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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. The amount of displacement - as measured from the still surface line.
Variable
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
Noether's Theorem
Amplitude
2. Two equations if they have the same solution set.
Equivalent Equations
Multiplication
Answer the Question
Fundamental Theorem of Arithmetic
3. (a
The Associative Property of Multiplication
Principal Curvatures
Greatest Common Factor (GCF)
Division is not Associative
4. Rules for Rounding - To round a number to a particular place - follow these steps:
Standard Deviation
Markov Chains
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
each whole number can be uniquely decomposed into products of primes.
5. The inverse of multiplication
Extrinsic View
B - 125 = 1200
division
Exponents
6. (a + b) + c = a + (b + c)
Associative Property of Addition:
Poincare Disk
Distributive Property:
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.
7. 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
Properties of Equality
The inverse of subtraction is addition
The Riemann Hypothesis
The Same
8. A point in one dimension requires only one number to define it. The number line is a good example of a one-dimensional space.
Least Common Multiple (LCM)
Grouping Symbols
Line Land
Group
9. If the sum of its digits is divisible by 9 (ex: 3591 is divisible by 9 since 3 + 5 + 9 + 1 = 18 is divisible by 9).
Wave Equation
The Distributive Property (Subtraction)
˜
A number is divisible by 9
10. 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.'
The Prime Number Theorem
Set up a Variable Dictionary.
a + c = b + c
Line Land
11. 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).
The BML Traffic Model
Galois Theory
A number is divisible by 3
Division is not Commutative
12. Writing Mathematical equations - arrange your work one equation
The index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.
Invarient
Spaceland
per line
13. 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
perimeter
Flat Land
Problem of the Points
1. The unit 2. Prime numbers 3. Composite numbers
14. A graph in which every node is connected to every other node is called a complete graph.
Look Back
Complete Graph
Non-Orientability
Stereographic Projection
15. N = {1 - 2 - 3 - 4 - 5 - . . .}.
Multiplicative Identity:
the set of natural numbers
Multiplication by Zero
Hypersphere
16. Aka The Osculating Circle - a way to measure the curvature of a line.
The Kissing Circle
Set up an Equation
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
Standard Deviation
17. Use parentheses - brackets - or curly braces to delimit the part of an expression you want evaluated first.
perimeter
The inverse of subtraction is addition
Central Limit Theorem
Grouping Symbols
18. Multiplication is equivalent to
Dimension
A number is divisible by 10
repeated addition
Associate Property of Addition
19. 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.
Poincare Disk
Public Key Encryption
The Kissing Circle
Symmetry
20. 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
evaluate the expression in the innermost pair of grouping symbols first.
A number is divisible by 9
Aleph-Null
21. 1. Find the prime factorizations of each number.
The inverse of subtraction is addition
Greatest Common Factor (GCF)
Symmetry
4 + x = 12
22. 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
Non-Orientability
Division is not Commutative
23. This method can create a flat map from a curved surface while preserving all angles in any features present.
The Same
Complete Graph
A number is divisible by 9
Stereographic Projection
24. In any ratio of two whole numbers - expressed as a fraction - we can interpret the first (top) number to be the 'counter -' or numerator
The inverse of subtraction is addition
Hyperland
Denominator
evaluate the expression in the innermost pair of grouping symbols first.
25. We can think of the space between primes as 'prime deserts -' strings of consecutive numbers - none of which are prime.
One equal sign per line
Group
Prime Deserts
A number is divisible by 3
26. A number is divisible by 2
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
Rarefactior
Unique Factorization Theorem
Intrinsic View
27. A topological object that can be used to study the allowable states of a given system.
Genus
Polynomial
Configuration Space
Multiplicative Inverse:
28. W = {0 - 1 - 2 - 3 - 4 - 5 - . . .} is called
Rational
Poincare Disk
The Set of Whole Numbers
Topology
29. Perform all additions and subtractions in the order presented
Set up a Variable Dictionary.
Principal Curvatures
left to right
Topology
30. A point in three-dimensional space requires three numbers to fix its location.
Solution
Division by Zero
Spaceland
set
31. Arise from the attempt to measure all quantities with a common unit of measure.
Continuous
Primes
Associative Property of Multiplication:
Rational
32. If grouping symbols are nested
evaluate the expression in the innermost pair of grouping symbols first.
Noether's Theorem
Associate Property of Addition
Equation
33. A · b = b · a
Commutative Property of Multiplication:
The Additive Identity Property
Complete Graph
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
34. Some numbers make geometric shapes when arranged as a collection of dots - for example - 16 makes a square - and 10 makes a triangle.
Order of Operations - PEMDAS 'Please Excuse My Dear Aunt Sally'
Divisible
Associative Property of Addition:
Figurate Numbers
35. This result relates conserved physical quantities - like conservation of energy - to continuous symmetries of spacetime.
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36. In some ways - the opposite of a multitude is a magnitude - which is ___________. In other words - there are no well defined partitions.
Problem of the Points
Continuous
Markov Chains
Associative Property of Addition:
37. An arrangement where order matters.
Ramsey Theory
Commutative Property of Multiplication
Spherical Geometry
Permutation
38. A
Division is not Commutative
Associate Property of Addition
Commutative Property of Addition:
The Associative Property of Multiplication
39. 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
Law of Large Numbers
Pigeonhole Principle
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 Kissing Circle
40. Every solution to a word problem must include a carefully crafted equation that accurately describes the constraints in the problem statement.
Prime Deserts
Prime Number
Countable
Set up an Equation
41. Non-Euclidean geometries abide by some - but not all of Euclid's five postulates.
The Multiplicative Identity Property
Non-Euclidian Geometry
Irrational
a - c = b - c
42. A flat map of hyperbolic space.
Poincare Disk
Hamilton Cycle
Ramsey Theory
Cardinality
43. If a - b - and c are any whole numbers - then a
The Riemann Hypothesis
Spaceland
The Associative Property of Multiplication
Hamilton Cycle
44. 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
Least Common Multiple (LCM)
Division is not Commutative
Line Land
45. A + b = b + a
Group
Commutative Property of Addition:
Products and Factors
Associative Property of Addition:
46. The system that Euclid used in The Elements
Axiomatic Systems
Prime Number
Stereographic Projection
Permutation
47. Cannot be written as a ratio of natural numbers.
Divisible
Irrational
The Additive Identity Property
variable
48. If a is any whole number - then a
The Multiplicative Identity Property
Prime Deserts
Torus
Ramsey Theory
49. Breaks a complicated signal into a combination of simple sine waves. Fourier synthesis does the opposite - constructing a complicated signal from simple sine waves.
The inverse of addition is subtraction
Irrational
Fourier Analysis and Synthesis
4 + x = 12
50. 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
Set up an Equation
per line
Multiplicative Inverse: