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Test your basic knowledge |
CLEP General Math: Number Sense - Patterns - Algebraic Thinking
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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. 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.
A prime number
Wave Equation
Cardinality
The Commutative Property of Addition
2. All integers are thus divided into three classes:
Greatest Common Factor (GCF)
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
The Multiplicative Identity Property
1. The unit 2. Prime numbers 3. Composite numbers
3. An algebraic 'sentence' containing an unknown quantity.
a - c = b - c
a · c = b · c for c does not equal 0
The Additive Identity Property
Polynomial
4. The study of shape from the perspective of being on the surface of the shape.
Sign Rules for Division
Intrinsic View
A number is divisible by 3
De Bruijn Sequence
5. When writing mathematical statements - follow the mantra:
Discrete
Continuous Symmetry
Hypersphere
One equal sign per line
6. Means approximately equal.
The Multiplicative Identity Property
˜
Euclid's Postulates
Group
7. The amount of displacement - as measured from the still surface line.
Primes
Bijection
Poincare Disk
Amplitude
8. Arise from the attempt to measure all quantities with a common unit of measure.
Set up an Equation
counting numbers
Markov Chains
Rational
9. If a and b are any whole numbers - then a
Factor Tree Alternate Approach
Commutative Property of Multiplication
The Same
˜
10. If grouping symbols are nested
Products and Factors
Fourier Analysis and Synthesis
evaluate the expression in the innermost pair of grouping symbols first.
Associate Property of Addition
11. A(b + c) = a · b + a · c a(b - c) = a · b - a · c
Cardinality
Distributive Property:
Factor Trees
Unique Factorization Theorem
12. (a + b) + c = a + (b + c)
Associative Property of Addition:
Galton Board
Tone
General Relativity
13. When comparing two whole numbers a and b - only one of three possibilities is true: a < b or a = b or a > b.
Denominator
inline
A number is divisible by 10
Comparison Property
14. 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
Multiplicative Identity:
Division is not Commutative
Transfinite
The inverse of multiplication is division
15. 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 Associative Property of Multiplication
Continuous Symmetry
Multiplicative Identity:
Look Back
16. Reveals why we tend to find structure in seemingly random sets. Ramsey numbers indicate how big a set must be to guarantee the existence of certain minimal structures.
Ramsey Theory
does not change the solution set.
Multiplicative Identity:
bar graph
17. Is a symbol (usually a letter) that stands for a value that may vary.
In Euclidean four-space
Variable
Intrinsic View
Equivalent Equations
18. If its final digit is a 0.
A number is divisible by 10
set
General Relativity
Spherical Geometry
19. Points in two-dimensional space require two numbers to specify them completely. The Cartesian plane is a good way to envision two-dimensional space.
Bijection
Overtone
Flat Land
Rarefactior
20. A · 1/a = 1/a · a = 1
Aleph-Null
Look Back
Multiplicative Inverse:
Problem of the Points
21. Two equations if they have the same solution set.
Extrinsic View
Equivalent Equations
Additive Inverse:
Euclid's Postulates
22. If a is any whole number - then a
Torus
does not change the solution set.
bar graph
The Multiplicative Identity Property
23. Division by zero is undefined. Each of the expressions 6
set
evaluate the expression in the innermost pair of grouping symbols first.
Division by Zero
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
24. The state of appearing unchanged.
Invarient
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
The Distributive Property (Subtraction)
Torus
25. 1. Any two points can be joined by a straight line. 2. Any straight line segment can be extended indefinitely in a straight line. 3. Given any straight line segment - a circle can be drawn having the segment as radius and one endpoint as center. 4. A
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26. 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.'
set
Multiplicative Inverse:
The Prime Number Theorem
Frequency
27. 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
The inverse of subtraction is addition
Spherical Geometry
A number is divisible by 9
28. You must always solve the equation set up in the previous step.
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
De Bruijn Sequence
Solve the Equation
bar graph
29. 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.
Axiomatic Systems
Commutative Property of Multiplication:
Equation
30. This famous - as yet unproven - result relates to the distribution of prime numbers on the number line.
Commensurability
Flat Land
Division by Zero
The Riemann Hypothesis
31. 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.
Non-Euclidian Geometry
Public Key Encryption
Law of Large Numbers
Dividing both Sides of an Equation by the Same Quantity
32. The multitude concept presented numbers as collections of discrete units - rather like indivisible atoms.
Standard Deviation
Axiomatic Systems
Factor Trees
Discrete
33. 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.'
Noether's Theorem
Hyperland
Multiplicative Inverse:
A number is divisible by 5
34. In the expression 3
Products and Factors
A number is divisible by 3
counting numbers
a + c = b + c
35. A graph in which every node is connected to every other node is called a complete graph.
Sign Rules for Division
Products and Factors
Complete Graph
A number is divisible by 3
36. Original Balance minus River Tam's Withdrawal is Current Balance
Permutation
Poincare Disk
B - 125 = 1200
each whole number can be uniquely decomposed into products of primes.
37. 4 more than a certain number is 12
left to right
4 + x = 12
Commensurability
Multiplicative Inverse:
38. A · 1 = 1 · a = a
Group
Additive Identity:
Multiplicative Identity:
Hypercube
39. Instruments produce notes that have a fundamental frequency in combination with multiples of that frequency known as partials or overtones
Distributive Property:
Overtone
perimeter
Fundamental Theorem of Arithmetic
40. W = {0 - 1 - 2 - 3 - 4 - 5 - . . .} is called
The Set of Whole Numbers
Continuous Symmetry
Euler Characteristic
Complete Graph
41. Use parentheses - brackets - or curly braces to delimit the part of an expression you want evaluated first.
set
Complete Graph
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
Grouping Symbols
42. 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.
Fundamental Theorem of Arithmetic
Normal Distribution
a + c = b + c
Factor Tree Alternate Approach
43. The expression a/b means
Geometry
Associative Property of Addition:
Intrinsic View
a divided by b
44. We can think of the space between primes as 'prime deserts -' strings of consecutive numbers - none of which are prime.
Ramsey Theory
The BML Traffic Model
Prime Deserts
Cayley's Theorem
45. A point in one dimension requires only one number to define it. The number line is a good example of a one-dimensional space.
Commensurability
does not change the solution set.
Line Land
a divided by b
46. If a = b then
a · c = b · c for c does not equal 0
Non-Orientability
Division is not Associative
Spaceland
47. This area of mathematics relates symmetry to whether or not an equation has a 'simple' solution.
Countable
Expected Value
Multiplicative Identity:
Galois Theory
48. A + b = b + a
Countable
Commutative Property of Addition:
The Riemann Hypothesis
Solve the Equation
49. If a = b then
a
Complete Graph
Cayley's Theorem
Grouping Symbols
50. The distribution of averages of many trials is always normal - even if the distribution of each trial is not.
Factor Trees
Euclid's Postulates
Central Limit Theorem
Division is not Associative