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Test your basic knowledge |
CLEP General Math: Number Sense - Patterns - Algebraic Thinking
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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. 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
Intrinsic View
Least Common Multiple (LCM)
Continuous
Noether's Theorem
2. A · b = b · a
Additive Identity:
The BML Traffic Model
Non-Orientability
Commutative Property of Multiplication:
3. 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
Galton Board
Poincare Disk
Answer the Question
4. If its final digit is a 0 or 5.
Exponents
The inverse of addition is subtraction
a
A number is divisible by 5
5. Every solution to a word problem must include a carefully crafted equation that accurately describes the constraints in the problem statement.
B - 125 = 1200
Set up an Equation
variable
Commensurability
6. 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
Frequency
Fourier Analysis
Answer the Question
Denominator
7. In the expression 3
De Bruijn Sequence
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
Products and Factors
Solution
8. Adding the same quantity to both sides of an equation - if a = b - then adding c to both sides of the equation produces the equivalent equation a + c = b + c.
Cardinality
does not change the solution set.
A number is divisible by 9
Markov Chains
9. 1. Parentheses (or any grouping symbol {braces} - [square brackets] - |absolute value|)
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10. If a = b then
Multiplicative Identity:
Divisible
Division is not Commutative
a - c = b - c
11. A · 1/a = 1/a · a = 1
The Distributive Property (Subtraction)
Prime Deserts
Figurate Numbers
Multiplicative Inverse:
12. Trigonometric functions - such as sine and cosine - are useful for modeling sound waves - because they oscillate between values
Geometry
Periodic Function
Non-Euclidian Geometry
Hamilton Cycle
13. Dimension is how mathematicians express the idea of degrees of freedom
a · c = b · c for c does not equal 0
Dimension
Bijection
Variable
14. 4 more than a certain number is 12
The inverse of multiplication is division
Continuous
4 + x = 12
Non-Euclidian Geometry
15. Negative
The BML Traffic Model
Sign Rules for Division
The Associative Property of Multiplication
A number is divisible by 5
16. Is the shortest string that contains all possible permutations of a particular length from a given set.
De Bruijn Sequence
4 + x = 12
Hypersphere
repeated addition
17. Einstein's famous theory - relates gravity to the curvature of spacetime.
General Relativity
Galton Board
Multiplication
The Set of Whole Numbers
18. A topological object that can be used to study the allowable states of a given system.
Probability
The Commutative Property of Addition
Configuration Space
One equal sign per line
19. 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
Polynomial
The Commutative Property of Addition
Frequency
The index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.
20. Division by zero is undefined. Each of the expressions 6
prime factors
The Associative Property of Multiplication
Division by Zero
1. The unit 2. Prime numbers 3. Composite numbers
21. (a
B - 125 = 1200
Cayley's Theorem
perimeter
Division is not Associative
22. Are the fundamental building blocks of arithmetic.
division
Commutative Property of Addition:
Answer the Question
Primes
23. The whole number zero is called the additive identity. If a is any whole number - then a + 0 = a.
Stereographic Projection
Standard Deviation
The Additive Identity Property
inline
24. W = {0 - 1 - 2 - 3 - 4 - 5 - . . .} is called
The Set of Whole Numbers
A number is divisible by 5
Complete Graph
Bijection
25. The surface of a standard 'donut shape'.
Standard Deviation
The Riemann Hypothesis
Rational
Torus
26. A point in three-dimensional space requires three numbers to fix its location.
set
Spaceland
˜
Configuration Space
27. (a + b) + c = a + (b + c)
Associative Property of Addition:
Unique Factorization Theorem
Look Back
Spherical Geometry
28. ____________ theory enables us to use mathematics to characterize and predict the behavior of random events. By 'random' we mean 'unpredictable' in the sense that in a given specific situation - our knowledge of current conditions gives us no way to
Equivalent Equations
a
Probability
Variable
29. Used to display measurements. The measurement was taken is placed on the horizontal axis - and the height of each bar equals the amount during that year.
Solution
Principal Curvatures
bar graph
Hyperbolic Geometry
30. 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
Set up a Variable Dictionary.
Frequency
Symmetry
Distributive Property:
31. 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
bar graph
Sign Rules for Division
Figurate Numbers
32. Topological objects are categorized by their _______ (number of holes). The genus of a surface is a feature of its global topology.
Solve the Equation
Genus
A number is divisible by 5
Irrational
33. We can think of the space between primes as 'prime deserts -' strings of consecutive numbers - none of which are prime.
Prime Deserts
Periodic Function
set
a + c = b + c
34. 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.'
1. The unit 2. Prime numbers 3. Composite numbers
Divisible
Expected Value
A number is divisible by 5
35. A + (-a) = (-a) + a = 0
Discrete
Additive Inverse:
A number is divisible by 5
The Associative Property of Multiplication
36. This method can create a flat map from a curved surface while preserving all angles in any features present.
Markov Chains
Stereographic Projection
Prime Number
Tone
37. Breaks a complicated signal into a combination of simple sine waves. Fourier synthesis does the opposite - constructing a complicated signal from simple sine waves.
left to right
counting numbers
The inverse of subtraction is addition
Fourier Analysis and Synthesis
38. 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).
A number is divisible by 3
Poincare Disk
Variable
Prime Number
39. 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
Group
Order of Operations - PEMDAS 'Please Excuse My Dear Aunt Sally'
Denominator
40. A + 0 = 0 + a = a
Countable
Rational
Galton Board
Additive Identity:
41. 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
Amplitude
The Prime Number Theorem
Intrinsic View
Group
42. 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
Flat Land
Axiomatic Systems
Intrinsic View
The Same
43. 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.
Multiplicative Identity:
Spaceland
Bijection
Pigeonhole Principle
44. × - ( )( ) - · - 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
Hyperland
Grouping Symbols
Pigeonhole Principle
45. 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.
Conditional Probability
Stereographic Projection
Unique Factorization Theorem
The Distributive Property (Subtraction)
46. The state of appearing unchanged.
Least Common Multiple (LCM)
Topology
One equal sign per line
Invarient
47. If we start with a number x and multiply by a number a - then dividing the result by the number a returns us to the original number x. In symbols - a
Frequency
Non-Euclidian Geometry
The inverse of multiplication is division
Least Common Multiple (LCM)
48. 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 -
Symmetry
The inverse of subtraction is addition
Variable
Countable
49. Two equations if they have the same solution set.
Invarient
Multiplication by Zero
inline
Equivalent Equations
50. 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.
Hyperbolic Geometry
Poincare Disk
Amplitude
The Riemann Hypothesis