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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. 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.
Dividing both Sides of an Equation by the Same Quantity
Conditional Probability
The Additive Identity Property
Polynomial
2. This method can create a flat map from a curved surface while preserving all angles in any features present.
Order of Operations - PEMDAS 'Please Excuse My Dear Aunt Sally'
Fourier Analysis
Stereographic Projection
Intrinsic View
3. A topological invariant that relates a surface's vertices - edges - and faces.
Commensurability
Overtone
Euler Characteristic
Solve the Equation
4. 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 · c = b · c for c does not equal 0
Associative Property of Addition:
Axiomatic Systems
Transfinite
5. 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
a - c = b - c
The Commutative Property of Addition
Non-Euclidian Geometry
Look Back
6. You must always solve the equation set up in the previous step.
Normal Distribution
Bijection
The Same
Solve the Equation
7. Non-Euclidean geometries abide by some - but not all of Euclid's five postulates.
Non-Euclidian Geometry
Multiplication by Zero
Transfinite
Hyperbolic Geometry
8. W = {0 - 1 - 2 - 3 - 4 - 5 - . . .} is called
The inverse of addition is subtraction
The Prime Number Theorem
The inverse of multiplication is division
The Set of Whole Numbers
9. An arrangement where order matters.
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
Permutation
Galton Board
Symmetry
10. 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
a
Bijection
Equivalent Equations
11. When writing mathematical statements - follow the mantra:
Distributive Property:
One equal sign per line
Dividing both Sides of an Equation by the Same Quantity
The BML Traffic Model
12. 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.
The Prime Number Theorem
Expected Value
Unique Factorization Theorem
Irrational
13. 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.
inline
Law of Large Numbers
The inverse of subtraction is addition
Group
14. A · b = b · a
Extrinsic View
˜
Continuous Symmetry
Commutative Property of Multiplication:
15. 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.
Non-Orientability
Extrinsic View
Modular Arithmetic
Irrational
16. When comparing two whole numbers a and b - only one of three possibilities is true: a < b or a = b or a > b.
Unique Factorization Theorem
Comparison Property
Associate Property of Addition
Geometry
17. The whole number zero is called the additive identity. If a is any whole number - then a + 0 = a.
Multiplicative Identity:
Frequency
Noether's Theorem
The Additive Identity Property
18. Use parentheses - brackets - or curly braces to delimit the part of an expression you want evaluated first.
Grouping Symbols
Rarefactior
evaluate the expression in the innermost pair of grouping symbols first.
Genus
19. A graph in which every node is connected to every other node is called a complete graph.
a
Irrational
Modular Arithmetic
Complete Graph
20. 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 -
4 + x = 12
Hamilton Cycle
Order of Operations - PEMDAS 'Please Excuse My Dear Aunt Sally'
The inverse of addition is subtraction
21. Instruments produce notes that have a fundamental frequency in combination with multiples of that frequency known as partials or overtones
The index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.
Countable
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
Overtone
22. A + 0 = 0 + a = a
The inverse of subtraction is addition
does not change the solution set.
Multiplicative Inverse:
Additive Identity:
23. (a · b) · c = a · (b · c)
Associative Property of Multiplication:
A number is divisible by 3
Fourier Analysis and Synthesis
Continuous Symmetry
24. 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
does not change the solution set.
Factor Trees
Bijection
division
25. If a = b then
A number is divisible by 10
A number is divisible by 5
a
per line
26. 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
bar graph
The inverse of multiplication is division
Division is not Commutative
1. The unit 2. Prime numbers 3. Composite numbers
27. Is the shortest string that contains all possible permutations of a particular length from a given set.
Set up a Variable Dictionary.
Wave Equation
De Bruijn Sequence
Hypersphere
28. Trigonometric functions - such as sine and cosine - are useful for modeling sound waves - because they oscillate between values
Periodic Function
Least Common Multiple (LCM)
A number is divisible by 3
Equivalent Equations
29. A
Configuration Space
Polynomial
Line Land
Division is not Commutative
30. 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.
A number is divisible by 5
does not change the solution set.
Equivalent Equations
Hyperland
31. 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.
Permutation
Commensurability
Euclid's Postulates
32. 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).
A number is divisible by 3
Amplitude
Set up an Equation
The Set of Whole Numbers
33. If a = b then
the set of natural numbers
a - c = b - c
Figurate Numbers
Normal Distribution
34. The system that Euclid used in The Elements
Associative Property of Multiplication:
Axiomatic Systems
per line
The Kissing Circle
35. Uses second derivatives to relate acceleration in space to acceleration in time.
Discrete
bar graph
Dimension
Wave Equation
36. The expression a/b means
does not change the solution set.
Irrational
Multiplying both Sides of an Equation by the Same Quantity
a divided by b
37. 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.'
Amplitude
Hyperbolic Geometry
Divisible
Public Key Encryption
38. N = {1 - 2 - 3 - 4 - 5 - . . .}.
Equivalent Equations
Genus
Hyperland
the set of natural numbers
39. Positive integers are
Factor Tree Alternate Approach
counting numbers
The Associative Property of Multiplication
Pigeonhole Principle
40. Three is the common property of the group of sets containing three members. This idea is called '__________ -' which is a synonym for 'size.' The set {a -b -c} is a representative set of the cardinal number 3.
Frequency
Public Key Encryption
Solve the Equation
Cardinality
41. 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
The Additive Identity Property
Group
Rarefactior
Commutative Property of Multiplication:
42. Dimension is how mathematicians express the idea of degrees of freedom
Dimension
4 + x = 12
Modular Arithmetic
Composite Numbers
43. × - ( )( ) - · - 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
The Prime Number Theorem
left to right
Multiplication
˜
44. If its final digit is a 0.
Sign Rules for Division
Polynomial
Grouping Symbols
A number is divisible by 10
45. 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 Kissing Circle
The inverse of subtraction is addition
Equation
Problem of the Points
46. Some numbers make geometric shapes when arranged as a collection of dots - for example - 16 makes a square - and 10 makes a triangle.
A number is divisible by 3
Figurate Numbers
Hyperland
Commensurability
47. 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)
a - c = b - c
Non-Euclidian Geometry
Equivalent Equations
48. (a
Division is not Associative
A number is divisible by 10
The Multiplicative Identity Property
Grouping Symbols
49. If a = b then a + c = b + c If a = b then a - c = b - c If a = b then a
Properties of Equality
The Set of Whole Numbers
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
50. Aka The Osculating Circle - a way to measure the curvature of a line.
Look Back
The Kissing Circle
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.
Stereographic Projection