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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. This area of mathematics relates symmetry to whether or not an equation has a 'simple' solution.
Galois Theory
Central Limit Theorem
a
Tone
2. 1. Find the prime factorizations of each number.
Hypersphere
Principal Curvatures
Cardinality
Greatest Common Factor (GCF)
3. The process of taking a complicated signal and breaking it into sine and cosine components.
set
Law of Large Numbers
Fourier Analysis
Prime Deserts
4. A point in one dimension requires only one number to define it. The number line is a good example of a one-dimensional space.
Line Land
Noether's Theorem
Fundamental Theorem of Arithmetic
Rarefactior
5. Trigonometric functions - such as sine and cosine - are useful for modeling sound waves - because they oscillate between values
Transfinite
Commutative Property of Multiplication
Greatest Common Factor (GCF)
Periodic Function
6. A flat map of hyperbolic space.
Prime Deserts
Dividing both Sides of an Equation by the Same Quantity
Poincare Disk
per line
7. A factor tree is a way to visualize a number's
Set up a Variable Dictionary.
Central Limit Theorem
Figurate Numbers
prime factors
8. A
Additive Identity:
Exponents
Division is not Commutative
Multiplication by Zero
9. Instruments produce notes that have a fundamental frequency in combination with multiples of that frequency known as partials or overtones
Overtone
Wave Equation
Least Common Multiple (LCM)
Complete Graph
10. 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 -
Aleph-Null
Division is not Associative
The inverse of subtraction is addition
Wave Equation
11. 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
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.
each whole number can be uniquely decomposed into products of primes.
Frequency
Fundamental Theorem of Arithmetic
12. 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
Least Common Multiple (LCM)
Permutation
Commutative Property of Multiplication:
Wave Equation
13. If a = b then
a
Hamilton Cycle
Pigeonhole Principle
The Prime Number Theorem
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.
Galton Board
The Multiplicative Identity Property
does not change the solution set.
Aleph-Null
15. 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.
A number is divisible by 3
Unique Factorization Theorem
The inverse of multiplication is division
Ramsey Theory
16. Dimension is how mathematicians express the idea of degrees of freedom
Dimension
Pigeonhole Principle
a · c = b · c for c does not equal 0
Associative Property of Multiplication:
17. Are the fundamental building blocks of arithmetic.
Primes
The index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.
Spaceland
Solution
18. A '___________' infinite set is one that can be put into one-to-one correspondence with the set of natural numbers.
The Commutative Property of Addition
prime factors
Hamilton Cycle
Countable
19. An arrangement where order matters.
evaluate the expression in the innermost pair of grouping symbols first.
Permutation
Multiplicative Identity:
Associate Property of Addition
20. A(b + c) = a · b + a · c a(b - c) = a · b - a · c
4 + x = 12
Greatest Common Factor (GCF)
Distributive Property:
Hyperland
21. The expression a/b means
Euclid's Postulates
a divided by b
Cardinality
Stereographic Projection
22. 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
the set of natural numbers
Answer the Question
Look Back
Group
23. The system that Euclid used in The Elements
Axiomatic Systems
Unique Factorization Theorem
Variable
Overtone
24. The cardinality of sets that cannot be put into one-to-one correspondence with the counting numbers - such as the set of real numbers - is referred to as c. The designations A_0 and c are known as 'transfinite' cardinalities.
A number is divisible by 5
Markov Chains
Transfinite
Expected Value
25. Let a and b represent two whole numbers. Then - a + b = b + a.
Division by Zero
a + c = b + c
The Commutative Property of Addition
Euclid's Postulates
26. 1. Parentheses (or any grouping symbol {braces} - [square brackets] - |absolute value|)
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27. 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
Tone
Multiplication by Zero
˜
Symmetry
28. 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).
per line
A number is divisible by 9
Hypercube
Transfinite
29. 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.
Geometry
Invarient
The Associative Property of Multiplication
The inverse of addition is subtraction
30. Determines the likelihood of events that are not independent of one another.
The inverse of addition is subtraction
Non-Orientability
Look Back
Conditional Probability
31. In some ways - the opposite of a multitude is a magnitude - which is ___________. In other words - there are no well defined partitions.
Euclid's Postulates
Properties of Equality
Continuous
Extrinsic View
32. Original Balance minus River Tam's Withdrawal is Current Balance
B - 125 = 1200
Hamilton Cycle
Exponents
Axiomatic Systems
33. If its final digit is a 0 or 5.
A number is divisible by 5
Rarefactior
The inverse of addition is subtraction
The Multiplicative Identity Property
34. Solving Equations
A prime number
Irrational
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
division
35. 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
The inverse of multiplication is division
Aleph-Null
Sign Rules for Division
Pigeonhole Principle
36. Aka The Osculating Circle - a way to measure the curvature of a line.
Hypercube
Box Diagram
Hamilton Cycle
The Kissing Circle
37. A topological invariant that relates a surface's vertices - edges - and faces.
Euler Characteristic
The Additive Identity Property
Group
Periodic Function
38. To describe and extend a numerical pattern
Amplitude
Comparison Property
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.
Fourier Analysis and Synthesis
39. This result says that the symmetries of geometric objects can be expressed as groups of permutations.
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40. 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
per line
Multiplying both Sides of an Equation by the Same Quantity
Factor Trees
Non-Orientability
41. (a + b) + c = a + (b + c)
Additive Identity:
Associative Property of Addition:
A prime number
The Same
42. All integers are thus divided into three classes:
1. The unit 2. Prime numbers 3. Composite numbers
Ramsey Theory
Commutative Property of Multiplication
Tone
43. The inverse of multiplication
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
Public Key Encryption
a + c = b + c
division
44. 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.
Commensurability
Normal Distribution
Irrational
The BML Traffic Model
45. Writing Mathematical equations - arrange your work one equation
Grouping Symbols
per line
Torus
Overtone
46. Add and subtract
inline
Division is not Associative
Division is not Commutative
A number is divisible by 10
47. A number is divisible by 2
Multiplication by Zero
Least Common Multiple (LCM)
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
Continuous
48. If its final digit is a 0.
Non-Orientability
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
Composite Numbers
A number is divisible by 10
49. Some numbers make geometric shapes when arranged as a collection of dots - for example - 16 makes a square - and 10 makes a triangle.
Variable
Figurate Numbers
The Kissing Circle
The Commutative Property of Addition
50. If a = b then a + c = b + c If a = b then a - c = b - c If a = b then a
The Riemann Hypothesis
General Relativity
Multiplication
Properties of Equality