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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. 1. Parentheses (or any grouping symbol {braces} - [square brackets] - |absolute value|)
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2. If a - b - and c are any whole numbers - then a
The Associative Property of Multiplication
Euler Characteristic
Galton Board
The index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.
3. Points in two-dimensional space require two numbers to specify them completely. The Cartesian plane is a good way to envision two-dimensional space.
Flat Land
Grouping Symbols
˜
Conditional Probability
4. This method can create a flat map from a curved surface while preserving all angles in any features present.
The Prime Number Theorem
Hyperbolic Geometry
Stereographic Projection
Permutation
5. Let a - b - and c represent whole numbers. Then - (a + b) + c = a + (b + c).
Products and Factors
left to right
Associate Property of Addition
The Riemann Hypothesis
6. 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
Equivalent Equations
Hypersphere
Cardinality
Spaceland
7. An object possessing continuous symmetries can remain invariant while one symmetry is turned into another. A circle is an example of an object with continuous symmetries.
Continuous Symmetry
Transfinite
The Associative Property of Multiplication
Aleph-Null
8. The multitude concept presented numbers as collections of discrete units - rather like indivisible atoms.
The BML Traffic Model
Discrete
The Additive Identity Property
Continuous
9. 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).
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
Factor Trees
The Multiplicative Identity Property
A number is divisible by 3
10. The system that Euclid used in The Elements
Non-Orientability
Axiomatic Systems
The Prime Number Theorem
Answer the Question
11. Is a path that visits every node in a graph and ends where it began.
Euler Characteristic
Hamilton Cycle
Division is not Commutative
Hyperbolic Geometry
12. Negative
Sign Rules for Division
inline
Non-Orientability
Exponents
13. When writing mathematical statements - follow the mantra:
One equal sign per line
The Multiplicative Identity Property
Rarefactior
Non-Euclidian Geometry
14. A topological invariant that relates a surface's vertices - edges - and faces.
Torus
Euler Characteristic
A number is divisible by 3
Associative Property of Multiplication:
15. 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
a
Division is not Commutative
The Kissing Circle
Rarefactior
16. 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.
The Distributive Property (Subtraction)
Intrinsic View
Dividing both Sides of an Equation by the Same Quantity
Geometry
17. 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
Hypersphere
Exponents
Irrational
Pigeonhole Principle
18. A · b = b · a
General Relativity
Commutative Property of Multiplication:
Commensurability
The BML Traffic Model
19. We can think of the space between primes as 'prime deserts -' strings of consecutive numbers - none of which are prime.
each whole number can be uniquely decomposed into products of primes.
Multiplying both Sides of an Equation by the Same Quantity
Fourier Analysis
Prime Deserts
20. 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.
Continuous Symmetry
Hyperbolic Geometry
Composite Numbers
Extrinsic View
21. This famous - as yet unproven - result relates to the distribution of prime numbers on the number line.
Permutation
set
Continuous
The Riemann Hypothesis
22. The expression a/b means
Division is not Associative
a divided by b
A prime number
Torus
23. The study of shape from the perspective of being on the surface of the shape.
Intrinsic View
Solution
Distributive Property:
Division is not Commutative
24. 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.
Law of Large Numbers
The Distributive Property (Subtraction)
Multiplicative Inverse:
The Prime Number Theorem
25. 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.
perimeter
Irrational
Unique Factorization Theorem
Ramsey Theory
26. Are the fundamental building blocks of arithmetic.
Primes
Genus
Symmetry
Dimension
27. The expression a^m means a multiplied by itself m times. The number a is called the base of the exponential expression and the number m is called the exponent. The exponent m tells us to repeat the base a as a factor m times.
Polynomial
Exponents
The Prime Number 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
28. Index p radicand
a · c = b · c for c does not equal 0
Continuous
The index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.
Division is not Commutative
29. If its final digit is a 0.
Grouping Symbols
A number is divisible by 10
4 + x = 12
Extrinsic View
30. Is the shortest string that contains all possible permutations of a particular length from a given set.
Flat Land
Permutation
A number is divisible by 10
De Bruijn Sequence
31. A number is divisible by 2
Variable
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
Genus
Law of Large Numbers
32. 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.
Non-Orientability
Normal Distribution
Frequency
General Relativity
33. Einstein's famous theory - relates gravity to the curvature of spacetime.
General Relativity
Rarefactior
Group
Answer the Question
34. Requirements for Word Problem Solutions.
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
Solve the Equation
Geometry
Law of Large Numbers
35. If grouping symbols are nested
evaluate the expression in the innermost pair of grouping symbols first.
Principal Curvatures
Division by Zero
Division is not Associative
36. An algebraic 'sentence' containing an unknown quantity.
Group
Polynomial
Torus
Figurate Numbers
37. A + 0 = 0 + a = a
Line Land
Associative Property of Multiplication:
Additive Identity:
Denominator
38. The study of shape from an external perspective.
Division is not Associative
counting numbers
Complete Graph
Extrinsic View
39. Let a and b represent two whole numbers. Then - a + b = b + a.
Fundamental Theorem of Arithmetic
The BML Traffic Model
The Commutative Property of Addition
Properties of Equality
40. Cantor called the cardinality of all the sets that can be put into one-to-one correspondence with the counting numbers - or 'Aleph Null.'
Countable
Aleph-Null
Greatest Common Factor (GCF)
Group
41. 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
Multiplication
Line Land
perimeter
Frequency
42. 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.
Problem of the Points
Spherical Geometry
Variable
the set of natural numbers
43. An important part of problem solving is identifying
Rarefactior
per line
Associative Property of Addition:
variable
44. 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
Composite Numbers
Order of Operations - PEMDAS 'Please Excuse My Dear Aunt Sally'
Frequency
Non-Euclidian Geometry
45. Collection of objects. list all the objects in the set and enclosing the list in curly braces.
Multiplying both Sides of an Equation by the Same Quantity
Complete Graph
set
Central Limit Theorem
46. A graph in which every node is connected to every other node is called a complete graph.
Noether's Theorem
Dimension
Complete Graph
counting numbers
47. 4 more than a certain number is 12
Overtone
4 + x = 12
Discrete
Division is not Associative
48. A · 1/a = 1/a · a = 1
Multiplicative Inverse:
The inverse of multiplication is division
Overtone
a · c = b · c for c does not equal 0
49. 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.
left to right
The BML Traffic Model
Rarefactior
Overtone
50. Add and subtract
4 + x = 12
Flat Land
Wave Equation
inline
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