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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. 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.
Commutative Property of Multiplication
Axiomatic Systems
Law of Large Numbers
Figurate Numbers
2. Dimension is how mathematicians express the idea of degrees of freedom
Dimension
Galois Theory
The Additive Identity Property
B - 125 = 1200
3. 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.
Commutative Property of Multiplication:
Public Key Encryption
Spherical Geometry
Extrinsic View
4. This result says that the symmetries of geometric objects can be expressed as groups of permutations.
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5. 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 divided by b
A number is divisible by 3
Properties of Equality
evaluate the expression in the innermost pair of grouping symbols first.
6. Points in two-dimensional space require two numbers to specify them completely. The Cartesian plane is a good way to envision two-dimensional space.
Set up a Variable Dictionary.
Flat Land
Variable
Associative Property of Multiplication:
7. 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.
Genus
counting numbers
Hyperbolic Geometry
Divisible
8. This area of mathematics relates symmetry to whether or not an equation has a 'simple' solution.
Least Common Multiple (LCM)
a
Rational
Galois Theory
9. A factor tree is a way to visualize a number's
Hypersphere
Figurate Numbers
Rarefactior
prime factors
10. Some numbers make geometric shapes when arranged as a collection of dots - for example - 16 makes a square - and 10 makes a triangle.
Prime Deserts
Figurate Numbers
Group
The index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.
11. Uses second derivatives to relate acceleration in space to acceleration in time.
Wave Equation
Problem of the Points
Prime Deserts
Cardinality
12. Our standard notions of Pythagorean distance and angle via the inner product extend quite nicely from three-space.
Hypercube
per line
In Euclidean four-space
Flat Land
13. Add and subtract
The inverse of multiplication is division
repeated addition
inline
Polynomial
14. 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
Torus
left to right
Set up a Variable Dictionary.
Standard Deviation
15. A way to measure how far away a given individual result is from the average result.
˜
The Set of Whole Numbers
Primes
Standard Deviation
16. A number is divisible by 2
Intrinsic View
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
Wave Equation
Cardinality
17. 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
a divided by b
Associative Property of Addition:
18. If a = b then a + c = b + c If a = b then a - c = b - c If a = b then a
Equation
Fourier Analysis
Commutative Property of Addition:
Properties of Equality
19. Determines the likelihood of events that are not independent of one another.
Configuration Space
A number is divisible by 5
Rational
Conditional Probability
20. 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.
Principal Curvatures
Irrational
Division by Zero
left to right
21. 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.
Non-Euclidian Geometry
Solution
A prime number
Noether's Theorem
22. 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.
bar graph
Equivalent Equations
Hamilton Cycle
Expected Value
23. Mathematical statement that equates two mathematical expressions.
Equation
Order of Operations - PEMDAS 'Please Excuse My Dear Aunt Sally'
The inverse of subtraction is addition
does not change the solution set.
24. Trigonometric functions - such as sine and cosine - are useful for modeling sound waves - because they oscillate between values
prime factors
Primes
Periodic Function
Frequency
25. Multiplication is equivalent to
prime factors
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.
repeated addition
inline
26. An instrument's _____ - the sound it produces - is a complex mixture of waves of different frequencies.
Overtone
General Relativity
Multiplicative Identity:
Tone
27. Originally known as analysis situs
Axiomatic Systems
Topology
variable
Public Key Encryption
28. Division by zero is undefined. Each of the expressions 6
Equation
repeated addition
Commutative Property of Multiplication:
Division by Zero
29. × - ( )( ) - · - 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
Overtone
Multiplication
Principal Curvatures
Commutative Property of Multiplication
30. 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
Products and Factors
Comparison Property
Order of Operations - PEMDAS 'Please Excuse My Dear Aunt Sally'
31. When comparing two whole numbers a and b - only one of three possibilities is true: a < b or a = b or a > b.
Additive Inverse:
Comparison Property
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.
The Distributive Property (Subtraction)
32. This important result says that every natural number greater than one can be expressed as a product of primes in exactly one way.
Group
Fundamental Theorem of Arithmetic
Continuous
Central Limit Theorem
33. A(b + c) = a · b + a · c a(b - c) = a · b - a · c
Principal Curvatures
Distributive Property:
The Set of Whole Numbers
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
34. Is a symbol (usually a letter) that stands for a value that may vary.
The Prime Number Theorem
Greatest Common Factor (GCF)
Variable
˜
35. A
Standard Deviation
Dividing both Sides of an Equation by the Same Quantity
Group
Division is not Commutative
36. The study of shape from the perspective of being on the surface of the shape.
Continuous Symmetry
Intrinsic View
Associate Property of Addition
Amplitude
37. Cannot be written as a ratio of natural numbers.
Irrational
Hamilton Cycle
Least Common Multiple (LCM)
The inverse of multiplication is division
38. Original Balance minus River Tam's Withdrawal is Current Balance
Multiplying both Sides of an Equation by the Same Quantity
Division is not Associative
B - 125 = 1200
Commutative Property of Addition:
39. 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
Set up a Variable Dictionary.
Problem of the Points
Continuous Symmetry
Hypersphere
40. 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
The Distributive Property (Subtraction)
Hypercube
Associative Property of Multiplication:
Cardinality
41. Two equations if they have the same solution set.
Solve the Equation
In Euclidean four-space
Euclid's Postulates
Equivalent Equations
42. 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.
Public Key Encryption
A number is divisible by 5
4 + x = 12
Solution
43. Let a - b - and c be any whole numbers. Then - a
Denominator
The Distributive Property (Subtraction)
Ramsey Theory
Fundamental Theorem of Arithmetic
44. The amount of displacement - as measured from the still surface line.
bar graph
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
Commensurability
Amplitude
45. The process of taking a complicated signal and breaking it into sine and cosine components.
Law of Large Numbers
Continuous Symmetry
Complete Graph
Fourier Analysis
46. You must always solve the equation set up in the previous step.
Normal Distribution
Answer the Question
Hypersphere
Solve the Equation
47. Einstein's famous theory - relates gravity to the curvature of spacetime.
Central Limit Theorem
General Relativity
1. The unit 2. Prime numbers 3. Composite numbers
Torus
48. 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 -
Unique Factorization Theorem
Spaceland
Primes
The inverse of addition is subtraction
49. Collection of objects. list all the objects in the set and enclosing the list in curly braces.
Geometry
set
Continuous
Aleph-Null
50. A '___________' infinite set is one that can be put into one-to-one correspondence with the set of natural numbers.
Products and Factors
Irrational
Countable
A number is divisible by 3