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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. 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
Hypersphere
Factor Trees
Multiplicative Identity:
a
2. To describe and extend a numerical pattern
The Distributive Property (Subtraction)
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.
Fundamental Theorem of Arithmetic
The Prime Number Theorem
3. Use parentheses - brackets - or curly braces to delimit the part of an expression you want evaluated first.
Grouping Symbols
Properties of Equality
1. The unit 2. Prime numbers 3. Composite numbers
Spherical Geometry
4. Aka The Osculating Circle - a way to measure the curvature of a line.
Public Key Encryption
a + c = b + c
Countable
The Kissing Circle
5. The multitude concept presented numbers as collections of discrete units - rather like indivisible atoms.
The Commutative Property of Addition
The Riemann Hypothesis
Discrete
Topology
6. A flat map of hyperbolic space.
Aleph-Null
Poincare Disk
The Additive Identity Property
Expected Value
7. (a + b) + c = a + (b + c)
Solution
Associative Property of Addition:
set
Set up an Equation
8. Cannot be written as a ratio of natural numbers.
˜
Irrational
Discrete
Rarefactior
9. 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.
Geometry
Non-Orientability
Non-Euclidian Geometry
a - c = b - c
10. 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 -
Ramsey Theory
Aleph-Null
The inverse of addition is subtraction
Irrational
11. Two equations if they have the same solution set.
Division is not Commutative
The Prime Number Theorem
Equivalent Equations
Overtone
12. Also known as gluing diagrams - are a convenient way to examine intrinsic topology.
Law of Large Numbers
Genus
Box Diagram
Division is not Commutative
13. Non-Euclidean geometries abide by some - but not all of Euclid's five postulates.
Non-Euclidian Geometry
Composite Numbers
Multiplying both Sides of an Equation by the Same Quantity
Continuous Symmetry
14. ____________ 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
Dividing both Sides of an Equation by the Same Quantity
Rational
Probability
The inverse of subtraction is addition
15. If a = b then
Galois Theory
Factor Tree Alternate Approach
a - c = b - c
Pigeonhole Principle
16. Let a - b - and c represent whole numbers. Then - (a + b) + c = a + (b + c).
Non-Euclidian Geometry
Countable
Associate Property of Addition
Central Limit Theorem
17. If a = b then a + c = b + c If a = b then a - c = b - c If a = b then a
Principal Curvatures
Properties of Equality
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
18. 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
Look Back
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
evaluate the expression in the innermost pair of grouping symbols first.
perimeter
19. (a · b) · c = a · (b · c)
Frequency
counting numbers
Properties of Equality
Associative Property of Multiplication:
20. Points in two-dimensional space require two numbers to specify them completely. The Cartesian plane is a good way to envision two-dimensional space.
Extrinsic View
Flat Land
Order of Operations - PEMDAS 'Please Excuse My Dear Aunt Sally'
a + c = b + c
21. (a
Division is not Associative
Principal Curvatures
left to right
A number is divisible by 9
22. A + (-a) = (-a) + a = 0
Multiplication
Additive Inverse:
Ramsey Theory
division
23. 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.
Law of Large Numbers
prime factors
set
each whole number can be uniquely decomposed into products of primes.
24. A way to analyze sequences of events where the outcomes of prior events affect the probability of outcomes of subsequent events.
Properties of Equality
Markov Chains
Multiplying both Sides of an Equation by the Same Quantity
Fourier Analysis and Synthesis
25. Has no factors other than 1 and itself
Euclid's Postulates
Least Common Multiple (LCM)
A prime number
Equivalent Equations
26. Topological objects are categorized by their _______ (number of holes). The genus of a surface is a feature of its global topology.
Bijection
Genus
A prime number
set
27. Our standard notions of Pythagorean distance and angle via the inner product extend quite nicely from three-space.
Associative Property of Addition:
A number is divisible by 3
Set up a Variable Dictionary.
In Euclidean four-space
28. Negative
Sign Rules for Division
Distributive Property:
Unique Factorization Theorem
Hyperland
29. Objects are topologically equivalent if they can be continuously deformed into one another. Properties that are preserved during this process are called topological invariants.
Flat Land
set
Irrational
Law of Large Numbers
30. 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
Division is not Associative
Solve the Equation
The inverse of multiplication is division
Multiplicative Identity:
31. 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.
Transfinite
Ramsey Theory
Irrational
Unique Factorization Theorem
32. A · 1/a = 1/a · a = 1
The Kissing Circle
Hypersphere
Multiplicative Inverse:
A prime number
33. An important part of problem solving is identifying
Principal Curvatures
variable
Fourier Analysis and Synthesis
Fundamental Theorem of Arithmetic
34. An equation is a numerical value that satisfies the equation. That is - when the variable in the equation is replaced by the solution - a true statement results.
Stereographic Projection
Euclid's Postulates
Fourier Analysis
Solution
35. 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).
Commutative Property of Multiplication
Prime Number
De Bruijn Sequence
Prime Deserts
36. If a is any whole number - then a
Wave Equation
Variable
The Multiplicative Identity Property
Non-Euclidian Geometry
37. Arise from the attempt to measure all quantities with a common unit of measure.
Sign Rules for Division
Rational
The Multiplicative Identity Property
1. The unit 2. Prime numbers 3. Composite numbers
38. If a represents any whole number - then a
Law of Large Numbers
Multiplication by Zero
Unique Factorization Theorem
Greatest Common Factor (GCF)
39. If a whole number is not a prime number - then it is called a...
Cayley's Theorem
counting numbers
The inverse of multiplication is division
Composite Numbers
40. A '___________' infinite set is one that can be put into one-to-one correspondence with the set of natural numbers.
Configuration Space
repeated addition
Countable
Overtone
41. An arrangement where order matters.
evaluate the expression in the innermost pair of grouping symbols first.
Permutation
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
Properties of Equality
42. An algebraic 'sentence' containing an unknown quantity.
Continuous Symmetry
Look Back
Polynomial
Multiplying both Sides of an Equation by the Same Quantity
43. A way to measure how far away a given individual result is from the average result.
Multiplication by Zero
Standard Deviation
Sign Rules for Division
Order of Operations - PEMDAS 'Please Excuse My Dear Aunt Sally'
44. This famous - as yet unproven - result relates to the distribution of prime numbers on the number line.
The Riemann Hypothesis
The index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.
Comparison Property
Polynomial
45. Used to display measurements. The measurement was taken is placed on the horizontal axis - and the height of each bar equals the amount during that year.
a · c = b · c for c does not equal 0
Bijection
Associate Property of Addition
bar graph
46. 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.
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
Modular Arithmetic
A number is divisible by 10
The Riemann Hypothesis
47. 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
Associative Property of Addition:
Fourier Analysis and Synthesis
Periodic Function
48. In some ways - the opposite of a multitude is a magnitude - which is ___________. In other words - there are no well defined partitions.
Greatest Common Factor (GCF)
Composite Numbers
Normal Distribution
Continuous
49. Instruments produce notes that have a fundamental frequency in combination with multiples of that frequency known as partials or overtones
In Euclidean four-space
The inverse of addition is subtraction
The Riemann Hypothesis
Overtone
50. 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
Transfinite
Hamilton Cycle
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