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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. A number is divisible by 2
The Set of Whole Numbers
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
Prime Number
Primes
2. Positive integers are
Continuous Symmetry
Comparison Property
counting numbers
Associate Property of Addition
3. Topological objects are categorized by their _______ (number of holes). The genus of a surface is a feature of its global topology.
Genus
repeated addition
Configuration Space
Multiplication by Zero
4. 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
Line Land
A number is divisible by 3
Division is not Commutative
Factor Trees
5. Is a symbol (usually a letter) that stands for a value that may vary.
Variable
Markov Chains
Hamilton Cycle
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.
6. Solving Equations
Amplitude
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
Prime Number
Hypersphere
7. 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 Set of Whole Numbers
The Prime Number Theorem
Multiplicative Identity:
a
8. 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
The BML Traffic Model
Division is not Associative
Prime Number
9. Every solution to a word problem must include a carefully crafted equation that accurately describes the constraints in the problem statement.
A number is divisible by 3
Set up an Equation
a
Frequency
10. Cannot be written as a ratio of natural numbers.
Irrational
Solution
A prime number
Additive Inverse:
11. 4 more than a certain number is 12
Multiplication by Zero
Invarient
4 + x = 12
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
12. An important part of problem solving is identifying
variable
The Additive Identity Property
Factor Tree Alternate Approach
Multiplication
13. A topological invariant that relates a surface's vertices - edges - and faces.
Conditional Probability
Euler Characteristic
Intrinsic View
Non-Orientability
14. Originally known as analysis situs
The inverse of addition is subtraction
set
One equal sign per line
Topology
15. Also known as gluing diagrams - are a convenient way to examine intrinsic topology.
Box Diagram
set
Greatest Common Factor (GCF)
Cardinality
16. A + 0 = 0 + a = a
a · c = b · c for c does not equal 0
Set up an Equation
Additive Identity:
Look Back
17. 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.
Products and Factors
Modular Arithmetic
De Bruijn Sequence
Commutative Property of Addition:
18. The distribution of averages of many trials is always normal - even if the distribution of each trial is not.
per line
Central Limit Theorem
Primes
Standard Deviation
19. Is a path that visits every node in a graph and ends where it began.
A number is divisible by 9
Hamilton Cycle
Division is not Commutative
Figurate Numbers
20. 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
each whole number can be uniquely decomposed into products of primes.
inline
The Same
Associative Property of Addition:
21. Negative
The Multiplicative Identity Property
Sign Rules for Division
Line Land
Expected Value
22. The whole number zero is called the additive identity. If a is any whole number - then a + 0 = a.
Exponents
Spaceland
Set up an Equation
The Additive Identity Property
23. Some numbers make geometric shapes when arranged as a collection of dots - for example - 16 makes a square - and 10 makes a triangle.
Least Common Multiple (LCM)
Spaceland
Figurate Numbers
inline
24. Is the shortest string that contains all possible permutations of a particular length from a given set.
Hypersphere
De Bruijn Sequence
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
Invarient
25. 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.'
Factor Trees
Hyperland
Divisible
Set up an Equation
26. A + b = b + a
Commutative Property of Addition:
Intrinsic View
Prime Number
Spherical Geometry
27. An arrangement where order matters.
Overtone
Ramsey Theory
Permutation
Pigeonhole Principle
28. To describe and extend a numerical pattern
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.
Primes
Divisible
Distributive Property:
29. 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
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
Periodic Function
Geometry
30. Let a - b - and c represent whole numbers. Then - (a + b) + c = a + (b + c).
Greatest Common Factor (GCF)
Associate Property of Addition
Discrete
The Multiplicative Identity Property
31. 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.
The inverse of subtraction is addition
Associative Property of Addition:
1. The unit 2. Prime numbers 3. Composite numbers
Galton Board
32. Division by zero is undefined. Each of the expressions 6
Group
Commutative Property of Multiplication
Rational
Division by Zero
33. 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.
Dimension
Associative Property of Addition:
The Same
Transfinite
34. The multitude concept presented numbers as collections of discrete units - rather like indivisible atoms.
Markov Chains
Discrete
Stereographic Projection
evaluate the expression in the innermost pair of grouping symbols first.
35. The expression a/b means
Multiplicative Identity:
a divided by b
Geometry
Multiplying both Sides of an Equation by the Same Quantity
36. All integers are thus divided into three classes:
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
Invarient
left to right
1. The unit 2. Prime numbers 3. Composite numbers
37. A whole number (other than 1) is a _____________ if its only factors (divisors) are 1 and itself. Equivalently - a number is prime if and only if it has exactly two factors (divisors).
The index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.
does not change the solution set.
The Distributive Property (Subtraction)
Prime Number
38. Original Balance minus River Tam's Withdrawal is Current Balance
B - 125 = 1200
Central Limit Theorem
˜
Rational
39. 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.
Cayley's Theorem
Fundamental Theorem of Arithmetic
Law of Large Numbers
The Prime Number Theorem
40. Are the fundamental building blocks of arithmetic.
Genus
bar graph
Primes
Division by Zero
41. 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
Variable
Fourier Analysis
Hypersphere
Symmetry
42. We can think of the space between primes as 'prime deserts -' strings of consecutive numbers - none of which are prime.
A number is divisible by 10
Order of Operations - PEMDAS 'Please Excuse My Dear Aunt Sally'
Prime Deserts
a · c = b · c for c does not equal 0
43. 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.
left to right
Group
a - c = b - c
44. The state of appearing unchanged.
In Euclidean four-space
Invarient
Order of Operations - PEMDAS 'Please Excuse My Dear Aunt Sally'
a + c = b + c
45. Objects are topologically equivalent if they can be continuously deformed into one another. Properties that are preserved during this process are called topological invariants.
Public Key Encryption
Irrational
perimeter
Fourier Analysis
46. In the expression 3
set
Commutative Property of Multiplication
Products and Factors
Countable
47. If grouping symbols are nested
Stereographic Projection
Problem of the Points
evaluate the expression in the innermost pair of grouping symbols first.
Euler Characteristic
48. Is the length around an object. Used to calculate such things as fencing around a yard - trimming a piece of material - and the amount of baseboard needed for a room.It is not necessary to have a formula since it is always just calculated by adding t
perimeter
each whole number can be uniquely decomposed into products of primes.
Fourier Analysis
Central Limit Theorem
49. 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.'
Axiomatic Systems
Fundamental Theorem of Arithmetic
Hyperland
Equation
50. Mathematical statement that equates two mathematical expressions.
Multiplying both Sides of an Equation by the Same Quantity
The Kissing Circle
Equation
A number is divisible by 9