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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. 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.
Hypersphere
Standard Deviation
Geometry
Hyperland
2. 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
Unique Factorization Theorem
Hypersphere
Symmetry
Ramsey Theory
3. Division by zero is undefined. Each of the expressions 6
1. The unit 2. Prime numbers 3. Composite numbers
a divided by b
Division by Zero
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
4. The study of shape from the perspective of being on the surface of the shape.
Galois Theory
Intrinsic View
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
Unique Factorization Theorem
5. Index p radicand
1. The unit 2. Prime numbers 3. Composite numbers
Prime Deserts
The index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.
Noether's Theorem
6. Original Balance minus River Tam's Withdrawal is Current Balance
Group
inline
Commutative Property of Addition:
B - 125 = 1200
7. If a whole number is not a prime number - then it is called a...
Stereographic Projection
Invarient
Division by Zero
Composite Numbers
8. Use parentheses - brackets - or curly braces to delimit the part of an expression you want evaluated first.
Symmetry
Grouping Symbols
The Multiplicative Identity Property
Countable
9. Perform all additions and subtractions in the order presented
left to right
Torus
Standard Deviation
Associate Property of Addition
10. We can think of the space between primes as 'prime deserts -' strings of consecutive numbers - none of which are prime.
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
Markov Chains
Prime Deserts
11. If a = b then
Multiplying both Sides of an Equation by the Same Quantity
Noether's Theorem
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
a · c = b · c for c does not equal 0
12. When writing mathematical statements - follow the mantra:
Spaceland
One equal sign per line
The BML Traffic Model
A number is divisible by 3
13. This result says that the symmetries of geometric objects can be expressed as groups of permutations.
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14. If a is any whole number - then a
Composite Numbers
Pigeonhole Principle
Problem of the Points
The Multiplicative Identity Property
15. 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.
Distributive Property:
Multiplicative Inverse:
Dividing both Sides of an Equation by the Same Quantity
does not change the solution set.
16. 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.
left to right
Normal Distribution
Overtone
Continuous Symmetry
17. 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
Axiomatic Systems
1. The unit 2. Prime numbers 3. Composite numbers
Invarient
Factor Trees
18. An instrument's _____ - the sound it produces - is a complex mixture of waves of different frequencies.
The Prime Number Theorem
Configuration Space
counting numbers
Tone
19. Let a and b represent two whole numbers. Then - a + b = b + a.
Hypersphere
General Relativity
Poincare Disk
The Commutative Property of Addition
20. N = {1 - 2 - 3 - 4 - 5 - . . .}.
Answer the Question
the set of natural numbers
Galton Board
Box Diagram
21. Has no factors other than 1 and itself
Irrational
A prime number
Products and Factors
The Commutative Property of Addition
22. The process of taking a complicated signal and breaking it into sine and cosine components.
Overtone
Fourier Analysis
Equation
A number is divisible by 9
23. The whole number zero is called the additive identity. If a is any whole number - then a + 0 = a.
variable
The Additive Identity Property
Aleph-Null
evaluate the expression in the innermost pair of grouping symbols first.
24. This result relates conserved physical quantities - like conservation of energy - to continuous symmetries of spacetime.
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25. 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.'
Associative Property of Multiplication:
De Bruijn Sequence
Divisible
Modular Arithmetic
26. 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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27. The amount of displacement - as measured from the still surface line.
Amplitude
Set up an Equation
division
does not change the solution set.
28. 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.
Configuration Space
Modular Arithmetic
Probability
Transfinite
29. 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.
Figurate Numbers
Non-Orientability
B - 125 = 1200
Associative Property of Addition:
30. This area of mathematics relates symmetry to whether or not an equation has a 'simple' solution.
a - c = b - c
inline
Galois Theory
Greatest Common Factor (GCF)
31. 1. Find the prime factorizations of each number.
Invarient
Greatest Common Factor (GCF)
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 set of natural numbers
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
Composite Numbers
Non-Euclidian Geometry
The inverse of multiplication is division
In Euclidean four-space
33. Are the fundamental building blocks of arithmetic.
set
1. The unit 2. Prime numbers 3. Composite numbers
Primes
General Relativity
34. 4 more than a certain number is 12
Factor Trees
a divided by b
Genus
4 + x = 12
35. This important result says that every natural number greater than one can be expressed as a product of primes in exactly one way.
Non-Euclidian Geometry
Invarient
Associative Property of Addition:
Fundamental Theorem of Arithmetic
36. In some ways - the opposite of a multitude is a magnitude - which is ___________. In other words - there are no well defined partitions.
Overtone
Distributive Property:
Topology
Continuous
37. The inverse of multiplication
division
Extrinsic View
Composite Numbers
Non-Euclidian Geometry
38. Breaks a complicated signal into a combination of simple sine waves. Fourier synthesis does the opposite - constructing a complicated signal from simple sine waves.
Ramsey Theory
Look Back
per line
Fourier Analysis and Synthesis
39. 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.'
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.
The inverse of addition is subtraction
Dimension
The Prime Number Theorem
40. Codifies the 'average behavior' of a random event and is a key concept in the application of probability.
The Associative Property of Multiplication
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.
Geometry
Expected Value
41. A + (-a) = (-a) + a = 0
A number is divisible by 9
Additive Inverse:
The index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.
Galton Board
42. A point in one dimension requires only one number to define it. The number line is a good example of a one-dimensional space.
Irrational
Line Land
Multiplying both Sides of an Equation by the Same Quantity
Expected Value
43. Two equations if they have the same solution set.
Equivalent Equations
Extrinsic View
Non-Orientability
Probability
44. This famous - as yet unproven - result relates to the distribution of prime numbers on the number line.
˜
Non-Euclidian Geometry
The Riemann Hypothesis
Problem of the Points
45. An object possessing continuous symmetries can remain invariant while one symmetry is turned into another. A circle is an example of an object with continuous symmetries.
Markov Chains
Solution
Associative Property of Multiplication:
Continuous Symmetry
46. If a = b then
a + c = b + c
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
Grouping Symbols
Polynomial
47. A point in four-space - also known as 4-D space - requires four numbers to fix its position. Four-space has a fourth independent direction - described by 'ana' and 'kata.'
1. Set up a Variable Dictionary. 3. Solve the Equation. 4. Answer the Question. 5. Look Back.
Hyperland
Factor Tree Alternate Approach
Topology
48. All integers are thus divided into three classes:
The index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.
left to right
1. The unit 2. Prime numbers 3. Composite numbers
Fundamental Theorem of Arithmetic
49. (a
Division is not Associative
A number is divisible by 9
The inverse of addition is subtraction
Cayley's Theorem
50. Some numbers make geometric shapes when arranged as a collection of dots - for example - 16 makes a square - and 10 makes a triangle.
The Distributive Property (Subtraction)
Countable
Figurate Numbers
A number is divisible by 9