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Test your basic knowledge |
CLEP General Math: Number Sense - Patterns - Algebraic Thinking
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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. 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.
Order of Operations - PEMDAS 'Please Excuse My Dear Aunt Sally'
Polynomial
Markov Chains
Modular Arithmetic
2. The system that Euclid used in The Elements
Axiomatic Systems
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.
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
Irrational
3. Negative
Sign Rules for Division
Stereographic Projection
Prime Deserts
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
4. Instruments produce notes that have a fundamental frequency in combination with multiples of that frequency known as partials or overtones
Denominator
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
Overtone
The Prime Number Theorem
5. A factor tree is a way to visualize a number's
Dividing both Sides of an Equation by the Same Quantity
Products and Factors
Public Key Encryption
prime factors
6. If its final digit is a 0 or 5.
Invarient
Dividing both Sides of an Equation by the Same Quantity
Topology
A number is divisible by 5
7. Arise from the attempt to measure all quantities with a common unit of measure.
Sign Rules for Division
The Associative Property of Multiplication
The index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.
Rational
8. A · 1 = 1 · a = a
division
Law of Large Numbers
Multiplicative Identity:
Line Land
9. This method can create a flat map from a curved surface while preserving all angles in any features present.
repeated addition
a
Stereographic Projection
Solve the Equation
10. 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
Commutative Property of Multiplication:
Look Back
Commensurability
Amplitude
11. 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
does not change the solution set.
Extrinsic View
Hypersphere
Primes
12. Mathematical statement that equates two mathematical expressions.
Equation
Modular Arithmetic
does not change the solution set.
Galton Board
13. Trigonometric functions - such as sine and cosine - are useful for modeling sound waves - because they oscillate between values
Periodic Function
a · c = b · c for c does not equal 0
Products and Factors
Cardinality
14. (a
The BML Traffic Model
Division is not Associative
Grouping Symbols
Variable
15. If a - b - and c are any whole numbers - then a
Markov Chains
Hamilton Cycle
The Associative Property of Multiplication
The Prime Number Theorem
16. All integers are thus divided into three classes:
the set of natural numbers
1. The unit 2. Prime numbers 3. Composite numbers
Greatest Common Factor (GCF)
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
17. Cantor called the cardinality of all the sets that can be put into one-to-one correspondence with the counting numbers - or 'Aleph Null.'
Prime Deserts
Aleph-Null
Hypersphere
Commensurability
18. Let a and b represent two whole numbers. Then - a + b = b + a.
Look Back
The Set of Whole Numbers
left to right
The Commutative Property of Addition
19. 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).
Greatest Common Factor (GCF)
Factor Trees
Additive Identity:
Prime Number
20. 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.
Probability
Multiplication
Markov Chains
Law of Large Numbers
21. 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.
Transfinite
Cardinality
The Set of Whole Numbers
Symmetry
22. 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.
perimeter
The Associative Property of Multiplication
Products and Factors
Normal Distribution
23. An algebraic 'sentence' containing an unknown quantity.
Polynomial
Markov Chains
Answer the Question
Dividing both Sides of an Equation by the Same Quantity
24. This area of mathematics relates symmetry to whether or not an equation has a 'simple' solution.
Set up an Equation
˜
Non-Orientability
Galois Theory
25. 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.'
Periodic Function
The Prime Number Theorem
Multiplicative Inverse:
˜
26. 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
Transfinite
Factor Tree Alternate Approach
Prime Number
counting numbers
27. 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
evaluate the expression in the innermost pair of grouping symbols first.
A number is divisible by 5
perimeter
Look Back
28. Let a - b - and c be any whole numbers. Then - a
Equivalent Equations
The Distributive Property (Subtraction)
A number is divisible by 10
Poincare Disk
29. Is a path that visits every node in a graph and ends where it began.
Solution
Hamilton Cycle
Extrinsic View
Properties of Equality
30. 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.
Genus
Figurate Numbers
Answer the Question
Public Key Encryption
31. If a = b then
Torus
set
a · c = b · c for c does not equal 0
Principal Curvatures
32. An arrangement where order matters.
Frequency
set
Commutative Property of Multiplication
Permutation
33. 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
Transfinite
Additive Inverse:
Multiplying both Sides of an Equation by the Same Quantity
Composite Numbers
34. Cannot be written as a ratio of natural numbers.
Amplitude
Irrational
Galois Theory
Countable
35. A way to measure how far away a given individual result is from the average result.
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
Invarient
Standard Deviation
The inverse of subtraction is addition
36. 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.'
Flat Land
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
Associate Property of Addition
Divisible
37. 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
perimeter
Symmetry
Hyperbolic Geometry
De Bruijn Sequence
38. This step is easily overlooked. For example - the problem might ask for Jane's age - but your equation's solution gives the age of Jane's sister Liz. Make sure you answer the original question asked in the problem. Your solution should be written in
Commensurability
Answer the Question
Conditional Probability
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
39. Dimension is how mathematicians express the idea of degrees of freedom
Dimension
Set up an Equation
Irrational
Hyperbolic Geometry
40. Is the shortest string that contains all possible permutations of a particular length from a given set.
Rarefactior
The Same
De Bruijn Sequence
Fourier Analysis and Synthesis
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.
a + c = b + c
1. The unit 2. Prime numbers 3. Composite numbers
Box Diagram
does not change the solution set.
42. This famous - as yet unproven - result relates to the distribution of prime numbers on the number line.
A number is divisible by 9
The Riemann Hypothesis
prime factors
Multiplication by Zero
43. 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)
Stereographic Projection
Complete Graph
A number is divisible by 9
44. In this type of geometry the angles of a triangle add up to more than 180 degrees. In such a system - one has to replace the parallel postulate with a version that admits no parallel lines as well as modify Euclid's first two postulates.
Standard Deviation
Fourier Analysis and Synthesis
Greatest Common Factor (GCF)
Spherical Geometry
45. Points in two-dimensional space require two numbers to specify them completely. The Cartesian plane is a good way to envision two-dimensional space.
Transfinite
Stereographic Projection
Flat Land
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
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
variable
The inverse of multiplication is division
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
Public Key Encryption
47. When writing mathematical statements - follow the mantra:
perimeter
One equal sign per line
The Same
the set of natural numbers
48. The surface of a standard 'donut shape'.
Torus
Non-Orientability
Countable
a divided by b
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.'
1. The unit 2. Prime numbers 3. Composite numbers
Central Limit Theorem
Fundamental Theorem of Arithmetic
Hyperland
50. A · b = b · a
De Bruijn Sequence
Commutative Property of Multiplication:
Modular Arithmetic
Galois Theory