEMDAS 'Please Excuse My Dear Aunt Sally'
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
Equation
Cayley's Theorem
34. 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
Noether's Theorem
a + c = b + c
Torus
35. 1. Parentheses (or any grouping symbol {braces} - [square brackets] - |absolute value|)
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36. × - ( )( ) - · - 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
Equivalent Equations
Problem of the Points
a divided by b
37. Points in two-dimensional space require two numbers to specify them completely. The Cartesian plane is a good way to envision two-dimensional space.
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
Flat Land
division
the set of natural numbers
38. To describe and extend a numerical pattern
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.
The Kissing Circle
General Relativity
Wave Equation
39. Every solution to a word problem must include a carefully crafted equation that accurately describes the constraints in the problem statement.
4 + x = 12
In Euclidean four-space
Primes
Set up an Equation
40. 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.
Extrinsic View
1. The unit 2. Prime numbers 3. Composite numbers
Spherical Geometry
Equation
41. A way to measure how far away a given individual result is from the average result.
Standard Deviation
The Distributive Property (Subtraction)
Multiplication by Zero
˜
42. The process of taking a complicated signal and breaking it into sine and cosine components.
1. The unit 2. Prime numbers 3. Composite numbers
Fourier Analysis
A prime number
Figurate Numbers
43. Two equations if they have the same solution set.
Equivalent Equations
Prime Deserts
Euler Characteristic
Line Land
44. Index p radicand
Dimension
The index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.
A number is divisible by 3
Intrinsic View
45. Is a symbol (usually a letter) that stands for a value that may vary.
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.
Transfinite
Extrinsic View
Variable
46. Is a path that visits every node in a graph and ends where it began.
Hamilton Cycle
Noether's Theorem
Axiomatic Systems
prime factors
47. A + 0 = 0 + a = a
Wave Equation
Unique Factorization Theorem
Distributive Property:
Additive Identity:
48. If a = b then
Composite Numbers
Hypersphere
Standard Deviation
a
49. 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
Bijection
Pigeonhole Principle
Axiomatic Systems
The inverse of addition is subtraction
50. The study of shape from an external perspective.
Extrinsic View
a
left to right
Hyperbolic Geometry