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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. If a = b then a + c = b + c If a = b then a - c = b - c If a = b then a
Polynomial
Properties of Equality
Complete Graph
Equivalent Equations
2. In the expression 3
perimeter
prime factors
Products and Factors
Box Diagram
3. (a
Equation
Division is not Associative
Irrational
Modular Arithmetic
4. A · b = b · a
Countable
Exponents
Frequency
Commutative Property of Multiplication:
5. 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.
A prime number
The Associative Property of Multiplication
Galton Board
Aleph-Null
6. Points in two-dimensional space require two numbers to specify them completely. The Cartesian plane is a good way to envision two-dimensional space.
Dividing both Sides of an Equation by the Same Quantity
Ramsey Theory
counting numbers
Flat Land
7. Codifies the 'average behavior' of a random event and is a key concept in the application of probability.
Bijection
Multiplicative Identity:
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
Expected Value
8. Two equations if they have the same solution set.
Central Limit Theorem
Equivalent Equations
Probability
Multiplication
9. Multiplication is equivalent to
Commutative Property of Multiplication:
each whole number can be uniquely decomposed into products of primes.
repeated addition
Factor Tree Alternate Approach
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.
Pigeonhole Principle
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
Law of Large Numbers
B - 125 = 1200
11. Dimension is how mathematicians express the idea of degrees of freedom
Order of Operations - PEMDAS 'Please Excuse My Dear Aunt Sally'
Hypersphere
Dimension
Dividing both Sides of an Equation by the Same Quantity
12. 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
Multiplying both Sides of an Equation by the Same Quantity
Hypersphere
variable
A number is divisible by 9
13. 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
Divisible
Set up a Variable Dictionary.
The index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.
De Bruijn Sequence
14. The surface of a standard 'donut shape'.
Configuration Space
Order of Operations - PEMDAS 'Please Excuse My Dear Aunt Sally'
Torus
a · c = b · c for c does not equal 0
15. Index p radicand
Periodic Function
The index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.
Polynomial
Division by Zero
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
Poincare Disk
Hypercube
Commutative Property of Multiplication
The Kissing Circle
17. A point in one dimension requires only one number to define it. The number line is a good example of a one-dimensional space.
Hypersphere
Factor Trees
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
Line Land
18. If a = b then
The inverse of addition is subtraction
The Kissing Circle
a - c = b - c
Bijection
19. The system that Euclid used in The Elements
Tone
Axiomatic Systems
Additive Inverse:
Line Land
20. If a represents any whole number - then a
Multiplication by Zero
A number is divisible by 3
Stereographic Projection
Look Back
21. 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
A number is divisible by 10
a · c = b · c for c does not equal 0
Torus
22. An arrangement where order matters.
Permutation
Spaceland
A number is divisible by 9
Principal Curvatures
23. A way to analyze sequences of events where the outcomes of prior events affect the probability of outcomes of subsequent events.
Amplitude
Markov Chains
Dimension
The inverse of multiplication is division
24. Means approximately equal.
counting numbers
Complete Graph
˜
Grouping Symbols
25. If a and b are any whole numbers - then a
Commutative Property of Multiplication
Answer the Question
Solve the Equation
Commutative Property of Addition:
26. 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.
Markov Chains
Principal Curvatures
Line Land
Division is not Commutative
27. W = {0 - 1 - 2 - 3 - 4 - 5 - . . .} is called
Hypercube
each whole number can be uniquely decomposed into products of primes.
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
The Set of Whole Numbers
28. 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
Euler Characteristic
Look Back
Primes
Comparison Property
29. A '___________' infinite set is one that can be put into one-to-one correspondence with the set of natural numbers.
The Distributive Property (Subtraction)
Fourier Analysis and Synthesis
Countable
Least Common Multiple (LCM)
30. The state of appearing unchanged.
Invarient
Transfinite
Commensurability
A number is divisible by 10
31. If we start with a number x and add a number a - then subtracting a from the result will return us to the original number x. x + a - a = x. so -
Conditional Probability
Solve the Equation
The inverse of addition is subtraction
Dimension
32. 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.'
Commutative Property of Multiplication
Hyperland
Continuous Symmetry
A prime number
33. Assuming that the air is of uniform density and pressure to begin with - a region of high pressure will be balanced by a region of low pressure - called rarefaction - immediately following the compression
Rarefactior
The inverse of multiplication is division
Cardinality
Commutative Property of Addition:
34. 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.
Division by Zero
Set up an Equation
Modular Arithmetic
Line Land
35. 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.
The BML Traffic Model
Probability
division
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.
36. Topological objects are categorized by their _______ (number of holes). The genus of a surface is a feature of its global topology.
Genus
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
Exponents
Hyperbolic Geometry
37. Is a path that visits every node in a graph and ends where it began.
Hamilton Cycle
Rational
Set up an Equation
Dividing both Sides of an Equation by the Same Quantity
38. A point in three-dimensional space requires three numbers to fix its location.
Distributive Property:
The inverse of addition is subtraction
Conditional Probability
Spaceland
39. The solutions to this gambling dilemma is traditionally held to be the start of modern probability theory.
Prime Number
Problem of the Points
Bijection
Composite Numbers
40. If a = b then
a
1. The unit 2. Prime numbers 3. Composite numbers
Tone
a divided by b
41. 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.
A number is divisible by 10
Answer the Question
variable
42. 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.
Spherical Geometry
Unique Factorization Theorem
Divisible
A number is divisible by 3
43. 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.
Transfinite
Euclid's Postulates
Division is not Commutative
Bijection
44. You must always solve the equation set up in the previous step.
Solve the Equation
Spaceland
does not change the solution set.
The inverse of subtraction is addition
45. 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).
Normal Distribution
A number is divisible by 3
Poincare Disk
Multiplicative Inverse:
46. A
Division is not Commutative
The index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.
Additive Identity:
Cayley's Theorem
47. The multitude concept presented numbers as collections of discrete units - rather like indivisible atoms.
Line Land
The Same
Least Common Multiple (LCM)
Discrete
48. 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.
Continuous Symmetry
Frequency
Dividing both Sides of an Equation by the Same Quantity
Factor Trees
49. If grouping symbols are nested
Fourier Analysis and Synthesis
Flat Land
Denominator
evaluate the expression in the innermost pair of grouping symbols first.
50. This area of mathematics relates symmetry to whether or not an equation has a 'simple' solution.
Hyperbolic Geometry
Galois Theory
Exponents
variable