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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. The expression a/b means
Greatest Common Factor (GCF)
Set up a Variable Dictionary.
a divided by b
Solution
2. 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.
4 + x = 12
Problem of the Points
Dividing both Sides of an Equation by the Same Quantity
Normal Distribution
3. In any ratio of two whole numbers - expressed as a fraction - we can interpret the first (top) number to be the 'counter -' or numerator
Markov Chains
Denominator
Hyperbolic Geometry
inline
4. Collection of objects. list all the objects in the set and enclosing the list in curly braces.
Composite Numbers
set
repeated addition
Invarient
5. 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.
Exponents
In Euclidean four-space
Fourier Analysis and Synthesis
Transfinite
6. Add and subtract
Multiplicative Inverse:
The Multiplicative Identity Property
inline
Bijection
7. The whole number zero is called the additive identity. If a is any whole number - then a + 0 = a.
Continuous Symmetry
Figurate Numbers
The Additive Identity Property
A number is divisible by 9
8. We can think of the space between primes as 'prime deserts -' strings of consecutive numbers - none of which are prime.
Box Diagram
Galois Theory
Prime Deserts
Ramsey Theory
9. If a = b then
Rational
a · c = b · c for c does not equal 0
a
The Set of Whole Numbers
10. This method can create a flat map from a curved surface while preserving all angles in any features present.
Stereographic Projection
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
Fourier Analysis and Synthesis
11. 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.
Torus
Pigeonhole Principle
Complete Graph
Bijection
12. Points in two-dimensional space require two numbers to specify them completely. The Cartesian plane is a good way to envision two-dimensional space.
A number is divisible by 3
Flat Land
Grouping Symbols
Variable
13. Every solution to a word problem must include a carefully crafted equation that accurately describes the constraints in the problem statement.
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 · c = b · c for c does not equal 0
Set up an Equation
Rarefactior
14. × - ( )( ) - · - 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
Spherical Geometry
Multiplication
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
Answer the Question
15. Use parentheses - brackets - or curly braces to delimit the part of an expression you want evaluated first.
Grouping Symbols
Associative Property of Multiplication:
Fourier Analysis and Synthesis
Additive Identity:
16. 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
Configuration Space
Ramsey Theory
Transfinite
Hypercube
17. (a · b) · c = a · (b · c)
Commensurability
Associative Property of Multiplication:
Commutative Property of Multiplication:
Multiplication by Zero
18. Means approximately equal.
˜
Associative Property of Addition:
Principal Curvatures
Spaceland
19. Negative
Principal Curvatures
Problem of the Points
A number is divisible by 5
Sign Rules for Division
20. A number is divisible by 2
each whole number can be uniquely decomposed into products of primes.
Invarient
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
Variable
21. If a whole number is not a prime number - then it is called a...
Division by Zero
Composite Numbers
Sign Rules for Division
Flat Land
22. Einstein's famous theory - relates gravity to the curvature of spacetime.
˜
a
Multiplicative Inverse:
General Relativity
23. 1. Parentheses (or any grouping symbol {braces} - [square brackets] - |absolute value|)
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24. Also known as 'clock math -' incorporates 'wrap around' effects by having some number other than zero play the role of zero in addition - subtraction - multiplication - and division.
Modular Arithmetic
Multiplication by Zero
Variable
The Commutative Property of Addition
25. If a = b then
a - c = b - c
left to right
Set up an Equation
Commutative Property of Multiplication
26. The inverse of multiplication
division
Symmetry
Greatest Common Factor (GCF)
evaluate the expression in the innermost pair of grouping symbols first.
27. Instruments produce notes that have a fundamental frequency in combination with multiples of that frequency known as partials or overtones
Commutative Property of Multiplication
Intrinsic View
a - c = b - c
Overtone
28. 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.
Prime Number
Hyperland
Euler Characteristic
Law of Large Numbers
29. If a represents any whole number - then a
Polynomial
A number is divisible by 5
Transfinite
Multiplication by Zero
30. Reveals why we tend to find structure in seemingly random sets. Ramsey numbers indicate how big a set must be to guarantee the existence of certain minimal structures.
Intrinsic View
Cardinality
Unique Factorization Theorem
Ramsey Theory
31. 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
Problem of the Points
Irrational
Symmetry
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
32. ____________ 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
The inverse of multiplication is division
Problem of the Points
B - 125 = 1200
Probability
33. An instrument's _____ - the sound it produces - is a complex mixture of waves of different frequencies.
A number is divisible by 5
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
Tone
˜
34. 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
Genus
Multiplying both Sides of an Equation by the Same Quantity
The index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.
Pigeonhole Principle
35. The solutions to this gambling dilemma is traditionally held to be the start of modern probability theory.
Multiplication
a · c = b · c for c does not equal 0
Problem of the Points
The Riemann Hypothesis
36. 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 -
The inverse of subtraction is addition
Commutative Property of Multiplication
Spaceland
Equivalent Equations
37. W = {0 - 1 - 2 - 3 - 4 - 5 - . . .} is called
Invarient
The Set of Whole Numbers
A number is divisible by 3
Divisible
38. 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.'
division
Factor Trees
Factor Tree Alternate Approach
Hyperland
39. The process of taking a complicated signal and breaking it into sine and cosine components.
Permutation
Factor Tree Alternate Approach
Fourier Analysis
The Prime Number Theorem
40. A way to analyze sequences of events where the outcomes of prior events affect the probability of outcomes of subsequent events.
Poincare Disk
Symmetry
Irrational
Markov Chains
41. 4 more than a certain number is 12
Bijection
Multiplication
4 + x = 12
Look Back
42. 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
Problem of the Points
Factor Trees
Rational
Least Common Multiple (LCM)
43. A factor tree is a way to visualize a number's
Box Diagram
Extrinsic View
prime factors
Irrational
44. This important result says that every natural number greater than one can be expressed as a product of primes in exactly one way.
Box Diagram
Fundamental Theorem of Arithmetic
Hyperland
Discrete
45. Perform all additions and subtractions in the order presented
The Distributive Property (Subtraction)
left to right
Commensurability
Axiomatic Systems
46. Non-Euclidean geometries abide by some - but not all of Euclid's five postulates.
set
The inverse of addition is subtraction
Intrinsic View
Non-Euclidian Geometry
47. Cantor called the cardinality of all the sets that can be put into one-to-one correspondence with the counting numbers - or 'Aleph Null.'
Principal Curvatures
The inverse of addition is subtraction
Expected Value
Aleph-Null
48. 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.
Euler Characteristic
Division is not Commutative
division
Unique Factorization Theorem
49. 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.'
Divisible
Euclid's Postulates
a + c = b + c
Division is not Commutative
50. An arrangement where order matters.
Permutation
Hamilton Cycle
Associate Property of Addition
Frequency