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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 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
Public Key Encryption
Primes
The inverse of multiplication is division
Greatest Common Factor (GCF)
2. Two equations if they have the same solution set.
Noether's Theorem
Factor Tree Alternate Approach
Equivalent Equations
The Kissing Circle
3. If a = b then a + c = b + c If a = b then a - c = b - c If a = b then a
Properties of Equality
evaluate the expression in the innermost pair of grouping symbols first.
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
a
4. 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.
General Relativity
Euler Characteristic
Principal Curvatures
Rarefactior
5. × - ( )( ) - · - 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
Greatest Common Factor (GCF)
Modular Arithmetic
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
Multiplication
6. A(b + c) = a · b + a · c a(b - c) = a · b - a · c
Distributive Property:
Rational
Overtone
The Kissing Circle
7. A point in one dimension requires only one number to define it. The number line is a good example of a one-dimensional space.
evaluate the expression in the innermost pair of grouping symbols first.
Bijection
Line Land
per line
8. Perform all additions and subtractions in the order presented
˜
Hypersphere
Comparison Property
left to right
9. The whole number zero is called the additive identity. If a is any whole number - then a + 0 = a.
counting numbers
The Additive Identity Property
a
Fundamental Theorem of Arithmetic
10. Dimension is how mathematicians express the idea of degrees of freedom
Dimension
Expected Value
General Relativity
Symmetry
11. Let a - b - and c be any whole numbers. Then - a
The Distributive Property (Subtraction)
Axiomatic Systems
A prime number
Invarient
12. 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).
Additive Inverse:
Hypercube
A number is divisible by 3
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
13. A number is divisible by 2
The Additive Identity Property
a - c = b - c
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
Commutative Property of Addition:
14. 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.
Cardinality
Variable
Complete Graph
A number is divisible by 3
15. If on a surface there is no meaningful way to tell an object's orientation (left or right handedness) - the surface is said to be non-orientable.
The Prime Number Theorem
The Associative Property of Multiplication
Non-Orientability
Multiplicative Inverse:
16. A way to measure how far away a given individual result is from the average result.
Set up an Equation
Multiplicative Inverse:
Cayley's Theorem
Standard Deviation
17. Arise from the attempt to measure all quantities with a common unit of measure.
Rational
Galton Board
Commutative Property of Multiplication
set
18. 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
Set up a Variable Dictionary.
Noether's Theorem
Group
prime factors
19. Originally known as analysis situs
Topology
Irrational
Primes
The Riemann Hypothesis
20. N = {1 - 2 - 3 - 4 - 5 - . . .}.
Dimension
repeated addition
Overtone
the set of natural numbers
21. This model is at the forefront of probability research. Mathematicians use it to model traffic patterns in an attempt to understand flow rates and gridlock - among other things.
Multiplication by Zero
The Prime Number Theorem
Products and Factors
The BML Traffic Model
22. If a = b then
The inverse of subtraction is addition
Grouping Symbols
4 + x = 12
a · c = b · c for c does not equal 0
23. Codifies the 'average behavior' of a random event and is a key concept in the application of probability.
set
Complete Graph
repeated addition
Expected Value
24. 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.
Topology
Solution
The Set of Whole Numbers
a + c = b + c
25. In the expression 3
Greatest Common Factor (GCF)
Products and Factors
Axiomatic Systems
Bijection
26. If a = b then
The Multiplicative Identity Property
a - c = b - c
Expected Value
The inverse of addition is subtraction
27. If a - b - and c are any whole numbers - then a
Division by Zero
The Associative Property of Multiplication
Poincare Disk
Bijection
28. Aka The Osculating Circle - a way to measure the curvature of a line.
Variable
The BML Traffic Model
Equivalent Equations
The Kissing Circle
29. 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)
Axiomatic Systems
Euclid's Postulates
The BML Traffic Model
Commensurability
30. 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.
1. The unit 2. Prime numbers 3. Composite numbers
left to right
Geometry
Cardinality
31. 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.
Irrational
The Same
Hamilton Cycle
Law of Large Numbers
32. If its final digit is a 0 or 5.
Answer the Question
A number is divisible by 5
Set up an Equation
Commutative Property of Multiplication:
33. Is a symbol (usually a letter) that stands for a value that may vary.
Variable
Products and Factors
Non-Euclidian Geometry
Properties of Equality
34. If a = b then
Aleph-Null
4 + x = 12
a
Prime Deserts
35. A + (-a) = (-a) + a = 0
Axiomatic Systems
Additive Inverse:
Multiplicative Identity:
per line
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 -
Geometry
Multiplicative Inverse:
A prime number
The inverse of subtraction is addition
37. The study of shape from an external perspective.
Unique Factorization Theorem
The Set of Whole Numbers
Markov Chains
Extrinsic View
38. 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
Non-Euclidian Geometry
Wave Equation
Hypercube
Factor Trees
39. Original Balance minus River Tam's Withdrawal is Current Balance
The Set of Whole Numbers
Factor Tree Alternate Approach
B - 125 = 1200
Wave Equation
40. Also known as gluing diagrams - are a convenient way to examine intrinsic topology.
perimeter
Box Diagram
Line Land
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
41. A + b = b + a
Bijection
Dividing both Sides of an Equation by the Same Quantity
Commutative Property of Addition:
Least Common Multiple (LCM)
42. 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.
each whole number can be uniquely decomposed into products of primes.
The Distributive Property (Subtraction)
Dividing both Sides of an Equation by the Same Quantity
Greatest Common Factor (GCF)
43. 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
Look Back
variable
B - 125 = 1200
Bijection
44. An algebraic 'sentence' containing an unknown quantity.
The Multiplicative Identity Property
Polynomial
The inverse of subtraction is addition
Grouping Symbols
45. To describe and extend a numerical pattern
Problem of the Points
Wave Equation
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 set of natural numbers
46. A · b = b · a
Commutative Property of Multiplication:
Non-Euclidian Geometry
Solution
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.
47. Let a - b - and c represent whole numbers. Then - (a + b) + c = a + (b + c).
Conditional Probability
Set up a Variable Dictionary.
Associate Property of Addition
Fourier Analysis
48. You must always solve the equation set up in the previous step.
Sign Rules for Division
Solve the Equation
Unique Factorization Theorem
Multiplicative Inverse:
49. The system that Euclid used in The Elements
variable
Composite Numbers
Axiomatic Systems
Grouping Symbols
50. (a
Division is not Associative
Conditional Probability
The Additive Identity Property
per line