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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. Determines the likelihood of events that are not independent of one another.
Equation
The Set of Whole Numbers
Conditional Probability
Configuration Space
2. 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).
Figurate Numbers
does not change the solution set.
Products and Factors
Prime Number
3. 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.
Hyperbolic Geometry
4 + x = 12
Polynomial
Configuration Space
4. Collection of objects. list all the objects in the set and enclosing the list in curly braces.
Torus
Products and Factors
Unique Factorization Theorem
set
5. 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
Group
Multiplicative Inverse:
Central Limit Theorem
Divisible
6. A topological object that can be used to study the allowable states of a given system.
Non-Euclidian Geometry
In Euclidean four-space
Configuration Space
The Additive Identity Property
7. 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
each whole number can be uniquely decomposed into products of primes.
Dividing both Sides of an Equation by the Same Quantity
Least Common Multiple (LCM)
8. When comparing two whole numbers a and b - only one of three possibilities is true: a < b or a = b or a > b.
Euler Characteristic
Continuous
Box Diagram
Comparison Property
9. 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
Non-Orientability
The Riemann Hypothesis
Factor Tree Alternate Approach
Spaceland
10. A graph in which every node is connected to every other node is called a complete graph.
Set up a Variable Dictionary.
a - c = b - c
a · c = b · c for c does not equal 0
Complete Graph
11. 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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12. 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.
a - c = b - c
The Commutative Property of Addition
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
Modular Arithmetic
13. Our standard notions of Pythagorean distance and angle via the inner product extend quite nicely from three-space.
Genus
Figurate Numbers
In Euclidean four-space
Composite Numbers
14. An instrument's _____ - the sound it produces - is a complex mixture of waves of different frequencies.
Comparison Property
Rarefactior
Tone
The Distributive Property (Subtraction)
15. Aka The Osculating Circle - a way to measure the curvature of a line.
Division is not Associative
Continuous
perimeter
The Kissing Circle
16. The expression a/b means
a divided by b
The Associative Property of Multiplication
each whole number can be uniquely decomposed into products of primes.
General Relativity
17. In the expression 3
Expected Value
Products and Factors
B - 125 = 1200
each whole number can be uniquely decomposed into products of primes.
18. When writing mathematical statements - follow the mantra:
Invarient
Irrational
Unique Factorization Theorem
One equal sign per line
19. 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
Set up a Variable Dictionary.
A number is divisible by 3
Probability
variable
20. To describe and extend a numerical pattern
Multiplicative Identity:
Associative Property of Multiplication:
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.
Noether's Theorem
21. 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.
Group
Ramsey Theory
Invarient
Fundamental Theorem of Arithmetic
22. Dimension is how mathematicians express the idea of degrees of freedom
Continuous
Spaceland
Euler Characteristic
Dimension
23. Let a - b - and c be any whole numbers. Then - a
Fourier Analysis
1. The unit 2. Prime numbers 3. Composite numbers
Expected Value
The Distributive Property (Subtraction)
24. Means approximately equal.
Factor Tree Alternate Approach
Grouping Symbols
Conditional Probability
˜
25. Every solution to a word problem must include a carefully crafted equation that accurately describes the constraints in the problem statement.
Hypersphere
Set up an Equation
Transfinite
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
26. An important part of problem solving is identifying
Line Land
counting numbers
variable
Aleph-Null
27. A point in one dimension requires only one number to define it. The number line is a good example of a one-dimensional space.
a - c = b - c
Line Land
Denominator
A prime number
28. If its final digit is a 0 or 5.
Exponents
Least Common Multiple (LCM)
A number is divisible by 5
The Additive Identity Property
29. 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.'
Answer the Question
1. The unit 2. Prime numbers 3. Composite numbers
The Prime Number Theorem
Unique Factorization Theorem
30. If a = b then a + c = b + c If a = b then a - c = b - c If a = b then a
Non-Orientability
Properties of Equality
Variable
Flat Land
31. Requirements for Word Problem Solutions.
The Commutative Property of Addition
Commutative Property of Addition:
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
Irrational
32. Let a - b - and c represent whole numbers. Then - (a + b) + c = a + (b + c).
Least Common Multiple (LCM)
Associate Property of Addition
Division is not Associative
Commutative Property of Multiplication
33. Cannot be written as a ratio of natural numbers.
Irrational
a - c = b - c
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
34. 4 more than a certain number is 12
4 + x = 12
Extrinsic View
Dividing both Sides of an Equation by the Same Quantity
B - 125 = 1200
35. This result relates conserved physical quantities - like conservation of energy - to continuous symmetries of spacetime.
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36. A + b = b + a
Configuration Space
The Same
Prime Deserts
Commutative Property of Addition:
37. Some numbers make geometric shapes when arranged as a collection of dots - for example - 16 makes a square - and 10 makes a triangle.
a - c = b - c
repeated addition
Problem of the Points
Figurate Numbers
38. The state of appearing unchanged.
One equal sign per line
Cayley's Theorem
The Prime Number Theorem
Invarient
39. The study of shape from an external perspective.
Extrinsic View
Spherical Geometry
Torus
Greatest Common Factor (GCF)
40. (a
Division is not Associative
Symmetry
Probability
The inverse of multiplication is division
41. 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
counting numbers
Hyperland
Dimension
Look Back
42. 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.
Cayley's Theorem
Associative Property of Multiplication:
perimeter
Principal Curvatures
43. A topological invariant that relates a surface's vertices - edges - and faces.
Composite Numbers
each whole number can be uniquely decomposed into products of primes.
Euler Characteristic
Extrinsic View
44. 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.'
Overtone
Hyperland
The Set of Whole Numbers
evaluate the expression in the innermost pair of grouping symbols first.
45. 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
The Commutative Property of Addition
The Kissing Circle
a + c = b + c
The inverse of multiplication is division
46. The solutions to this gambling dilemma is traditionally held to be the start of modern probability theory.
The Distributive Property (Subtraction)
Problem of the Points
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
Overtone
47. Instruments produce notes that have a fundamental frequency in combination with multiples of that frequency known as partials or overtones
Overtone
Amplitude
Order of Operations - PEMDAS 'Please Excuse My Dear Aunt Sally'
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
48. A factor tree is a way to visualize a number's
prime factors
Discrete
Set up a Variable Dictionary.
Hyperland
49. (a + b) + c = a + (b + c)
The Multiplicative Identity Property
Stereographic Projection
Dimension
Associative Property of Addition:
50. 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
Group
Commutative Property of Multiplication
Normal Distribution
Frequency