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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. Originally known as analysis situs
One equal sign per line
In Euclidean four-space
Topology
The Same
2. 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
The Distributive Property (Subtraction)
Distributive Property:
set
3. Positive integers are
inline
Amplitude
B - 125 = 1200
counting numbers
4. 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
Problem of the Points
Look Back
Amplitude
prime factors
5. If a = b then
prime factors
a - c = b - c
Torus
Polynomial
6. 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.
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 inverse of subtraction is addition
Law of Large Numbers
the set of natural numbers
7. This famous - as yet unproven - result relates to the distribution of prime numbers on the number line.
The Riemann Hypothesis
Sign Rules for Division
Tone
Expected Value
8. If grouping symbols are nested
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
˜
Hypercube
evaluate the expression in the innermost pair of grouping symbols first.
9. A number is divisible by 2
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
Equation
division
10. The fundamental theorem of arithmetic says that
each whole number can be uniquely decomposed into products of primes.
Denominator
In Euclidean four-space
Division by Zero
11. (a · b) · c = a · (b · c)
Equation
Associative Property of Multiplication:
A number is divisible by 5
Pigeonhole Principle
12. Let a - b - and c represent whole numbers. Then - (a + b) + c = a + (b + c).
In Euclidean four-space
Associate Property of Addition
Symmetry
Bijection
13. Has no factors other than 1 and itself
1. The unit 2. Prime numbers 3. Composite numbers
Wave Equation
Cayley's Theorem
A prime number
14. Objects are topologically equivalent if they can be continuously deformed into one another. Properties that are preserved during this process are called topological invariants.
Multiplication
The Kissing Circle
Irrational
Products and Factors
15. A point in four-space - also known as 4-D space - requires four numbers to fix its position. Four-space has a fourth independent direction - described by 'ana' and 'kata.'
Intrinsic View
Solution
The Kissing Circle
Hyperland
16. If a = b then
Dimension
Divisible
a + c = b + c
Polynomial
17. 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.
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
Poincare Disk
Multiplying both Sides of an Equation by the Same Quantity
does not change the solution set.
18. A + b = b + a
Commutative Property of Addition:
Commutative Property of Multiplication:
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
Pigeonhole Principle
19. Is a symbol (usually a letter) that stands for a value that may vary.
Configuration Space
Greatest Common Factor (GCF)
a - c = b - c
Variable
20. If a = b then a + c = b + c If a = b then a - c = b - c If a = b then a
Commutative Property of Addition:
Overtone
Symmetry
Properties of Equality
21. The study of shape from an external perspective.
Associate Property of Addition
Comparison Property
does not change the solution set.
Extrinsic View
22. 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
Distributive Property:
˜
Complete Graph
Symmetry
23. The expression a^m means a multiplied by itself m times. The number a is called the base of the exponential expression and the number m is called the exponent. The exponent m tells us to repeat the base a as a factor m times.
per line
Line Land
Exponents
A prime number
24. This method can create a flat map from a curved surface while preserving all angles in any features present.
Flat Land
Euler Characteristic
Stereographic Projection
Galois Theory
25. A graph in which every node is connected to every other node is called a complete graph.
Continuous Symmetry
Topology
Complete Graph
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
26. 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
Continuous Symmetry
Cardinality
Extrinsic View
The Same
27. Let a and b represent two whole numbers. Then - a + b = b + a.
The Commutative Property of Addition
Exponents
Fourier Analysis
A prime number
28. 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.
The inverse of addition is subtraction
Countable
Modular Arithmetic
Normal Distribution
29. ____________ theory enables us to use mathematics to characterize and predict the behavior of random events. By 'random' we mean 'unpredictable' in the sense that in a given specific situation - our knowledge of current conditions gives us no way to
A number is divisible by 5
Dimension
Probability
Noether's Theorem
30. 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
Conditional Probability
Wave Equation
Flat Land
31. Requirements for Word Problem Solutions.
Line Land
Commensurability
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
a + c = b + c
32. A
˜
Division is not Commutative
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.
Hamilton Cycle
33. Writing Mathematical equations - arrange your work one equation
per line
Continuous
The Riemann Hypothesis
Commutative Property of Multiplication
34. Of central importance in Ramsey Theory - and in combinatorics in general - is the 'pigeonhole principle -' also known as Dirichlet's box. This principle simply states that we cannot fit n+1 pigeons into n pigeonholes in such a way that only one pigeo
The Additive Identity Property
Ramsey Theory
Pigeonhole Principle
Group
35. This area of mathematics relates symmetry to whether or not an equation has a 'simple' solution.
Non-Orientability
Galois Theory
One equal sign per line
Exponents
36. 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
Unique Factorization Theorem
Factor Trees
Dimension
A number is divisible by 3
37. Let a and b be whole numbers. Then a is _______________ by b if and only if the remainder is zero when a is divided by b. In this case - we say that 'b is a divisor of a.'
Divisible
a
prime factors
Hyperland
38. 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).
left to right
In Euclidean four-space
Division is not Commutative
A number is divisible by 3
39. Original Balance minus River Tam's Withdrawal is Current Balance
B - 125 = 1200
The index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.
Multiplying both Sides of an Equation by the Same Quantity
Commutative Property of Addition:
40. Dimension is how mathematicians express the idea of degrees of freedom
De Bruijn Sequence
Dimension
Rational
A number is divisible by 9
41. This important result says that every natural number greater than one can be expressed as a product of primes in exactly one way.
Probability
Fundamental Theorem of Arithmetic
The Multiplicative Identity Property
bar graph
42. If its final digit is a 0.
A number is divisible by 10
Prime Number
Principal Curvatures
Central Limit Theorem
43. The system that Euclid used in The Elements
Non-Euclidian Geometry
Axiomatic Systems
Comparison Property
Noether's Theorem
44. The cardinality of sets that cannot be put into one-to-one correspondence with the counting numbers - such as the set of real numbers - is referred to as c. The designations A_0 and c are known as 'transfinite' cardinalities.
Transfinite
Dimension
Extrinsic View
Symmetry
45. An instrument's _____ - the sound it produces - is a complex mixture of waves of different frequencies.
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
Flat Land
Tone
set
46. In some ways - the opposite of a multitude is a magnitude - which is ___________. In other words - there are no well defined partitions.
Continuous
Euclid's Postulates
Cardinality
Prime Deserts
47. The state of appearing unchanged.
Divisible
Invarient
Continuous
1. The unit 2. Prime numbers 3. Composite numbers
48. This result relates conserved physical quantities - like conservation of energy - to continuous symmetries of spacetime.
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49. A · 1 = 1 · a = a
Non-Orientability
Multiplicative Identity:
Continuous Symmetry
Poincare Disk
50. Some numbers make geometric shapes when arranged as a collection of dots - for example - 16 makes a square - and 10 makes a triangle.
Hypersphere
Prime Number
The Same
Figurate Numbers