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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. 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
perimeter
Transfinite
Probability
Commensurability
2. A way to measure how far away a given individual result is from the average result.
Products and Factors
a - c = b - c
Standard Deviation
Principal Curvatures
3. A topological object that can be used to study the allowable states of a given system.
Flat Land
A number is divisible by 3
Configuration Space
Pigeonhole Principle
4. A · b = b · a
Continuous Symmetry
Standard Deviation
Commutative Property of Multiplication:
Problem of the Points
5. Is the shortest string that contains all possible permutations of a particular length from a given set.
De Bruijn Sequence
Look Back
Exponents
The Distributive Property (Subtraction)
6. This result relates conserved physical quantities - like conservation of energy - to continuous symmetries of spacetime.
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7. Public key encryption allows two parties to communicate securely over an un-secured computer network using the properties of prime numbers and modular arithmetic. RSA is the modern standard for public key encryption.
Public Key Encryption
Rarefactior
Probability
Flat Land
8. The study of shape from an external perspective.
Periodic Function
Least Common Multiple (LCM)
Extrinsic View
Dividing both Sides of an Equation by the Same Quantity
9. All integers are thus divided into three classes:
One equal sign per line
1. The unit 2. Prime numbers 3. Composite numbers
Tone
A number is divisible by 10
10. Rules for Rounding - To round a number to a particular place - follow these steps:
Problem of the Points
Grouping Symbols
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
The Associative Property of Multiplication
11. Let a - b - and c be any whole numbers. Then - a
The Distributive Property (Subtraction)
Divisible
Dividing both Sides of an Equation by the Same Quantity
a
12. Some numbers make geometric shapes when arranged as a collection of dots - for example - 16 makes a square - and 10 makes a triangle.
The Set of Whole Numbers
Equation
One equal sign per line
Figurate Numbers
13. Use parentheses - brackets - or curly braces to delimit the part of an expression you want evaluated first.
The Associative Property of Multiplication
Non-Orientability
division
Grouping Symbols
14. TA model of a sequence of random events. Each marble that passes through the system represents a trial consisting of as many random events as there are rows in the system.
Euclid's Postulates
Galton Board
Unique Factorization Theorem
Spherical Geometry
15. A '___________' infinite set is one that can be put into one-to-one correspondence with the set of natural numbers.
division
Stereographic Projection
Countable
Answer the Question
16. 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
4 + x = 12
Overtone
The inverse of subtraction is addition
Multiplying both Sides of an Equation by the Same Quantity
17. 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.
Principal Curvatures
Prime Number
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
Factor Trees
18. × - ( )( ) - · - 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
Set up a Variable Dictionary.
Associative Property of Addition:
Multiplicative Identity:
19. 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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20. Let a and b represent two whole numbers. Then - a + b = b + a.
The Commutative Property of Addition
Prime Deserts
The Associative Property of Multiplication
Expected Value
21. A flat map of hyperbolic space.
Poincare Disk
Commutative Property of Multiplication
Associate Property of Addition
Multiplication by Zero
22. Perform all additions and subtractions in the order presented
Factor Tree Alternate Approach
A number is divisible by 9
Central Limit Theorem
left to right
23. 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
The index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.
Extrinsic View
Law of Large Numbers
24. 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.
Rarefactior
Fourier Analysis and Synthesis
Spherical Geometry
prime factors
25. (a
perimeter
Division is not Associative
Noether's Theorem
A number is divisible by 3
26. Originally known as analysis situs
perimeter
The Multiplicative Identity Property
Topology
De Bruijn Sequence
27. 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
Division by Zero
Factor Trees
Torus
Least Common Multiple (LCM)
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
A number is divisible by 10
Solution
Division is not Commutative
Hypersphere
29. Einstein's famous theory - relates gravity to the curvature of spacetime.
General Relativity
Commutative Property of Multiplication
Periodic Function
Intrinsic View
30. A point in three-dimensional space requires three numbers to fix its location.
Topology
Spaceland
The Same
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.
31. 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.
Dividing both Sides of an Equation by the Same Quantity
per line
Permutation
repeated addition
32. 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
Bijection
counting numbers
Axiomatic Systems
Hypercube
33. 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
Overtone
Products and Factors
The Kissing Circle
34. In the expression 3
Products and Factors
Polynomial
Non-Orientability
Multiplication by Zero
35. 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).
Multiplicative Identity:
Continuous Symmetry
A number is divisible by 3
Division by Zero
36. 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
In Euclidean four-space
Wave Equation
Prime Number
Factor Tree Alternate Approach
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.
Flat Land
Public Key Encryption
Irrational
Associative Property of Multiplication:
38. We can think of the space between primes as 'prime deserts -' strings of consecutive numbers - none of which are prime.
Associative Property of Addition:
Genus
Expected Value
Prime Deserts
39. Three is the common property of the group of sets containing three members. This idea is called '__________ -' which is a synonym for 'size.' The set {a -b -c} is a representative set of the cardinal number 3.
Cardinality
Denominator
Non-Euclidian Geometry
Variable
40. 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).
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 9
Composite Numbers
Normal Distribution
41. A factor tree is a way to visualize a number's
Least Common Multiple (LCM)
Tone
Solve the Equation
prime factors
42. N = {1 - 2 - 3 - 4 - 5 - . . .}.
Set up a Variable Dictionary.
Multiplication
the set of natural numbers
Division is not Associative
43. 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
Genus
Look Back
The Same
The inverse of subtraction is addition
44. 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.'
Grouping Symbols
Hyperland
Associative Property of Addition:
Conditional Probability
45. A
Division is not Commutative
Continuous Symmetry
Answer the Question
Hamilton Cycle
46. If a is any whole number - then a
Unique Factorization Theorem
Hyperbolic Geometry
Tone
The Multiplicative Identity Property
47. Aka The Osculating Circle - a way to measure the curvature of a line.
The Kissing Circle
division
each whole number can be uniquely decomposed into products of primes.
Look Back
48. Is a path that visits every node in a graph and ends where it began.
The Riemann Hypothesis
Division is not Commutative
Hamilton Cycle
variable
49. A point in one dimension requires only one number to define it. The number line is a good example of a one-dimensional space.
Flat Land
Fourier Analysis
Set up a Variable Dictionary.
Line Land
50. 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.
Solution
Equivalent Equations
does not change the solution set.
per line