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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. This important result says that every natural number greater than one can be expressed as a product of primes in exactly one way.
variable
Associate Property of Addition
The Commutative Property of Addition
Fundamental Theorem of Arithmetic
2. A flat map of hyperbolic space.
The Distributive Property (Subtraction)
Poincare Disk
Associative Property of Addition:
Noether's Theorem
3. An arrangement where order matters.
a + c = b + c
Least Common Multiple (LCM)
Permutation
Overtone
4. A · b = b · a
The Kissing Circle
Commutative Property of Multiplication:
Spherical Geometry
Topology
5. 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
The Distributive Property (Subtraction)
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
Modular Arithmetic
Look Back
6. Whether or not we hear waves as sound has everything to do with their _____________ - or how many times every second the molecules switch from compression to rarefaction and back to compression again - and their intensity - or how much the air is com
Frequency
Multiplication by Zero
Permutation
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
7. 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.
Standard Deviation
Equation
Solve the Equation
Principal Curvatures
8. This result says that the symmetries of geometric objects can be expressed as groups of permutations.
9. Also known as gluing diagrams - are a convenient way to examine intrinsic topology.
Central Limit Theorem
Division by Zero
Box Diagram
Flat Land
10. Negative
Bijection
A number is divisible by 3
Sign Rules for Division
The Kissing Circle
11. 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.
Solve the Equation
Greatest Common Factor (GCF)
A number is divisible by 10
bar graph
12. 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
Unique Factorization Theorem
perimeter
Commutative Property of Addition:
13. 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.
4 + x = 12
Hypercube
Periodic Function
Law of Large Numbers
14. The process of taking a complicated signal and breaking it into sine and cosine components.
Commutative Property of Multiplication
A number is divisible by 3
Fourier Analysis
Dividing both Sides of an Equation by the Same Quantity
15. 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.
Overtone
perimeter
does not change the solution set.
Frequency
16. Division by zero is undefined. Each of the expressions 6
Division by Zero
Conditional Probability
A number is divisible by 9
Bijection
17. 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.
Complete Graph
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
Pigeonhole Principle
Unique Factorization Theorem
18. If a = b then a + c = b + c If a = b then a - c = b - c If a = b then a
Set up a Variable Dictionary.
Properties of Equality
Genus
Division is not Associative
19. Is a symbol (usually a letter) that stands for a value that may vary.
The index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.
Stereographic Projection
Variable
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
20. Points in two-dimensional space require two numbers to specify them completely. The Cartesian plane is a good way to envision two-dimensional space.
B - 125 = 1200
Flat Land
Commutative Property of Multiplication:
Composite Numbers
21. A number is divisible by 2
Overtone
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
Galois Theory
Associative Property of Addition:
22. 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
Ramsey Theory
The inverse of subtraction is addition
perimeter
Modular Arithmetic
23. Let a - b - and c represent whole numbers. Then - (a + b) + c = a + (b + c).
repeated addition
Permutation
Associate Property of Addition
Commutative Property of Multiplication:
24. The study of shape from an external perspective.
Extrinsic View
The Same
The Prime Number Theorem
Law of Large Numbers
25. 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
Polynomial
bar graph
The Distributive Property (Subtraction)
26. The surface of a standard 'donut shape'.
The inverse of addition is subtraction
Torus
Divisible
Ramsey Theory
27. The inverse of multiplication
Transfinite
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
Associative Property of Addition:
division
28. All integers are thus divided into three classes:
Central Limit Theorem
1. The unit 2. Prime numbers 3. Composite numbers
Unique Factorization Theorem
General Relativity
29. 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
Unique Factorization Theorem
Division is not Commutative
a - c = b - c
Answer the Question
30. Original Balance minus River Tam's Withdrawal is Current Balance
Principal Curvatures
B - 125 = 1200
Greatest Common Factor (GCF)
In Euclidean four-space
31. Writing Mathematical equations - arrange your work one equation
per line
Products and Factors
Order of Operations - PEMDAS 'Please Excuse My Dear Aunt Sally'
a + c = b + c
32. To describe and extend a numerical pattern
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.
division
The Multiplicative Identity Property
The inverse of subtraction is addition
33. If a - b - and c are any whole numbers - then a
The BML Traffic Model
Amplitude
Torus
The Associative Property of Multiplication
34. When comparing two whole numbers a and b - only one of three possibilities is true: a < b or a = b or a > b.
Pigeonhole Principle
Conditional Probability
The Riemann Hypothesis
Comparison Property
35. 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.
Normal Distribution
Ramsey Theory
Multiplicative Identity:
Markov Chains
36. 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.
Ramsey Theory
Spherical Geometry
Exponents
The Riemann Hypothesis
37. If a is any whole number - then a
Continuous Symmetry
Unique Factorization Theorem
The Multiplicative Identity Property
Solution
38. This famous - as yet unproven - result relates to the distribution of prime numbers on the number line.
Noether's Theorem
The Prime Number Theorem
The Riemann Hypothesis
Properties of Equality
39. If a and b are any whole numbers - then a
Factor Tree Alternate Approach
Fundamental Theorem of Arithmetic
Commutative Property of Multiplication
The Kissing Circle
40. Let a and b represent two whole numbers. Then - a + b = b + a.
The index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.
The Commutative Property of Addition
Problem of the Points
˜
41. 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.
Division by Zero
Dimension
Galton Board
Commutative Property of Multiplication:
42. The multitude concept presented numbers as collections of discrete units - rather like indivisible atoms.
Discrete
does not change the solution set.
Fourier Analysis and Synthesis
Law of Large Numbers
43. 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).
Multiplication
Prime Number
Sign Rules for Division
set
44. The identification of a 'one-to-one' correspondence--enables us to enumerate a set that may be difficult to count in terms of another set that is more easily counted.
Problem of the Points
Noether's Theorem
Bijection
Additive Inverse:
45. 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.'
variable
Multiplying both Sides of an Equation by the Same Quantity
The Prime Number Theorem
Order of Operations - PEMDAS 'Please Excuse My Dear Aunt Sally'
46. Our standard notions of Pythagorean distance and angle via the inner product extend quite nicely from three-space.
Fourier Analysis
Galton Board
Set up a Variable Dictionary.
In Euclidean four-space
47. Is a path that visits every node in a graph and ends where it began.
Ramsey Theory
Axiomatic Systems
Hamilton Cycle
Denominator
48. 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
Configuration Space
Symmetry
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
49. 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)
Hypersphere
left to right
Group
50. If a whole number is not a prime number - then it is called a...
Least Common Multiple (LCM)
Composite Numbers
Symmetry
Axiomatic Systems