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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 amount of displacement - as measured from the still surface line.
Amplitude
Euler Characteristic
1. The unit 2. Prime numbers 3. Composite numbers
Permutation
2. If a = b then
repeated addition
a - c = b - c
Sign Rules for Division
Group
3. 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
Group
Dimension
˜
The Associative Property of Multiplication
4. Points in two-dimensional space require two numbers to specify them completely. The Cartesian plane is a good way to envision two-dimensional space.
Normal Distribution
The Kissing Circle
Multiplication
Flat Land
5. 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
Symmetry
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
a
Factor Trees
6. 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 - c = b - c
Factor Tree Alternate Approach
A number is divisible by 9
Noether's Theorem
7. Negative
Hypersphere
variable
Sign Rules for Division
Principal Curvatures
8. If a = b then a + c = b + c If a = b then a - c = b - c If a = b then a
Multiplying both Sides of an Equation by the Same Quantity
Properties of Equality
A prime number
Non-Euclidian Geometry
9. N = {1 - 2 - 3 - 4 - 5 - . . .}.
Euclid's Postulates
Unique Factorization Theorem
Overtone
the set of natural numbers
10. A
1. The unit 2. Prime numbers 3. Composite numbers
Division is not Commutative
Polynomial
Fundamental Theorem of Arithmetic
11. If a - b - and c are any whole numbers - then a
Irrational
The Associative Property of Multiplication
Factor Tree Alternate Approach
a
12. Arise from the attempt to measure all quantities with a common unit of measure.
Rational
a · c = b · c for c does not equal 0
Poincare Disk
Divisible
13. Is a symbol (usually a letter) that stands for a value that may vary.
Multiplication by Zero
The Riemann Hypothesis
Spherical Geometry
Variable
14. 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 Associative Property of Multiplication
The inverse of subtraction is addition
Polynomial
The Additive Identity Property
15. 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
Symmetry
Pigeonhole Principle
a · c = b · c for c does not equal 0
Commutative Property of Multiplication:
16. All integers are thus divided into three classes:
1. The unit 2. Prime numbers 3. Composite numbers
Fourier Analysis and Synthesis
a divided by b
A number is divisible by 9
17. 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.
Markov Chains
perimeter
Axiomatic Systems
Bijection
18. A way to measure how far away a given individual result is from the average result.
Spherical Geometry
Order of Operations - PEMDAS 'Please Excuse My Dear Aunt Sally'
Standard Deviation
Conditional Probability
19. Means approximately equal.
˜
Rarefactior
Fourier Analysis and Synthesis
Prime Deserts
20. Perform all additions and subtractions in the order presented
Bijection
The Associative Property of Multiplication
left to right
Box Diagram
21. If a is any whole number - then a
repeated addition
The Multiplicative Identity Property
Commutative Property of Addition:
The Prime Number Theorem
22. A graph in which every node is connected to every other node is called a complete graph.
Complete Graph
Frequency
Law of Large Numbers
The BML Traffic Model
23. A point in one dimension requires only one number to define it. The number line is a good example of a one-dimensional space.
Permutation
Discrete
Line Land
bar graph
24. Every solution to a word problem must include a carefully crafted equation that accurately describes the constraints in the problem statement.
set
Set up an Equation
Expected Value
Irrational
25. Cannot be written as a ratio of natural numbers.
Multiplying both Sides of an Equation by the Same Quantity
Irrational
Torus
Line Land
26. This famous - as yet unproven - result relates to the distribution of prime numbers on the number line.
Flat Land
a divided by b
The Riemann Hypothesis
The index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.
27. Some numbers make geometric shapes when arranged as a collection of dots - for example - 16 makes a square - and 10 makes a triangle.
Modular Arithmetic
A number is divisible by 5
Figurate Numbers
Division is not Commutative
28. Add and subtract
Primes
Dividing both Sides of an Equation by the Same Quantity
inline
Box Diagram
29. 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.
Cardinality
Rarefactior
The Additive Identity Property
Galton Board
30. A(b + c) = a · b + a · c a(b - c) = a · b - a · c
Distributive Property:
Additive Inverse:
Wave Equation
Frequency
31. A · 1/a = 1/a · a = 1
Multiplicative Inverse:
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
The Multiplicative Identity Property
Division by Zero
32. 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.
Composite Numbers
Multiplicative Inverse:
Commutative Property of Multiplication
Public Key Encryption
33. Are the fundamental building blocks of arithmetic.
Primes
Division is not Commutative
Least Common Multiple (LCM)
Euler Characteristic
34. The state of appearing unchanged.
Unique Factorization Theorem
Figurate Numbers
Line Land
Invarient
35. A '___________' infinite set is one that can be put into one-to-one correspondence with the set of natural numbers.
Order of Operations - PEMDAS 'Please Excuse My Dear Aunt Sally'
Countable
Irrational
Variable
36. A flat map of hyperbolic space.
In Euclidean four-space
Poincare Disk
Commensurability
A number is divisible by 3
37. The system that Euclid used in The Elements
4 + x = 12
Axiomatic Systems
Products and Factors
Galois Theory
38. Non-Euclidean geometries abide by some - but not all of Euclid's five postulates.
Commutative Property of Multiplication:
Transfinite
Stereographic Projection
Non-Euclidian Geometry
39. 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.
Ramsey Theory
Set up an Equation
Periodic Function
Division is not Associative
40. The multitude concept presented numbers as collections of discrete units - rather like indivisible atoms.
Discrete
Normal Distribution
Hyperbolic Geometry
Expected Value
41. An important part of problem solving is identifying
variable
Amplitude
does not change the solution set.
Normal Distribution
42. × - ( )( ) - · - 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
Bijection
Greatest Common Factor (GCF)
bar graph
43. 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.
left to right
Geometry
Principal Curvatures
Invarient
44. If its final digit is a 0.
Discrete
Multiplying both Sides of an Equation by the Same Quantity
Galton Board
A number is divisible by 10
45. An equation is a numerical value that satisfies the equation. That is - when the variable in the equation is replaced by the solution - a true statement results.
Solution
Non-Orientability
Factor Trees
each whole number can be uniquely decomposed into products of primes.
46. 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.
Prime Deserts
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
Topology
47. 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
Hypersphere
Least Common Multiple (LCM)
Galois Theory
The Set of Whole Numbers
48. A · 1 = 1 · a = a
Sign Rules for Division
Multiplicative Identity:
Order of Operations - PEMDAS 'Please Excuse My Dear Aunt Sally'
Hyperland
49. Positive integers are
Problem of the Points
Hypercube
The inverse of subtraction is addition
counting numbers
50. Multiplication is equivalent to
repeated addition
Probability
One equal sign per line
The Associative Property of Multiplication