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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. 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 -
A number is divisible by 9
The inverse of addition is subtraction
Invarient
Answer the Question
2. A '___________' infinite set is one that can be put into one-to-one correspondence with the set of natural numbers.
Irrational
Countable
One equal sign per line
Irrational
3. If a - b - and c are any whole numbers - then a
Solution
The Associative Property of Multiplication
Prime Number
Commensurability
4. 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).
Dividing both Sides of an Equation by the Same Quantity
bar graph
Spherical Geometry
Prime Number
5. Codifies the 'average behavior' of a random event and is a key concept in the application of probability.
A number is divisible by 9
Multiplication
Expected Value
Complete Graph
6. Means approximately equal.
Expected Value
Commensurability
˜
repeated addition
7. When writing mathematical statements - follow the mantra:
One equal sign per line
The Same
Aleph-Null
Cayley's Theorem
8. A way to measure how far away a given individual result is from the average result.
Standard Deviation
A number is divisible by 9
bar graph
Irrational
9. The amount of displacement - as measured from the still surface line.
Polynomial
Discrete
Amplitude
Genus
10. 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 Distributive Property (Subtraction)
Primes
The Same
11. Mathematical statement that equates two mathematical expressions.
Equation
Fundamental Theorem of Arithmetic
Irrational
each whole number can be uniquely decomposed into products of primes.
12. Add and subtract
left to right
Topology
inline
Distributive Property:
13. Multiplication is equivalent to
In Euclidean four-space
repeated addition
Factor Trees
Discrete
14. 1. Find the prime factorizations of each number.
Greatest Common Factor (GCF)
Hypersphere
Fundamental Theorem of Arithmetic
˜
15. Einstein's famous theory - relates gravity to the curvature of spacetime.
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
General Relativity
division
B - 125 = 1200
16. If grouping symbols are nested
evaluate the expression in the innermost pair of grouping symbols first.
Division by Zero
Expected Value
a + c = b + c
17. The whole number zero is called the additive identity. If a is any whole number - then a + 0 = a.
The Additive Identity Property
Denominator
a
Euclid's Postulates
18. The solutions to this gambling dilemma is traditionally held to be the start of modern probability theory.
Problem of the Points
Topology
Associate Property of Addition
Denominator
19. Let a and b represent two whole numbers. Then - a + b = b + a.
Unique Factorization Theorem
The Commutative Property of Addition
division
B - 125 = 1200
20. Writing Mathematical equations - arrange your work one equation
Amplitude
Associative Property of Multiplication:
Solve the Equation
per line
21. Our standard notions of Pythagorean distance and angle via the inner product extend quite nicely from three-space.
The Same
A number is divisible by 5
Markov Chains
In Euclidean four-space
22. If a = b then
a
Expected Value
The BML Traffic Model
a · c = b · c for c does not equal 0
23. Because of the associate property of addition - when presented with a sum of three numbers - whether you start by adding the first two numbers or the last two numbers - the resulting sum is
Modular Arithmetic
The Same
Hypersphere
Frequency
24. (a · b) · c = a · (b · c)
Hypersphere
Ramsey Theory
Associative Property of Multiplication:
Dimension
25. Negative
if it is an even number (the last digit is 0 - 2 - 4 - 6 or 8)
The Prime Number Theorem
Division is not Associative
Sign Rules for Division
26. An algebraic 'sentence' containing an unknown quantity.
Polynomial
Conditional Probability
Solution
A number is divisible by 10
27. A topological invariant that relates a surface's vertices - edges - and faces.
Additive Inverse:
Fourier Analysis
Sign Rules for Division
Euler Characteristic
28. × - ( )( ) - · - 1. Multiply the numbers (ignoring the signs)2. The answer is positive if they have the same signs. 3. The answer is negative if they have different signs. 4. Alternatively - count the amount of negative numbers. If there are an even
Multiplication
Set up an Equation
Countable
De Bruijn Sequence
29. You must let your readers know what each variable in your problem represents. This can be accomplished in a number of ways: Statements such as 'Let P represent the perimeter of the rectangle.' - Labeling unknown values with variables in a table - Lab
General Relativity
˜
Set up a Variable Dictionary.
Law of Large Numbers
30. An important part of problem solving is identifying
variable
Bijection
Dividing both Sides of an Equation by the Same Quantity
A prime number
31. The study of shape from an external perspective.
the set of natural numbers
Extrinsic View
Distributive Property:
Euler Characteristic
32. 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
In Euclidean four-space
Pigeonhole Principle
Permutation
A number is divisible by 5
33. This important result says that every natural number greater than one can be expressed as a product of primes in exactly one way.
Public Key Encryption
Multiplication by Zero
inline
Fundamental Theorem of Arithmetic
34. Let a - b - and c be any whole numbers. Then - a
Bijection
Least Common Multiple (LCM)
The Distributive Property (Subtraction)
Multiplying both Sides of an Equation by the Same Quantity
35. Some numbers make geometric shapes when arranged as a collection of dots - for example - 16 makes a square - and 10 makes a triangle.
4 + x = 12
Figurate Numbers
Factor Tree Alternate Approach
evaluate the expression in the innermost pair of grouping symbols first.
36. Uses second derivatives to relate acceleration in space to acceleration in time.
Composite Numbers
division
Wave Equation
Expected Value
37. 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
Galois Theory
Multiplicative Inverse:
Prime Number
38. Arise from the attempt to measure all quantities with a common unit of measure.
Multiplicative Inverse:
Rational
4 + x = 12
Stereographic Projection
39. Objects are topologically equivalent if they can be continuously deformed into one another. Properties that are preserved during this process are called topological invariants.
Complete Graph
Prime Number
Irrational
Spaceland
40. 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
Conditional Probability
Factor Tree Alternate Approach
Continuous Symmetry
41. This famous - as yet unproven - result relates to the distribution of prime numbers on the number line.
The Riemann Hypothesis
Conditional Probability
Noether's Theorem
Additive Inverse:
42. An arrangement where order matters.
Poincare Disk
Permutation
Continuous Symmetry
bar graph
43. A way to analyze sequences of events where the outcomes of prior events affect the probability of outcomes of subsequent events.
Greatest Common Factor (GCF)
Prime Deserts
Markov Chains
Poincare Disk
44. The fundamental theorem of arithmetic says that
each whole number can be uniquely decomposed into products of primes.
Set up an Equation
Expected Value
Answer the Question
45. You must always solve the equation set up in the previous step.
Solve the Equation
left to right
The Kissing Circle
Standard Deviation
46. We can think of the space between primes as 'prime deserts -' strings of consecutive numbers - none of which are prime.
Fourier Analysis
Irrational
Box Diagram
Prime Deserts
47. 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
Hyperland
Frequency
The inverse of multiplication is division
Discrete
48. 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
each whole number can be uniquely decomposed into products of primes.
Pigeonhole Principle
Greatest Common Factor (GCF)
Answer the Question
49. 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.
Solution
Euler Characteristic
Hypercube
set
50. Instruments produce notes that have a fundamental frequency in combination with multiples of that frequency known as partials or overtones
Factor Trees
The Riemann Hypothesis
Hyperbolic Geometry
Overtone