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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 means that for any two magnitudes - one should always be able to find a fundamental unit that fits some whole number of times into each of them (i.e. - a unit whose magnitude is a whole number factor of each of the original magnitudes)
The index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.
Central Limit Theorem
Figurate Numbers
Commensurability
2. The amount of displacement - as measured from the still surface line.
Comparison Property
Amplitude
One equal sign per line
Normal Distribution
3. 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.
Multiplication
bar graph
Amplitude
Modular Arithmetic
4. Is a symbol (usually a letter) that stands for a value that may vary.
a + c = b + c
Central Limit Theorem
Variable
The Prime Number Theorem
5. 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.
Polynomial
Commensurability
Irrational
Principal Curvatures
6. If its final digit is a 0 or 5.
Spaceland
Primes
A number is divisible by 5
Expected Value
7. Used to display measurements. The measurement was taken is placed on the horizontal axis - and the height of each bar equals the amount during that year.
Additive Identity:
Denominator
bar graph
˜
8. A + 0 = 0 + a = a
Commutative Property of Multiplication
Additive Identity:
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
Polynomial
9. 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
Fundamental Theorem of Arithmetic
Poincare Disk
Pigeonhole Principle
10. 1. Parentheses (or any grouping symbol {braces} - [square brackets] - |absolute value|)
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11. An instrument's _____ - the sound it produces - is a complex mixture of waves of different frequencies.
General Relativity
a · c = b · c for c does not equal 0
A number is divisible by 9
Tone
12. 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.'
Grouping Symbols
The Prime Number Theorem
Multiplicative Inverse:
Invarient
13. The whole number zero is called the additive identity. If a is any whole number - then a + 0 = a.
Normal Distribution
The Additive Identity Property
Invarient
Principal Curvatures
14. All integers are thus divided into three classes:
1. The unit 2. Prime numbers 3. Composite numbers
Principal Curvatures
Figurate Numbers
The Associative Property of Multiplication
15. Determines the likelihood of events that are not independent of one another.
The Additive Identity Property
Hypercube
The Commutative Property of Addition
Conditional Probability
16. If a = b then
a + c = b + c
Frequency
A number is divisible by 10
Hamilton Cycle
17. In this type of geometry the angles of a triangle add up to less than 180 degrees. In such a system - one has to replace the parallel postulate with a version that admits many parallel lines.
Hyperbolic Geometry
Fourier Analysis
repeated addition
Invarient
18. In any ratio of two whole numbers - expressed as a fraction - we can interpret the first (top) number to be the 'counter -' or numerator
a · c = b · c for c does not equal 0
Associative Property of Addition:
Denominator
Commutative Property of Multiplication
19. 1. Find the prime factorizations of each number.
Non-Orientability
Associative Property of Addition:
Greatest Common Factor (GCF)
a divided by b
20. This ubiquitous result describes the outcomes of many trials of events from a wide array of contexts. It says that most results cluster around the average with few results far above or far below average.
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
evaluate the expression in the innermost pair of grouping symbols first.
Normal Distribution
Geometry
21. Writing Mathematical equations - arrange your work one equation
Tone
Invarient
per line
Spherical Geometry
22. This result says that the symmetries of geometric objects can be expressed as groups of permutations.
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23. Is a path that visits every node in a graph and ends where it began.
Standard Deviation
Hamilton Cycle
Hypercube
perimeter
24. 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
Standard Deviation
Rarefactior
Look Back
The Associative Property of Multiplication
25. 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
Rational
Denominator
Rarefactior
Group
26. Every solution to a word problem must include a carefully crafted equation that accurately describes the constraints in the problem statement.
a · c = b · c for c does not equal 0
Division by Zero
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
Set up an Equation
27. A flat map of hyperbolic space.
perimeter
Poincare Disk
Pigeonhole Principle
Central Limit Theorem
28. Some favor repeatedly dividing by 2 until the result is no longer divisible by 2. Then try repeatedly dividing by the next prime until the result is no longer divisible by that prime. The process terminates when the last resulting quotient is equal t
Countable
Factor Tree Alternate Approach
Extrinsic View
Frequency
29. Perform all additions and subtractions in the order presented
left to right
Look Back
Additive Inverse:
Law of Large Numbers
30. A '___________' infinite set is one that can be put into one-to-one correspondence with the set of natural 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
Box Diagram
Countable
Hamilton Cycle
31. 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 Same
The Additive Identity Property
Unique Factorization Theorem
Prime Number
32. (a
Denominator
Sign Rules for Division
Division is not Associative
Fourier Analysis and Synthesis
33. × - ( )( ) - · - 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
Cardinality
The Riemann Hypothesis
Multiplication
The Same
34. Trigonometric functions - such as sine and cosine - are useful for modeling sound waves - because they oscillate between values
In Euclidean four-space
Periodic Function
Rarefactior
division
35. A way to analyze sequences of events where the outcomes of prior events affect the probability of outcomes of subsequent events.
Equivalent Equations
Polynomial
Spaceland
Markov Chains
36. Rules for Rounding - To round a number to a particular place - follow these steps:
Products and Factors
The Prime Number Theorem
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
Associative Property of Addition:
37. An arrangement where order matters.
repeated addition
Wave Equation
Permutation
Answer the Question
38. 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.
Multiplicative Inverse:
Geometry
set
Periodic Function
39. When writing mathematical statements - follow the mantra:
Factor Trees
One equal sign per line
Problem of the Points
Expected Value
40. We can think of the space between primes as 'prime deserts -' strings of consecutive numbers - none of which are prime.
Intrinsic View
Comparison Property
Countable
Prime Deserts
41. Topological objects are categorized by their _______ (number of holes). The genus of a surface is a feature of its global topology.
Extrinsic View
Commensurability
Genus
Flat Land
42. 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
Galois Theory
1. The unit 2. Prime numbers 3. Composite numbers
Denominator
Hypercube
43. An algebraic 'sentence' containing an unknown quantity.
the set of natural numbers
Cayley's Theorem
Polynomial
a · c = b · c for c does not equal 0
44. Has no factors other than 1 and itself
A number is divisible by 3
A number is divisible by 10
Conditional Probability
A prime number
45. 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.
per line
Countable
Normal Distribution
Transfinite
46. 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
Spherical Geometry
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
De Bruijn Sequence
The inverse of multiplication is division
47. Original Balance minus River Tam's Withdrawal is Current Balance
the set of natural numbers
Discrete
B - 125 = 1200
Equivalent Equations
48. 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 inverse of subtraction is addition
In Euclidean four-space
The Associative Property of Multiplication
Markov Chains
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.'
Hyperland
Continuous
Probability
Wave Equation
50. 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.'
The Prime Number Theorem
Composite Numbers
Divisible
Rational