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Test your basic knowledge |
CLEP General Math: Number Sense - Patterns - Algebraic Thinking
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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 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.
Non-Orientability
Principal Curvatures
The Multiplicative Identity Property
Standard Deviation
2. 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)
Division is not Commutative
Commensurability
Permutation
Axiomatic Systems
3. Also known as gluing diagrams - are a convenient way to examine intrinsic topology.
De Bruijn Sequence
Geometry
B - 125 = 1200
Box Diagram
4. In some ways - the opposite of a multitude is a magnitude - which is ___________. In other words - there are no well defined partitions.
4 + x = 12
Continuous
a · c = b · c for c does not equal 0
per line
5. 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.
Galton Board
Standard Deviation
Extrinsic View
Least Common Multiple (LCM)
6. Is a symbol (usually a letter) that stands for a value that may vary.
Frequency
Variable
The Associative Property of Multiplication
Hyperland
7. All integers are thus divided into three classes:
Commutative Property of Multiplication:
Figurate Numbers
variable
1. The unit 2. Prime numbers 3. Composite numbers
8. 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
Additive Identity:
Look Back
Set up a Variable Dictionary.
Pigeonhole Principle
9. A sphere can be thought of as a stack of circular discs of increasing - then decreasing - radii. The process of slicing is one way to visualize higher-dimensional objects via level curves and surfaces. A hypersphere can be thought of as a 'stack' of
Denominator
Exponents
Hypersphere
Noether's Theorem
10. A '___________' infinite set is one that can be put into one-to-one correspondence with the set of natural numbers.
per line
Countable
Divisible
Distributive Property:
11. If we start with a number x and add a number a - then subtracting a from the result will return us to the original number x. x + a - a = x. so -
Line Land
The inverse of addition is subtraction
Poincare Disk
Associate Property of Addition
12. 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
Flat Land
Solution
Public Key Encryption
13. 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
Symmetry
Multiplication by Zero
Bijection
Hyperbolic Geometry
14. A · 1/a = 1/a · a = 1
Multiplicative Inverse:
Spaceland
Products and Factors
Galton Board
15. 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.'
Box Diagram
Polynomial
A number is divisible by 5
Divisible
16. N = {1 - 2 - 3 - 4 - 5 - . . .}.
Frequency
the set of natural numbers
4 + x = 12
De Bruijn Sequence
17. 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.
Hypercube
Bijection
Division by Zero
Division is not Commutative
18. Determines the likelihood of events that are not independent of one another.
Conditional Probability
bar graph
A number is divisible by 5
Intrinsic View
19. 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
Pigeonhole Principle
Denominator
Factor Trees
Commensurability
20. The state of appearing unchanged.
A number is divisible by 9
Bijection
Invarient
Continuous Symmetry
21. The whole number zero is called the additive identity. If a is any whole number - then a + 0 = a.
Fundamental Theorem of Arithmetic
The Additive Identity Property
Distributive Property:
Multiplication
22. (a + b) + c = a + (b + c)
Associative Property of Addition:
The Prime Number Theorem
Polynomial
Hamilton Cycle
23. This method can create a flat map from a curved surface while preserving all angles in any features present.
Group
Continuous
Answer the Question
Stereographic Projection
24. 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.
˜
Multiplicative Inverse:
Fourier Analysis
Geometry
25. 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).
Hyperland
Commensurability
Central Limit Theorem
Prime Number
26. Einstein's famous theory - relates gravity to the curvature of spacetime.
Extrinsic View
Multiplication
Commutative Property of Multiplication:
General Relativity
27. In any ratio of two whole numbers - expressed as a fraction - we can interpret the first (top) number to be the 'counter -' or numerator
Law of Large Numbers
Denominator
Associative Property of Addition:
Continuous
28. 4 more than a certain number is 12
4 + x = 12
Commensurability
Equation
Law of Large Numbers
29. Means approximately equal.
˜
Normal Distribution
Dividing both Sides of an Equation by the Same Quantity
The inverse of multiplication is division
30. If its final digit is a 0.
A number is divisible by 10
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
Torus
per line
31. The four-dimensional analog of the cube - square - and line segment. A hypercube is formed by taking a 3-D cube - pushing a copy of it into the fourth dimension - and connecting it with cubes. Envisioning this object in lower dimensions requires that
a - c = b - c
Multiplicative Identity:
Hypercube
General Relativity
32. A point in three-dimensional space requires three numbers to fix its location.
Spaceland
Properties of Equality
Commutative Property of Multiplication
Equivalent Equations
33. × - ( )( ) - · - 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
Multiplication
Properties of Equality
variable
Associate Property of Addition
34. Instruments produce notes that have a fundamental frequency in combination with multiples of that frequency known as partials or overtones
Hyperbolic Geometry
Overtone
Poincare Disk
Grouping Symbols
35. Original Balance minus River Tam's Withdrawal is Current Balance
Composite Numbers
Commensurability
B - 125 = 1200
Continuous Symmetry
36. A number is divisible by 2
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
Poincare Disk
Principal Curvatures
Permutation
37. When writing mathematical statements - follow the mantra:
Sign Rules for Division
One equal sign per line
A prime number
Variable
38. 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
Factor Tree Alternate Approach
The BML Traffic Model
The Associative Property of Multiplication
Commutative Property of Addition:
39. Are the fundamental building blocks of arithmetic.
Principal Curvatures
Additive Inverse:
Primes
Commutative Property of Multiplication
40. Trigonometric functions - such as sine and cosine - are useful for modeling sound waves - because they oscillate between values
Associative Property of Addition:
a · c = b · c for c does not equal 0
a divided by b
Periodic Function
41. If a = b then
left to right
Conditional Probability
a · c = b · c for c does not equal 0
The inverse of addition is subtraction
42. A way to measure how far away a given individual result is from the average result.
Galton Board
repeated addition
Primes
Standard Deviation
43. 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
Flat Land
each whole number can be uniquely decomposed into products of primes.
Frequency
The index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.
44. 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
a
The inverse of subtraction is addition
The inverse of multiplication is division
45. Solving Equations
A number is divisible by 5
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
Division is not Commutative
Fourier Analysis and Synthesis
46. 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 inverse of multiplication is division
Flat Land
Set up an Equation
each whole number can be uniquely decomposed into products of primes.
47. This famous - as yet unproven - result relates to the distribution of prime numbers on the number line.
A number is divisible by 10
The Riemann Hypothesis
a - c = b - c
Dimension
48. Rules for Rounding - To round a number to a particular place - follow these steps:
Equivalent Equations
Conditional Probability
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
Denominator
49. If its final digit is a 0 or 5.
Division is not Associative
A number is divisible by 5
Problem of the Points
The inverse of addition is subtraction
50. Let a - b - and c represent whole numbers. Then - (a + b) + c = a + (b + c).
evaluate the expression in the innermost pair of grouping symbols first.
Principal Curvatures
Associate Property of Addition
Intrinsic View
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