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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. Assuming that the air is of uniform density and pressure to begin with - a region of high pressure will be balanced by a region of low pressure - called rarefaction - immediately following the compression
a
Polynomial
1. The unit 2. Prime numbers 3. Composite numbers
Rarefactior
2. 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
Symmetry
Pigeonhole Principle
Sign Rules for Division
Expected Value
3. 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.
Modular Arithmetic
Cayley's Theorem
Poincare Disk
Public Key Encryption
4. Are the fundamental building blocks of arithmetic.
Rarefactior
Multiplicative Identity:
Primes
Galton Board
5. If a = b then
Multiplicative Identity:
The inverse of multiplication is division
a + c = b + c
Continuous Symmetry
6. Some numbers make geometric shapes when arranged as a collection of dots - for example - 16 makes a square - and 10 makes a triangle.
Figurate Numbers
Prime Deserts
The Kissing Circle
Stereographic Projection
7. An algebraic 'sentence' containing an unknown quantity.
Solve the Equation
Polynomial
Fundamental Theorem of Arithmetic
Hypercube
8. In this type of geometry the angles of a triangle add up to more than 180 degrees. In such a system - one has to replace the parallel postulate with a version that admits no parallel lines as well as modify Euclid's first two postulates.
Products and Factors
A number is divisible by 10
Symmetry
Spherical Geometry
9. 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
Pigeonhole Principle
Dimension
Hypersphere
left to right
10. The amount of displacement - as measured from the still surface line.
Amplitude
counting numbers
Additive Inverse:
Order of Operations - PEMDAS 'Please Excuse My Dear Aunt Sally'
11. This model is at the forefront of probability research. Mathematicians use it to model traffic patterns in an attempt to understand flow rates and gridlock - among other things.
Multiplicative Inverse:
The BML Traffic Model
Solve the Equation
Normal Distribution
12. A topological object that can be used to study the allowable states of a given system.
bar graph
Composite Numbers
Amplitude
Configuration Space
13. If its final digit is a 0 or 5.
Commutative Property of Multiplication
A number is divisible by 5
Polynomial
Non-Orientability
14. Uses second derivatives to relate acceleration in space to acceleration in time.
Wave Equation
Irrational
Standard Deviation
In Euclidean four-space
15. (a · b) · c = a · (b · c)
Answer the Question
bar graph
Markov Chains
Associative Property of Multiplication:
16. Let a - b - and c be any whole numbers. Then - a
The Distributive Property (Subtraction)
Problem of the Points
Continuous
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
17. Whether or not we hear waves as sound has everything to do with their _____________ - or how many times every second the molecules switch from compression to rarefaction and back to compression again - and their intensity - or how much the air is com
Configuration Space
Frequency
Extrinsic View
Prime Number
18. 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.
Galois Theory
Hyperbolic Geometry
Equivalent Equations
Variable
19. The system that Euclid used in The Elements
Axiomatic Systems
Prime Deserts
Frequency
Expected Value
20. Add and subtract
Composite Numbers
The inverse of multiplication is division
inline
Division is not Commutative
21. This famous - as yet unproven - result relates to the distribution of prime numbers on the number line.
set
The Riemann Hypothesis
Additive Inverse:
Overtone
22. Mathematical statement that equates two mathematical expressions.
Countable
The BML Traffic Model
Equation
Associative Property of Multiplication:
23. 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.'
Primes
Divisible
Tone
Division is not Associative
24. Our standard notions of Pythagorean distance and angle via the inner product extend quite nicely from three-space.
Standard Deviation
Bijection
In Euclidean four-space
Cardinality
25. Aka The Osculating Circle - a way to measure the curvature of a line.
A number is divisible by 5
The Kissing Circle
Principal Curvatures
Non-Euclidian Geometry
26. In a mathematical sense - it is a transformation that leaves an object invariant. Symmetry is perhaps most familiar as an artistic or aesthetic concept. Designs are said to be symmetric if they exhibit specific kinds of balance - repetition - and/or
Group
Symmetry
Hypersphere
Box Diagram
27. Solving Equations
Overtone
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
Additive Inverse:
Cardinality
28. The four-dimensional analog of the cube - square - and line segment. A hypercube is formed by taking a 3-D cube - pushing a copy of it into the fourth dimension - and connecting it with cubes. Envisioning this object in lower dimensions requires that
The Kissing Circle
Denominator
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.
Hypercube
29. N = {1 - 2 - 3 - 4 - 5 - . . .}.
Problem of the Points
the set of natural numbers
Look Back
The inverse of multiplication is division
30. ____________ 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
Associate Property of Addition
Probability
Non-Orientability
a · c = b · c for c does not equal 0
31. 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
Tone
Solution
Euler Characteristic
32. A · 1 = 1 · a = a
Composite Numbers
Order of Operations - PEMDAS 'Please Excuse My Dear Aunt Sally'
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
Multiplicative Identity:
33. 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.
Bijection
the set of natural numbers
Least Common Multiple (LCM)
Division is not Commutative
34. A way to analyze sequences of events where the outcomes of prior events affect the probability of outcomes of subsequent events.
Markov Chains
Cayley's Theorem
counting numbers
Rarefactior
35. An arrangement where order matters.
Rarefactior
Permutation
Transfinite
Grouping Symbols
36. A point in three-dimensional space requires three numbers to fix its location.
A number is divisible by 10
Irrational
Spaceland
Additive Inverse:
37. 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
Irrational
Answer the Question
Permutation
Problem of the Points
38. A + (-a) = (-a) + a = 0
Additive Inverse:
Galois Theory
evaluate the expression in the innermost pair of grouping symbols first.
Poincare Disk
39. You must always solve the equation set up in the previous step.
Fundamental Theorem of Arithmetic
The inverse of subtraction is addition
The index (which becomes the exponent when translating) is the number of times you multiply the number by itself to get radicand.
Solve the Equation
40. Codifies the 'average behavior' of a random event and is a key concept in the application of probability.
1. The unit 2. Prime numbers 3. Composite numbers
Expected Value
Multiplication by Zero
Comparison Property
41. 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.
Hyperland
Geometry
Least Common Multiple (LCM)
variable
42. Has no factors other than 1 and itself
A prime number
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 Prime Number Theorem
Solution
43. The study of shape from the perspective of being on the surface of the shape.
Solution
The inverse of addition is subtraction
a · c = b · c for c does not equal 0
Intrinsic View
44. If a = b then
Torus
Factor Trees
evaluate the expression in the innermost pair of grouping symbols first.
a · c = b · c for c does not equal 0
45. 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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46. Let a and b represent two whole numbers. Then - a + b = b + a.
In Euclidean four-space
The Commutative Property of Addition
Divisible
evaluate the expression in the innermost pair of grouping symbols first.
47. Original Balance minus River Tam's Withdrawal is Current Balance
The BML Traffic Model
B - 125 = 1200
Hyperland
Look Back
48. 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 Associative Property of Multiplication
Rarefactior
Unique Factorization Theorem
inline
49. A · 1/a = 1/a · a = 1
Multiplicative Inverse:
Grouping Symbols
Complete Graph
Prime Number
50. W = {0 - 1 - 2 - 3 - 4 - 5 - . . .} is called
The Set of Whole Numbers
Continuous Symmetry
Wave Equation
1. The unit 2. Prime numbers 3. Composite numbers