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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. If a = b then
Continuous
a + c = b + c
Equivalent Equations
A number is divisible by 9
2. 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.
Overtone
Modular Arithmetic
Intrinsic View
Spherical Geometry
3. Arise from the attempt to measure all quantities with a common unit of measure.
Rational
Sign Rules for Division
Additive Inverse:
The Riemann Hypothesis
4. The process of taking a complicated signal and breaking it into sine and cosine components.
Flat Land
The Riemann Hypothesis
Answer the Question
Fourier Analysis
5. 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 Prime Number Theorem
left to right
Extrinsic View
Line Land
6. × - ( )( ) - · - 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
Multiplication
Markov Chains
The Riemann Hypothesis
Multiplicative Identity:
7. When comparing two whole numbers a and b - only one of three possibilities is true: a < b or a = b or a > b.
Comparison Property
Spaceland
Conditional Probability
Hyperland
8. A · 1/a = 1/a · a = 1
Non-Orientability
Pigeonhole Principle
Associate Property of Addition
Multiplicative Inverse:
9. Let a - b - and c represent whole numbers. Then - (a + b) + c = a + (b + c).
Associate Property of Addition
The Same
a · c = b · c for c does not equal 0
1. The unit 2. Prime numbers 3. Composite numbers
10. The study of shape from the perspective of being on the surface of the shape.
Exponents
a
Intrinsic View
Look Back
11. 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.
The Associative Property of Multiplication
Law of Large Numbers
Non-Orientability
Ramsey Theory
12. (a
The Associative Property of Multiplication
Continuous
Composite Numbers
Division is not Associative
13. Cannot be written as a ratio of natural numbers.
Comparison Property
evaluate the expression in the innermost pair of grouping symbols first.
Conditional Probability
Irrational
14. The expression a/b means
Multiplication
bar graph
a divided by b
Distributive Property:
15. 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
Polynomial
In Euclidean four-space
Periodic Function
Group
16. 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.
Spherical Geometry
Hyperbolic Geometry
1. The unit 2. Prime numbers 3. Composite numbers
a + c = b + c
17. Let a and b represent two whole numbers. Then - a + b = b + a.
The Commutative Property of Addition
Non-Orientability
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
Hypersphere
18. A + (-a) = (-a) + a = 0
Geometry
Additive Inverse:
Intrinsic View
Public Key Encryption
19. A way to measure how far away a given individual result is from the average result.
Irrational
Hyperbolic Geometry
Topology
Standard Deviation
20. Has no factors other than 1 and itself
A prime number
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
Configuration Space
Public Key Encryption
21. Means approximately equal.
Galton Board
a + c = b + c
Additive Inverse:
˜
22. If a = b then
evaluate the expression in the innermost pair of grouping symbols first.
a - c = b - c
Permutation
variable
23. TA model of a sequence of random events. Each marble that passes through the system represents a trial consisting of as many random events as there are rows in the system.
set
Galton Board
evaluate the expression in the innermost pair of grouping symbols first.
Stereographic Projection
24. Solving Equations
˜
Galton Board
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
Order of Operations - PEMDAS 'Please Excuse My Dear Aunt Sally'
25. This famous - as yet unproven - result relates to the distribution of prime numbers on the number line.
Galois Theory
Solve the Equation
The Riemann Hypothesis
Box Diagram
26. 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.
Periodic Function
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.
does not change the solution set.
Rarefactior
27. Uses second derivatives to relate acceleration in space to acceleration in time.
Markov Chains
Solution
Denominator
Wave Equation
28. A · b = b · a
division
Commutative Property of Multiplication:
Topology
A number is divisible by 5
29. A flat map of hyperbolic space.
Permutation
each whole number can be uniquely decomposed into products of primes.
Poincare Disk
Standard Deviation
30. The state of appearing unchanged.
Invarient
Hamilton Cycle
Properties of Equality
Extrinsic View
31. 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.
Symmetry
Rarefactior
Genus
Spherical Geometry
32. Einstein's famous theory - relates gravity to the curvature of spacetime.
General Relativity
Greatest Common Factor (GCF)
˜
Rarefactior
33. 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
Noether's Theorem
Set up a Variable Dictionary.
˜
A prime number
34. This result says that the symmetries of geometric objects can be expressed as groups of permutations.
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35. 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
Box Diagram
Least Common Multiple (LCM)
The inverse of multiplication is division
36. An arrangement where order matters.
a + c = b + c
Poincare Disk
Permutation
Grouping Symbols
37. A topological invariant that relates a surface's vertices - edges - and faces.
Dimension
repeated addition
Denominator
Euler Characteristic
38. If a is any whole number - then a
Galton Board
The Commutative Property of Addition
Products and Factors
The Multiplicative Identity Property
39. (a · b) · c = a · (b · c)
perimeter
Exponents
Non-Orientability
Associative Property of Multiplication:
40. 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.
Law of Large Numbers
Markov Chains
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
Unique Factorization Theorem
41. Codifies the 'average behavior' of a random event and is a key concept in the application of probability.
Greatest Common Factor (GCF)
Stereographic Projection
Distributive Property:
Expected Value
42. 1. Parentheses (or any grouping symbol {braces} - [square brackets] - |absolute value|)
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43. 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
Grouping Symbols
Factor Tree Alternate Approach
Cardinality
Properties of Equality
44. Requirements for Word Problem Solutions.
Sign Rules for Division
Solution
Torus
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
45. A number is divisible by 2
Set up a Variable Dictionary.
Least Common Multiple (LCM)
Symmetry
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
46. A(b + c) = a · b + a · c a(b - c) = a · b - a · c
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.
Distributive Property:
B - 125 = 1200
Least Common Multiple (LCM)
47. N = {1 - 2 - 3 - 4 - 5 - . . .}.
Aleph-Null
Symmetry
the set of natural numbers
Expected Value
48. 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).
A number is divisible by 5
Prime Number
The Kissing Circle
Additive Inverse:
49. An important part of problem solving is identifying
inline
Spherical Geometry
variable
Factor Trees
50. Some numbers make geometric shapes when arranged as a collection of dots - for example - 16 makes a square - and 10 makes a triangle.
Hypercube
The Commutative Property of Addition
Figurate Numbers
Dimension