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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. 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.
4 + x = 12
Bijection
Hyperbolic Geometry
Probability
2. 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).
A number is divisible by 9
Multiplication by Zero
Conditional Probability
Law of Large Numbers
3. A topological invariant that relates a surface's vertices - edges - and faces.
The Additive Identity Property
Least Common Multiple (LCM)
Amplitude
Euler Characteristic
4. You must let your readers know what each variable in your problem represents. This can be accomplished in a number of ways: Statements such as 'Let P represent the perimeter of the rectangle.' - Labeling unknown values with variables in a table - Lab
Set up a Variable Dictionary.
Equation
a divided by b
evaluate the expression in the innermost pair of grouping symbols first.
5. The answer to the question of why the primes occur where they do on the number line has eluded mathematicians for centuries. Gauss's Prime Number Theorem is perhaps one of the most famous attempts to find the 'pattern behind the primes.'
The Prime Number Theorem
General Relativity
a - c = b - c
Wave Equation
6. If a whole number is not a prime number - then it is called a...
Composite Numbers
Amplitude
Invarient
Problem of the Points
7. Arise from the attempt to measure all quantities with a common unit of measure.
Intrinsic View
Wave Equation
Rational
In Euclidean four-space
8. Trigonometric functions - such as sine and cosine - are useful for modeling sound waves - because they oscillate between values
The Same
Periodic Function
each whole number can be uniquely decomposed into products of primes.
Configuration Space
9. If a and b are any whole numbers - then a
Torus
Sign Rules for Division
Commutative Property of Multiplication
Stereographic Projection
10. 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.
The BML Traffic Model
Law of Large Numbers
Greatest Common Factor (GCF)
Cayley's Theorem
11. 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
The Kissing Circle
Law of Large Numbers
The inverse of multiplication is division
Amplitude
12. 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
Complete Graph
Expected Value
Discrete
13. If a is any whole number - then a
The Multiplicative Identity Property
Equivalent Equations
Associative Property of Addition:
a + c = b + c
14. Means approximately equal.
per line
prime factors
Frequency
˜
15. N = {1 - 2 - 3 - 4 - 5 - . . .}.
Fourier Analysis and Synthesis
Properties of Equality
the set of natural numbers
Frequency
16. 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.
does not change the solution set.
The index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.
Galton Board
Dividing both Sides of an Equation by the Same Quantity
17. Is the shortest string that contains all possible permutations of a particular length from a given set.
De Bruijn Sequence
Modular Arithmetic
a
Grouping Symbols
18. An instrument's _____ - the sound it produces - is a complex mixture of waves of different frequencies.
Tone
Additive Inverse:
Periodic Function
Exponents
19. Uses second derivatives to relate acceleration in space to acceleration in time.
per line
Fourier Analysis
Wave Equation
a · c = b · c for c does not equal 0
20. Original Balance minus River Tam's Withdrawal is Current Balance
Rational
A number is divisible by 9
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
B - 125 = 1200
21. Our standard notions of Pythagorean distance and angle via the inner product extend quite nicely from three-space.
In Euclidean four-space
Central Limit Theorem
The inverse of addition is subtraction
Expected Value
22. Instruments produce notes that have a fundamental frequency in combination with multiples of that frequency known as partials or overtones
Discrete
Distributive Property:
Overtone
a - c = b - c
23. Is a symbol (usually a letter) that stands for a value that may vary.
Variable
per line
In Euclidean four-space
Cardinality
24. 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
Least Common Multiple (LCM)
The Same
set
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
25. 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
Rational
Factor Tree Alternate Approach
left to right
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
26. The study of shape from an external perspective.
Law of Large Numbers
Extrinsic View
Overtone
Continuous
27. To describe and extend a numerical pattern
Commutative Property of Addition:
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.
Problem of the Points
28. 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.
bar graph
variable
Additive Inverse:
set
29. This result relates conserved physical quantities - like conservation of energy - to continuous symmetries of spacetime.
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30. 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
Multiplying both Sides of an Equation by the Same Quantity
evaluate the expression in the innermost pair of grouping symbols first.
Hypercube
Answer the Question
31. The state of appearing unchanged.
The inverse of addition is subtraction
inline
Invarient
The index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.
32. It is important to note that this step does not imply that you should simply check your solution in your equation. After all - it's possible that your equation incorrectly models the problem's situation - so you could have a valid solution to an inco
Non-Orientability
Associative Property of Addition:
Look Back
Exponents
33. This method can create a flat map from a curved surface while preserving all angles in any features present.
Flat Land
Stereographic Projection
left to right
Equation
34. If a = b then
Variable
a + c = b + c
The index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.
The Distributive Property (Subtraction)
35. Mathematical statement that equates two mathematical expressions.
The Prime Number Theorem
Prime Number
Box Diagram
Equation
36. A number is divisible by 2
1. The unit 2. Prime numbers 3. Composite numbers
Grouping Symbols
a - c = b - c
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
37. 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.
Unique Factorization Theorem
Principal Curvatures
Intrinsic View
Divisible
38. A(b + c) = a · b + a · c a(b - c) = a · b - a · c
a - c = b - c
Additive Identity:
Genus
Distributive Property:
39. 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.
Spherical Geometry
prime factors
Hyperbolic Geometry
Law of Large Numbers
40. A + b = b + a
Commutative Property of Addition:
Topology
Torus
Genus
41. The system that Euclid used in The Elements
Axiomatic Systems
Commutative Property of Multiplication:
Commensurability
Markov Chains
42. 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
Law of Large Numbers
Ramsey Theory
Group
counting numbers
43. If its final digit is a 0 or 5.
Modular Arithmetic
Dimension
A number is divisible by 5
Variable
44. GThe mathematical study of space. The geometry of a space goes hand in hand with how one defines the shortest distance between two points in that space.
Multiplying both Sides of an Equation by the Same Quantity
Geometry
Conditional Probability
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
45. Negative
set
Hypersphere
The BML Traffic Model
Sign Rules for Division
46. Aka The Osculating Circle - a way to measure the curvature of a line.
Order of Operations - PEMDAS 'Please Excuse My Dear Aunt Sally'
The index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.
the set of natural numbers
The Kissing Circle
47. When writing mathematical statements - follow the mantra:
per line
Products and Factors
One equal sign per line
The Set of Whole Numbers
48. Einstein's famous theory - relates gravity to the curvature of spacetime.
General Relativity
perimeter
1. The unit 2. Prime numbers 3. Composite numbers
A number is divisible by 9
49. Perform all additions and subtractions in the order presented
Countable
left to right
Fourier Analysis and Synthesis
Invarient
50. Cannot be written as a ratio of natural numbers.
inline
a - c = b - c
Conditional Probability
Irrational