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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. 1. Find the prime factorizations of each number.
Greatest Common Factor (GCF)
One equal sign per line
Multiplicative Identity:
Multiplication
2. The cardinality of sets that cannot be put into one-to-one correspondence with the counting numbers - such as the set of real numbers - is referred to as c. The designations A_0 and c are known as 'transfinite' cardinalities.
Tone
The Kissing Circle
Transfinite
does not change the solution set.
3. A · 1 = 1 · a = a
Multiplicative Identity:
The inverse of addition is subtraction
Configuration Space
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
4. Is a path that visits every node in a graph and ends where it began.
Hamilton Cycle
Markov Chains
Unique Factorization Theorem
Galton Board
5. Collection of objects. list all the objects in the set and enclosing the list in curly braces.
B - 125 = 1200
set
Equivalent Equations
Hyperland
6. 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.
The Kissing Circle
˜
Non-Orientability
Euclid's Postulates
7. An algebraic 'sentence' containing an unknown quantity.
Polynomial
Principal Curvatures
Geometry
set
8. An instrument's _____ - the sound it produces - is a complex mixture of waves of different frequencies.
Tone
The Riemann Hypothesis
Prime Number
Commensurability
9. The solutions to this gambling dilemma is traditionally held to be the start of modern probability theory.
Problem of the Points
Multiplying both Sides of an Equation by the Same Quantity
Order of Operations - PEMDAS 'Please Excuse My Dear Aunt Sally'
The Multiplicative Identity Property
10. 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.
Solve the Equation
The Multiplicative Identity Property
Principal Curvatures
Cayley's Theorem
11. If a = b then
Flat Land
a
Ramsey Theory
bar graph
12. An important part of problem solving is identifying
Rational
Equivalent Equations
variable
a · c = b · c for c does not equal 0
13. A point in one dimension requires only one number to define it. The number line is a good example of a one-dimensional space.
Line Land
˜
Additive Identity:
Intrinsic View
14. 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)
Commensurability
variable
Line Land
Factor Tree Alternate Approach
15. Let a - b - and c represent whole numbers. Then - (a + b) + c = a + (b + c).
The inverse of addition is subtraction
Associate Property of Addition
Figurate Numbers
Ramsey Theory
16. A + (-a) = (-a) + a = 0
Euler Characteristic
Solve the Equation
Sign Rules for Division
Additive Inverse:
17. A topological object that can be used to study the allowable states of a given system.
Configuration Space
A number is divisible by 10
repeated addition
Dimension
18. Means approximately equal.
˜
Denominator
The Associative Property of Multiplication
Commutative Property of Addition:
19. 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).
Irrational
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
A number is divisible by 3
per line
20. Writing Mathematical equations - arrange your work one equation
bar graph
Multiplication by Zero
Commensurability
per line
21. Two equations if they have the same solution set.
Continuous
Dividing both Sides of an Equation by the Same Quantity
Equivalent Equations
Symmetry
22. 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
does not change the solution set.
Bijection
the set of natural numbers
23. At each level of the tree - break the current number into a product of two factors. The process is complete when all of the 'circled leaves' at the bottom of the tree are prime numbers. Arranging the factors in the 'circled leaves' in order. The fina
Factor Trees
Standard Deviation
Spherical Geometry
Axiomatic Systems
24. A factor tree is a way to visualize a number's
Set up an Equation
Division by Zero
variable
prime factors
25. A flat map of hyperbolic space.
A number is divisible by 3
Additive Inverse:
Countable
Poincare Disk
26. Einstein's famous theory - relates gravity to the curvature of spacetime.
In Euclidean four-space
The Associative Property of Multiplication
Answer the Question
General Relativity
27. Index p radicand
Euclid's Postulates
Associative Property of Multiplication:
Topology
The index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.
28. 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.
1. The unit 2. Prime numbers 3. Composite numbers
Law of Large Numbers
Genus
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
29. Does not change the solution set. That is - if a = b - then multiplying both sides of the equation by c produces the equivalent equation a
a + c = b + c
Associative Property of Addition:
Multiplying both Sides of an Equation by the Same Quantity
Pigeonhole Principle
30. 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
Properties of Equality
Figurate Numbers
per line
31. If a = b then
Order of Operations - PEMDAS 'Please Excuse My Dear Aunt Sally'
a - c = b - c
Fundamental Theorem of Arithmetic
Variable
32. 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
The Set of Whole Numbers
Commutative Property of Multiplication:
Group
33. Codifies the 'average behavior' of a random event and is a key concept in the application of probability.
Pigeonhole Principle
Cardinality
Torus
Expected Value
34. You must always solve the equation set up in the previous step.
Stereographic Projection
Solve the Equation
Rarefactior
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
35. (a
Sign Rules for Division
Division is not Associative
a + c = b + c
Wave Equation
36. A '___________' infinite set is one that can be put into one-to-one correspondence with the set of natural numbers.
Dividing both Sides of an Equation by the Same Quantity
Countable
a + c = b + c
Prime Number
37. This famous - as yet unproven - result relates to the distribution of prime numbers on the number line.
The Riemann Hypothesis
set
Equation
a
38. Some numbers make geometric shapes when arranged as a collection of dots - for example - 16 makes a square - and 10 makes a triangle.
Cardinality
Conditional Probability
Figurate Numbers
Multiplication
39. Does not change the solution set. That is - if a = b - then dividing both sides of the equation by c produces the equivalent equation a/c = b/c - provided c = 0.
Set up a Variable Dictionary.
Group
Dividing both Sides of an Equation by the Same Quantity
A number is divisible by 3
40. This result says that the symmetries of geometric objects can be expressed as groups of permutations.
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41. Let a and b represent two whole numbers. Then - a + b = b + a.
Flat Land
Tone
The Commutative Property of Addition
Hyperbolic Geometry
42. If a - b - and c are any whole numbers - then a
Problem of the Points
Dimension
Fourier Analysis
The Associative Property of Multiplication
43. In some ways - the opposite of a multitude is a magnitude - which is ___________. In other words - there are no well defined partitions.
Division is not Commutative
The Multiplicative Identity Property
Conditional Probability
Continuous
44. This step is easily overlooked. For example - the problem might ask for Jane's age - but your equation's solution gives the age of Jane's sister Liz. Make sure you answer the original question asked in the problem. Your solution should be written in
Public Key Encryption
Answer the Question
Rational
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
45. In the expression 3
Look Back
The Set of Whole Numbers
Products and Factors
Euler Characteristic
46. If we start with a number x and subtract a number a - then adding a to the result will return us to the original number x. In symbols - x - a + a = x. So -
Cardinality
Denominator
The inverse of subtraction is addition
One equal sign per line
47. (a + b) + c = a + (b + c)
Associative Property of Addition:
Sign Rules for Division
Hypersphere
Division is not Commutative
48. 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.
bar graph
Commutative Property of Addition:
Genus
a · c = b · c for c does not equal 0
49. Has no factors other than 1 and itself
A prime number
Prime Number
Non-Orientability
Genus
50. 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.
Spaceland
Bijection
De Bruijn Sequence
Principal Curvatures