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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. Use parentheses - brackets - or curly braces to delimit the part of an expression you want evaluated first.
inline
Sign Rules for Division
Grouping Symbols
Principal Curvatures
2. Are the fundamental building blocks of arithmetic.
Primes
bar graph
Fundamental Theorem of Arithmetic
Set up an Equation
3. (a + b) + c = a + (b + c)
Associative Property of Addition:
Rarefactior
Symmetry
The inverse of addition is subtraction
4. Also known as gluing diagrams - are a convenient way to examine intrinsic topology.
Box Diagram
each whole number can be uniquely decomposed into products of primes.
De Bruijn Sequence
Euler Characteristic
5. 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.
Unique Factorization Theorem
repeated addition
the set of natural numbers
4 + x = 12
6. A(b + c) = a · b + a · c a(b - c) = a · b - a · c
Hypercube
Poincare Disk
Hamilton Cycle
Distributive Property:
7. N = {1 - 2 - 3 - 4 - 5 - . . .}.
Set up a Variable Dictionary.
Spherical Geometry
the set of natural numbers
Euler Characteristic
8. The multitude concept presented numbers as collections of discrete units - rather like indivisible atoms.
Discrete
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
Prime Number
Hamilton Cycle
9. 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
Expected Value
Non-Euclidian Geometry
Genus
Factor Tree Alternate Approach
10. Objects are topologically equivalent if they can be continuously deformed into one another. Properties that are preserved during this process are called topological invariants.
Irrational
does not change the solution set.
˜
Equation
11. 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).
Polynomial
Set up an Equation
Solve the Equation
Prime Number
12. Originally known as analysis situs
Symmetry
Discrete
evaluate the expression in the innermost pair of grouping symbols first.
Topology
13. Division by zero is undefined. Each of the expressions 6
each whole number can be uniquely decomposed into products of primes.
Division by Zero
The Prime Number Theorem
Bijection
14. 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.
Rational
Public Key Encryption
Multiplicative Inverse:
Hyperland
15. The solutions to this gambling dilemma is traditionally held to be the start of modern probability theory.
Problem of the Points
Polynomial
each whole number can be uniquely decomposed into products of primes.
A prime number
16. Multiplication is equivalent to
repeated addition
Products and Factors
a divided by b
Hyperbolic Geometry
17. If a is any whole number - then a
Conditional Probability
Comparison Property
Poincare Disk
The Multiplicative Identity Property
18. 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.
Irrational
Sign Rules for Division
Normal Distribution
Rarefactior
19. Codifies the 'average behavior' of a random event and is a key concept in the application of probability.
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
Expected Value
Modular Arithmetic
counting numbers
20. Trigonometric functions - such as sine and cosine - are useful for modeling sound waves - because they oscillate between values
A number is divisible by 5
Hyperland
Invarient
Periodic Function
21. Some numbers make geometric shapes when arranged as a collection of dots - for example - 16 makes a square - and 10 makes a triangle.
Figurate Numbers
Cardinality
Greatest Common Factor (GCF)
Complete Graph
22. Let a - b - and c represent whole numbers. Then - (a + b) + c = a + (b + c).
Dimension
Products and Factors
Hypercube
Associate Property of Addition
23. The surface of a standard 'donut shape'.
Torus
Greatest Common Factor (GCF)
left to right
Flat Land
24. This area of mathematics relates symmetry to whether or not an equation has a 'simple' solution.
a · c = b · c for c does not equal 0
Galois Theory
The Set of Whole Numbers
The Multiplicative Identity Property
25. If its final digit is a 0.
Equivalent Equations
Line Land
The Associative Property of Multiplication
A number is divisible by 10
26. Two equations if they have the same solution set.
Frequency
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
Equivalent Equations
does not change the solution set.
27. The study of shape from an external perspective.
Prime Deserts
Public Key Encryption
Extrinsic View
Commutative Property of Multiplication
28. 1. Find the prime factorizations of each number.
Greatest Common Factor (GCF)
The Distributive Property (Subtraction)
Galois Theory
Hyperland
29. Is a symbol (usually a letter) that stands for a value that may vary.
The BML Traffic Model
Continuous
Variable
repeated addition
30. Means approximately equal.
does not change the solution set.
Set up an Equation
Irrational
˜
31. In the expression 3
variable
Overtone
Least Common Multiple (LCM)
Products and Factors
32. All integers are thus divided into three classes:
Cayley's Theorem
Noether's Theorem
1. The unit 2. Prime numbers 3. Composite numbers
Associative Property of Multiplication:
33. Breaks a complicated signal into a combination of simple sine waves. Fourier synthesis does the opposite - constructing a complicated signal from simple sine waves.
Frequency
Cayley's Theorem
Fourier Analysis and Synthesis
Ramsey Theory
34. A · b = b · a
Conditional Probability
The inverse of addition is subtraction
Commutative Property of Multiplication:
Countable
35. 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
The Same
division
per line
Equation
36. 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 -
Law of Large Numbers
The inverse of subtraction is addition
Solve the Equation
Figurate Numbers
37. 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 inverse of multiplication is division
left to right
Prime Deserts
The Prime Number Theorem
38. If a - b - and c are any whole numbers - then a
The Associative Property of Multiplication
Group
A number is divisible by 5
Ramsey Theory
39. Determines the likelihood of events that are not independent of one another.
Genus
Euclid's Postulates
B - 125 = 1200
Conditional Probability
40. Instruments produce notes that have a fundamental frequency in combination with multiples of that frequency known as partials or overtones
Principal Curvatures
Overtone
Equation
Fourier Analysis and Synthesis
41. This result says that the symmetries of geometric objects can be expressed as groups of permutations.
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42. A flat map of hyperbolic space.
Poincare Disk
Tone
Products and Factors
Set up a Variable Dictionary.
43. 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
A prime number
the set of natural numbers
Hamilton Cycle
Answer the Question
44. You must let your readers know what each variable in your problem represents. This can be accomplished in a number of ways: Statements such as 'Let P represent the perimeter of the rectangle.' - Labeling unknown values with variables in a table - Lab
Prime Number
Group
Overtone
Set up a Variable Dictionary.
45. The fundamental theorem of arithmetic says that
Polynomial
bar graph
each whole number can be uniquely decomposed into products of primes.
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
46. In any ratio of two whole numbers - expressed as a fraction - we can interpret the first (top) number to be the 'counter -' or numerator
Denominator
Overtone
Comparison Property
Additive Identity:
47. An instrument's _____ - the sound it produces - is a complex mixture of waves of different frequencies.
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.
Bijection
Tone
The Distributive Property (Subtraction)
48. A point in three-dimensional space requires three numbers to fix its location.
The Prime Number Theorem
The Riemann Hypothesis
Spaceland
General Relativity
49. Original Balance minus River Tam's Withdrawal is Current Balance
Discrete
B - 125 = 1200
each whole number can be uniquely decomposed into products of primes.
Torus
50. If a whole number is not a prime number - then it is called a...
Composite Numbers
per line
Figurate Numbers
Problem of the Points