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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. Objects are topologically equivalent if they can be continuously deformed into one another. Properties that are preserved during this process are called topological invariants.
Associate Property of Addition
Irrational
The BML Traffic Model
Poincare Disk
2. Our standard notions of Pythagorean distance and angle via the inner product extend quite nicely from three-space.
In Euclidean four-space
Irrational
A number is divisible by 10
The Additive Identity Property
3. 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.
The Associative Property of Multiplication
Public Key Encryption
Non-Euclidian Geometry
bar graph
4. A · b = b · a
Multiplication by Zero
Periodic Function
The Prime Number Theorem
Commutative Property of Multiplication:
5. 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.
The Additive Identity Property
In Euclidean four-space
Dividing both Sides of an Equation by the Same Quantity
Genus
6. Multiplication is equivalent to
Ramsey Theory
repeated addition
Overtone
Geometry
7. Perform all additions and subtractions in the order presented
The Distributive Property (Subtraction)
Hypersphere
left to right
Tone
8. The expression a^m means a multiplied by itself m times. The number a is called the base of the exponential expression and the number m is called the exponent. The exponent m tells us to repeat the base a as a factor m times.
Exponents
Genus
Variable
Properties of Equality
9. Mathematical statement that equates two mathematical expressions.
Hyperbolic Geometry
Equation
Properties of Equality
prime factors
10. Division by zero is undefined. Each of the expressions 6
Division by Zero
Solution
The index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.
Figurate Numbers
11. Every solution to a word problem must include a carefully crafted equation that accurately describes the constraints in the problem statement.
Law of Large Numbers
The Kissing Circle
left to right
Set up an Equation
12. If a = b then
Solution
Irrational
1. The unit 2. Prime numbers 3. Composite numbers
a
13. If its final digit is a 0.
Comparison Property
The Multiplicative Identity Property
A number is divisible by 10
Irrational
14. A · 1 = 1 · a = a
Multiplicative Identity:
Periodic Function
Box Diagram
The Commutative Property of Addition
15. The solutions to this gambling dilemma is traditionally held to be the start of modern probability theory.
Multiplicative Identity:
the set of natural numbers
Commutative Property of Multiplication:
Problem of the Points
16. ____________ 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
˜
Probability
Stereographic Projection
The Multiplicative Identity Property
17. 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).
The Same
Additive Inverse:
Prime Number
does not change the solution set.
18. 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.
Multiplication by Zero
Variable
bar graph
Line Land
19. Means approximately equal.
Normal Distribution
Dividing both Sides of an Equation by the Same Quantity
˜
each whole number can be uniquely decomposed into products of primes.
20. In some ways - the opposite of a multitude is a magnitude - which is ___________. In other words - there are no well defined partitions.
In Euclidean four-space
Hypercube
Continuous
The index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.
21. Determines the likelihood of events that are not independent of one another.
Hypercube
Configuration Space
Conditional Probability
Hamilton Cycle
22. The system that Euclid used in The Elements
Geometry
Irrational
The Distributive Property (Subtraction)
Axiomatic Systems
23. A way to measure how far away a given individual result is from the average result.
Standard Deviation
Frequency
Flat Land
Overtone
24. A · 1/a = 1/a · a = 1
Expected Value
Multiplicative Inverse:
Complete Graph
Division is not Associative
25. Adding the same quantity to both sides of an equation - if a = b - then adding c to both sides of the equation produces the equivalent equation a + c = b + c.
Galois Theory
Non-Euclidian Geometry
Expected Value
does not change the solution set.
26. 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
counting numbers
Hamilton Cycle
Continuous
Factor Trees
27. We can think of the space between primes as 'prime deserts -' strings of consecutive numbers - none of which are prime.
Prime Deserts
1. The unit 2. Prime numbers 3. Composite numbers
Topology
A number is divisible by 10
28. 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.
Hamilton Cycle
Distributive Property:
Galton Board
Solve the Equation
29. Solving Equations
Commensurability
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 Commutative Property of Addition
Associative Property of Addition:
30. 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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31. Let a and b represent two whole numbers. Then - a + b = b + a.
Division by Zero
˜
The Commutative Property of Addition
Discrete
32. 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
Commutative Property of Multiplication:
Tone
Conditional Probability
33. If a represents any whole number - then a
counting numbers
Frequency
A number is divisible by 3
Multiplication by Zero
34. 1. Find the prime factorizations of each number. To find the prime factorization one method is a factor tree where you begin with any two factors and proceed by dividing the numbers until all the ends are prime factors. 2. Star factors which are shar
Least Common Multiple (LCM)
a · c = b · c for c does not equal 0
Comparison Property
Hyperbolic Geometry
35. If a is any whole number - then a
The Multiplicative Identity Property
Comparison Property
˜
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
36. If a = b then
Euclid's Postulates
a + c = b + c
Variable
Hypercube
37. 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.'
Non-Euclidian Geometry
Division is not Associative
Least Common Multiple (LCM)
Divisible
38. Every whole number can be uniquely factored as a product of primes. This result guarantees that if the prime factors are ordered from smallest to largest - everyone will get the same result when breaking a number into a product of prime factors.
The Set of Whole Numbers
Unique Factorization Theorem
Multiplicative Inverse:
Permutation
39. (a · b) · c = a · (b · c)
Associative Property of Multiplication:
Euler Characteristic
Multiplicative Identity:
˜
40. An algebraic 'sentence' containing an unknown quantity.
each whole number can be uniquely decomposed into products of primes.
Hamilton Cycle
Polynomial
Line Land
41. N = {1 - 2 - 3 - 4 - 5 - . . .}.
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
Ramsey Theory
the set of natural numbers
bar graph
42. This result relates conserved physical quantities - like conservation of energy - to continuous symmetries of spacetime.
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43. Negative
division
Sign Rules for Division
B - 125 = 1200
Additive Identity:
44. A(b + c) = a · b + a · c a(b - c) = a · b - a · c
a · c = b · c for c does not equal 0
Distributive Property:
a
Rational
45. 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
A number is divisible by 9
Multiplication
Non-Euclidian Geometry
46. If grouping symbols are nested
Sign Rules for Division
evaluate the expression in the innermost pair of grouping symbols first.
The inverse of subtraction is addition
The inverse of addition is subtraction
47. The study of shape from an external perspective.
Noether's Theorem
Extrinsic View
Factor Trees
Hyperland
48. 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
Products and Factors
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
4 + x = 12
49. Is a symbol (usually a letter) that stands for a value that may vary.
Irrational
Variable
Continuous Symmetry
Hypersphere
50. 4 more than a certain number is 12
the set of natural numbers
4 + x = 12
Continuous
Figurate Numbers